tag:blogger.com,1999:blog-30717192521369682052024-02-19T07:59:03.115-08:00Following LearningSimon Gregg's thoughts on lessonsSimon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.comBlogger147125tag:blogger.com,1999:blog-3071719252136968205.post-62196624364095233702023-08-09T14:38:00.000-07:002023-08-09T14:38:04.503-07:00Taking some things with me from Early Years<p>I'm leaving the three, four and five year olds, and heading up to Grade 2 (which in UK is called Year 3).</p><p>There's so much I love about the way we work with the youngest children, and I'm hoping I'll take some of that with me.</p><p>Just two of the things for now, illustrated with two photos from the last week of the summer term.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJELCfyX3XBGT4CnW0ysBldCSdDBCscPeH10K_jKkSJCQHKfN-sJlHVjr5EClUYvS_WLv_UuebJ47-OUwAS3vg3Uhmdr_V8INmS0IyGeTFK1hmskjQUmGHRuoA6VB_YcR-wzrsTHz_Q2TK2a5OII1ef3vJ1qMPTASv67Y75ga8F5gMlapzbbEK-bzfKh0/s548/e%20dancing.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="548" data-original-width="361" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJELCfyX3XBGT4CnW0ysBldCSdDBCscPeH10K_jKkSJCQHKfN-sJlHVjr5EClUYvS_WLv_UuebJ47-OUwAS3vg3Uhmdr_V8INmS0IyGeTFK1hmskjQUmGHRuoA6VB_YcR-wzrsTHz_Q2TK2a5OII1ef3vJ1qMPTASv67Y75ga8F5gMlapzbbEK-bzfKh0/s320/e%20dancing.JPG" width="211" /></a></div><div class="separator" style="clear: both; text-align: center;">Estelle on Sports Day with students</div><h4 style="text-align: left;">We join in</h4><div>We don't want that 'I am the knowing, observing, and assessing adult' hanging over the students. We break that down by playing alongside the children. Plus, we have fun, and see what it's like to do the things they're doing, and we get ideas.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZbDi6c72X6Ghj-9tNoQrBnfb5UGvT5GxpezUhIXEEhwEfDLTL9dW_7EtIlcR0KrS89eDATlg6BY0KnDUr8y6V_X_tfP4nYwScbEMzak5Y50KYp0R5BMWkyOWPMZ-i7MzEvAGahICTMQT8QbkP__DGjBzb95NeehBVXPQdkm4nvUkWwfISNWcUV_uq8B8/s923/r%20making.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="860" data-original-width="923" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZbDi6c72X6Ghj-9tNoQrBnfb5UGvT5GxpezUhIXEEhwEfDLTL9dW_7EtIlcR0KrS89eDATlg6BY0KnDUr8y6V_X_tfP4nYwScbEMzak5Y50KYp0R5BMWkyOWPMZ-i7MzEvAGahICTMQT8QbkP__DGjBzb95NeehBVXPQdkm4nvUkWwfISNWcUV_uq8B8/s320/r%20making.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Rachel at the making table with two students</div><h4 style="text-align: left;">We are quiet</h4><div>(Not always of course)<br /><div>We can sometimes be larger than life, charismatic and inspiring, but lots of the time we are quiet. The students have the agency. We are with them, but not dominating the situation. The students know what they want to achieve. It helps to have us there, and there can be good conversations, but mostly it's the students concentrating on what they're doing.</div></div><div><br /></div><div>These are two of the things I want to take with me.</div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com4tag:blogger.com,1999:blog-3071719252136968205.post-8085414599535926232023-02-03T13:14:00.003-08:002023-02-03T13:34:21.491-08:00Play as the foundation<p></p><div class="separator" style="clear: both; text-align: left;">I get to see the richness of play on a daily basis with the 3, 4 and 5 year olds I work with. They learn through this play, even though it often looks very different to many an adult's idea of learning. It's through this play that their understanding of themselves and the physical and social world around them develops. They also learn what their powers are, how they can arrange things, make things happen, create important moments with others.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I've been thinking about how this is the perfect course to set off on to develop the kinds of abilities, or "competencies" that they will need as adults.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjk8arH_lutVXF9WrcSAw2ZQGB9XdFi8zM5MBk-CQ7pgHrGn8wh-_9Rlp8mBu0CyWDcpFAz1ZsJ7uxH3ssK3RGfRLATZT51YeexHIqNVUn6xwX6FPevr0hyqra8fuiXLbKCAgiKQD8ihRluadZTAzmpF5JJ4K-M1j3vdx--2p6neWNf1W9eZ4AdRJZ3" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjk8arH_lutVXF9WrcSAw2ZQGB9XdFi8zM5MBk-CQ7pgHrGn8wh-_9Rlp8mBu0CyWDcpFAz1ZsJ7uxH3ssK3RGfRLATZT51YeexHIqNVUn6xwX6FPevr0hyqra8fuiXLbKCAgiKQD8ihRluadZTAzmpF5JJ4K-M1j3vdx--2p6neWNf1W9eZ4AdRJZ3" width="320" /></a></div><p></p><p>Play is notoriously difficult to define, but I think <a href="https://www.psychologytoday.com/us/blog/freedom-learn/202205/what-is-play-how-children-define-it" target="_blank">Peter Gray's definition</a> makes sense. Play is:</p><p></p><ol style="text-align: left;"><li>Freely chosen & directed by the players</li><li>Intrinsically motivated </li><li>Structured by rules within the player’s mind</li><li>Always creative & usually imaginative</li><li>Conducted in an active, alert, relatively non-stressed frame of mind</li></ol><div>He elaborates on this, to show the power each of these characteristics for children's development and learning (my emphasis, in bold):</div><div><div><ol style="text-align: left;"><li>Because it is freely chosen and directed by the players, play is a major force for children’s learning how to <b>take initiative, direct their own behavior, negotiate with and get along with playmates, and solve their own problems.</b></li><li>Because it is intrinsically motivated, play is how children discover, pursue, and become skilled at what they love to do.</li><li>Because it is guided by mental rules, play is <b>how children learn to plan, structure, and create the boundaries (rules) for activities that engage them.</b></li><li>Because it is always creative and often highly imaginative, play is <b>how children exercise and build their capacities for creativity and imagination.</b></li><li>Finally, the mental state of play—active and alert but relatively non-stressed—has been shown in many studies to be the ideal state of mind for learning anything new or doing anything that requires creativity or the generation of new insights.</li></ol></div></div><div>I also came across this 'Learning Compass' <a href="https://www.oecd.org/education/2030-project/teaching-and-learning/learning/learning-compass-2030/" target="_blank">from the OECD</a>:</div><p></p><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="556" data-original-width="561" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFHd-5hsqzy8BfG2AV_3Jh46vreea9AczPeMepVWhVcMVik9viixqZMBdxiySqxG8WD_Ve7GK3XpyNJoEEOdUq5vbEFmbkwFo8m7y4t1KS9BdYfmk8k4bB7kWp7J2ZtJJBQsDONfuHHO9wb49EMp2HsMSUbAfX7-AYReO1A0KZhiKELrn2tyTdXOlE/w400-h396/learning%20compass.png" width="400" /></div><p></p><blockquote>"Developed as part of our Future of Education and Skills 2030 project, the Learning Compass puts forth a shared vision of what students should learn to be ready for tomorrow."</blockquote>There's some other important elements around the compass, which I've taken off; I wanted to focus on the compass circle itself.<p></p><p>Looking at the dark cyan ring - the 'transformative competencies' -</p><p></p><ul style="text-align: left;"><li>Taking responsibility</li><li>Reconciling tensions and dilemmas</li><li><span style="text-align: center;">Creating new value</span></li></ul><p></p><p>- I'm struck by how similar these are to the Gray's elaborations of aspects of play.</p><p>Just to make it clear, let's put them side by side:</p><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; text-align: center;">
<tbody><tr>
<td style="border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b>Play<o:p></o:p></b></p>
</td>
<td style="border-left: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b>Transformative
Competencies</b><o:p></o:p></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">play is how
children learn to plan, structure, and create the boundaries (rules) for
activities that engage them<o:p></o:p></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">Taking responsibility<o:p></o:p></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">take
initiative, direct their own behaviour, negotiate with and get along with
playmates, and solve their own problems<o:p></o:p></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">Reconciling
tensions and dilemmas<o:p></o:p></p>
</td>
</tr>
<tr>
<td style="border-top: none; border: 1pt solid windowtext; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">play is how
children exercise and build their capacities for creativity and imagination.<o:p></o:p></p>
</td>
<td style="border-bottom: 1pt solid windowtext; border-left: none; border-right: 1pt solid windowtext; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 153.4pt;" valign="top" width="205">
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;">Creating new
value<o:p></o:p></p>
</td>
</tr>
</tbody></table><p>Play is developing the kinds of competencies with which we might hope students finish their schooling, those with which they not only know about the world, but can make positive changes to it.</p><p>It makes me think that play could be right in the middle of that compass! Play develops skills, knowledge, values and attitudes.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNPi39ErWxDbZMXqZIGgMaQzhP473S0okCneqGnr4OMBUUEdJycHr2HZdzAsXUdWVjwRn7WKmB3o2xhg3XViizy-GApoAapxiJmAC6wtjB6xueJb2QNmEBmqkZhPM26ee1U2p8AycM81uUXv-UYtgAmS4L4j9WO0UnFW7ImNBv8LKq0mL5Vd6JWtQe/s720/play.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="719" data-original-width="720" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNPi39ErWxDbZMXqZIGgMaQzhP473S0okCneqGnr4OMBUUEdJycHr2HZdzAsXUdWVjwRn7WKmB3o2xhg3XViizy-GApoAapxiJmAC6wtjB6xueJb2QNmEBmqkZhPM26ee1U2p8AycM81uUXv-UYtgAmS4L4j9WO0UnFW7ImNBv8LKq0mL5Vd6JWtQe/s320/play.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">I'm thinking about play for young children here, but I'd like to see playful learning continuing beyond that age to maintain the self-directed approaches children have learnt so much from.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I think it's always useful to think about what that learning is like <i>in the specific case</i>. Luckily, I've blogged about some of these concrete examples. Here's a couple of links to earlier posts:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both;"><a href="https://followinglearning.blogspot.com/2021/10/arranging-things.html" target="_blank">Arranging things</a> - "What I’m trying to get a grip on doesn’t seem to simply reduce to dispositions though. It is a more disorganised-seeming, less direct way of obtaining knowledge about what daring and playfulness can achieve, what can be done with freedom and within necessity, how the social and physical environment can be remixed. It centres around agency, and uses whatever is at hand to achieve its undefined aims. It achieves its goal of developing capable and skillful being and making in the physical and social world, but its means are more indirect than what comes to mind when we think of theory-building: curiosity -> question -> search -> answers."</div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="914" data-original-width="1218" height="150" src="https://blogger.googleusercontent.com/img/a/AVvXsEh96F9-TMyTdSmmejbkIwHEw7OHftjeNLGp9HrdTk379UGDrLN8Jj7AKyW6gyK5q0X7r63ErJduQ4Il0OMPoDx6qaexgcw4_FJyFcp4hw3hIBgGPiVL0Djn4rs_lteHOneq9o5MzPt9R-FkgoOBk3Cz44PLUKkLCUqNEWqVgXyTKbxg7xpyX-bBDVW-=w200-h150" width="200" /></div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both;"><a href="https://followinglearning.blogspot.com/2022/12/folding-cutting-sticking-drawing.html" target="_blank">Folding, cutting, sticking, drawing</a> - "...it's really not necessary for me to be adding anything in to this process: there's so much happening already: theories being refined, interests pursued, skills honed, and much more."</div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="240" data-original-width="320" height="150" src="https://blogger.googleusercontent.com/img/a/AVvXsEgkLeuFtEDc8N-2RuKVfP77OgkFY-XiWyka82Azv5poyUaxBRXKNPn_h3_Rq8pLnIpjvquUo4VJhQgjTUIELgXOdySVhs0b7IsPj8TbFY4rSyU57pp6GZM4mJ3vFMTiNNUBUMLaxocQxiWdeid0Ab2oadJmD8WBx1R6d26vZbWLuMxg4EJpHSv7HDUq=w200-h150" width="200" /></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-89841319488504581792023-01-27T15:35:00.002-08:002023-01-27T15:49:00.319-08:00Mathematics Lessons to Look Forward To!<p>Jim's book is out!</p><p>Jim Noble is my friend and colleague in secondary. His classroom just a few metres from our Early Years playground, no doubt he's had to shut his door many times because of the racket we're making! I see him out there too. </p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="493" data-original-width="900" height="175" src="https://blogger.googleusercontent.com/img/a/AVvXsEjsH7prbP1qOTtZEq--sFs3WgVrX44DgZzEHCA_t1FoNp-QAxJYIbDpOA_uVAl5OzvY9ZcoD-rPMJiqghrbkHyc5M97r7c7U_lyp9CIn1dNAYhs32TMWUkHsyXjJR7dbJmwsyskTTDHOYIymYkacD8VCQgW4ZK-miVh6S1G0SUF2LOyPpAq1HIj5bD6" width="320" /></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">'If the world were a hundred people...'</span></div><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="1373" data-original-width="2048" height="215" src="https://blogger.googleusercontent.com/img/a/AVvXsEh6VBdqpvfY1jrF5EPyd0AhRFudz8jyth1d4AKavayoo2qaaxeSVLk2tsJ4uGXmjOe84bS5zDT-g7eiME9rnI4xYgK74KFdKIJMeLuGpS08_n9WtRyucc6wQkS5RUq8mCFXKsdqfKFfSyN75jWSD0S5G1PBKfzcmiStdY8bSENCb-l1S6lYgXuyZSPd" width="320" /></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">Human Loci: Creating a parabola</span></div><br />These are part of two of the lessons described in Jim's <a href="https://www.routledge.com/Mathematics-Lessons-to-Look-Forward-To-20-favourite-activities-and-themes/Noble/p/book/9781032210490" target="_blank"><i>Mathematics Lessons to Look Forward To!</i> </a>The book details twenty lessons that Jim returns to, experiments with, hones and polishes. <p></p><p></p><blockquote>"Every time I revisit a topic for myself or in preparation for teaching or mostly during teaching, I always notice something I haven’t seen before and this is often pointed out by a student."</blockquote><p></p><p>Jim is a great storyteller. He's often called on to be the one who puts important rites of passage in the life of the school into words: leaving speeches, introducing speakers and celebrations. He's always assured, natural, entertaining and considered in what he says. </p><p>This book is the same. And Jim is letting us into the heart of his teaching here, there's a vulnerability, at times, a touch of self-doubt or self-mockery. In the process, he takes us back to what makes the lessons tick for him, why they became exciting and vital.</p><p></p><blockquote>"Deep down I have convinced myself that the roots of ideas are an important part of them. I think the journey from first idea to activity is a really enjoyable, reflective part of the job."</blockquote><p></p><p>His lessons are not always outdoors of course, but they are all out of the routine, they all stand out as being alive, practical where possible... experiences as well as lessons. And fun.</p><p></p><blockquote>"It is fun. I have made no apology about this. I have found that I need this as much as students do. Something that adds variety to the global experience, something practical that gets students out of their seats and sometimes out of the classroom and something that makes us laugh a little is always welcome."</blockquote><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://www.routledge.com/Mathematics-Lessons-to-Look-Forward-To-20-favourite-activities-and-themes/Noble/p/book/9781032210490" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img alt="" data-original-height="1265" data-original-width="843" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEgBdocKir5IOwCxV1vgBA-QwTQehEQ82Fhj2j9bnV2DUMqBDK2vNT_cRltxnhchoCBE7HemSN224mpnLMP7aDi7hrqAAuUw4iiIb8a5cIRKIvuv8nwCkKuVlbFRR2t7D50qXaPv5DOhz7uFJPxXYvS4Mj386HR8IiEaENXpU8V_K9F_PpH9TaDcCyDQ=w267-h400" width="267" /></a></div><p></p><p>Reading a draft of the book, I was struck again by how we have so much in common in our outlook towards lessons. Is it that we've spent a lot of time together since 2004 when Jim came to the International School of Toulouse?</p><p>It's not just that we both photograph drain covers for their mathematical patterns, both enjoy seeing and making Islamic geometrical patterns, both value Seymore Pappert's seminal book <i>Mindstorms</i>...</p><p>Many - most! - of his twenty lessons do actually have their counterpart in the primary school.</p><p>We've both enjoyed 'Numbersearch' and these feature in the book:</p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="430" data-original-width="680" height="202" src="https://blogger.googleusercontent.com/img/a/AVvXsEhKPIcCJfEibJzq8HYjLNdYHAipb7m83eT83KD2ElcTeA3PKdeQ5C2Zylk1RGWJUtkFkzkE9nkknfNWhdHejesK6YU1-nWQnP2UmkkrgojCKFZ7IBEqcXvtqa8_pWg16ACukuynnk4jP-F2mUfkVh9p_V9v8DcuT4uMSvGt3YN2uxplpwMzG-q5Ynx_" width="320" /></div><div class="separator" style="clear: both; text-align: center;">If the white triangle is 1, what other numbers can you see?</div><p>Jim got pi involved:</p><p style="text-align: center;"><img alt="" data-original-height="456" data-original-width="524" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjYgFYTmP3wNdZwO-ujmAJjBW9bkyrhsISVwKp8krGBynnSoe2wxoeDYK7UJpnUkCHnpAPGvt--pLMnFEeZW4cYEbsux3i0VmjBR72-ARVuB7dAIiugIcUtD1kS0-LJaG9roJjZQ4idCr-aPV5iG3-JIaN_S9_8dFEY7slRzdUF42LKCbix4qbzjitE" width="276" /></p><p style="text-align: center;">If the white square is one...</p><p></p><p>Like Jim in secondary, I love to get my primary students coding the path of a robot using Scratch:</p><p></p><blockquote>“If I need to turn 5 equal turns that make a total of 360 then I need to turn 72 degrees”, which generalises to “for an n sided regular polygon, the turning angle is 360/n”. The thrill of making this conclusion is the same thrill as solving a puzzle. The word ‘discovery’ is much maligned and probably inappropriate as it implies a kind of wandering around until you find something then pick it up. This is much more mathematical in nature. You have a problem that needs solving, you have knowledge of the scenario at the ready and you put bits of this knowledge together to deduce new knowledge. Now that is doing mathematics.</blockquote><p></p><p>Or using dynamic geometry:</p><p></p><blockquote>How would you construct this rectangle? The others? I really do recommend having a go here. It is really interesting to focus on the different ways it can be done and there are some surprising challenges hidden away in there.</blockquote><p></p><p></p><blockquote>In this activity, the constructed dynamic rectangle is, in a sense, every rectangle. Students get to explore the notion that each construction has a degree of freedom that is entirely defined by the elements that were used to construct it and the order in which they were used. It is a profound mathematical idea that goes beyond geometry into set theory and the anatomy of a variable. In many ways it is a much more natural way to see mathematics that a set of static images might be and really helps get our heads around the idea of generalisation. “Many things here can vary, but the following will always be true”</blockquote><p></p><p>Jim asks the reader to have a go at parts the activities. Some of them I tried. I had a go for instance at <a href="https://www.geogebra.org/classic/wfa7s2ty" target="_blank">constructing a rectangle four different ways </a>using Geogebra. Each one has a different 'skeleton', the way it's constructed.</p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="1770" data-original-width="2634" height="215" src="https://blogger.googleusercontent.com/img/a/AVvXsEih18kn_RpLlglEWHUYcyFtWDWzAdSAlhBXtFs57G8x9gg-qx5aL0F6KKFeraTfsVJT66rlyXI6D5d8KXYO6og4AeoadfrVswZZzIrCCAI3j9q5CLfMF9zcmdazu_8xZU1fyQTki_j9lmT1CYHsMZANC_TyvaFolUWZOXjMH2Q0BSwmOPZz3nH85huJ" width="320" /></div>(I've come to the conclusion there's an infinite way of constructing a rectangle that can be stretched into any rectangle and these skeletons don't have to involve parallel sides, or perpendicular sides either.)<br /><p></p><p>There is really no other book like this! Jim takes each lesson from his treasure chest of pedagogical subject knowledge and turns it every way in the light for us. Which different ways could the lesson go? How does it relate to key ideas in mathematics? How does it relate to our understanding of what it means to know? How does it engage students? What connections are there with other subjects?</p><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="2080" data-original-width="1168" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjUKJmpKARRQozdCKejpdKbhezAwl7x6_v5F7d_F9go0G6NrVfxrJiBxtM490LNHotrgJH1yCTBKweqmgC4KSJ2BrGGYDAiimda9N4AvKybK1wv77w_CP3nw6Ii6Xjrd79hvymwE6xCQ6a_UCYeJc8FQwu05RLAM_w6eEBlc5tj0iPZ86rhBUmqD3JV" width="135" /></div>Jim showing piles of rice to Helen and Mike<br /></div><p></p><p>You can tell I'm recommending it!</p><p>Great teacher, great book!</p><p><br /></p><p>The lesson chapters:</p> 1 - What’s in the box<br /><br /> 2 - Cones<br /><br /> 3 - If the world was a village of 100 people<br /><br /> 4 - Goodness Gracious Great Piles of Rice<br /><br /> 5 - How do I love thee, let me count the ways<br /><br /> 6 - Number Searches<br /><br /> 7 - Human Loci<br /><br /> 8 - Statistics telling stories<br /><br /> 9 - Match Point<br /><br /> 10 - Prime Pictures<br /><br /> 11 - Population Growth<br /><br /> 12 - Starting from scratch<br /><br /> 13 - Indestructible<br /><br /> 14 - Dancing Quadratics<br /><br /> 15 - Hot Wheels<br /><br /> 16 - Maxbox<br /><br /> 17 - Dancing Vectors<br /><br /> 18 - Pleasure at the Fairground<br /><br /> 19 - Impossible Diagrams<br /><br /> 20 - CubismSimon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com4tag:blogger.com,1999:blog-3071719252136968205.post-38080505087053357652022-12-28T02:05:00.004-08:002022-12-30T12:02:37.993-08:00Folding, cutting, sticking, drawing<div>I want to write a little about one of the hubs of the classroom.</div><div><br /></div><div>It's what we call the writing table or drawing table. Which is maybe not the right name for it. A lot more happens than writing and drawing. It could perhaps be called the paper table. It's got a lot of stationery on it. Bits of paper of various sizes, glues, scissors. A lot of cutting, gluing, sticking, folding, stamping and printing happens. A lot of colouring in too. But, these names and simple descriptions aren't really adequate.</div><div><br /></div><div>It’s 'continuous provision', as we call it: it’s always there, and used every day. I imagine that it extends beyond school too: children often have stationery at home.<br /><br />Most early years classes have got something like this table. Certainly all four of our pre-K and Kindergarten classes have. This is what continuous provision is all about: a place where children can return again and again and make something, trying out new ideas, combining things they’ve done before, learning from each other. <br /><br />Since they came to the school when they were three, R and K have been doing this. They're not the only ones, but let's focus on them for now. They're four years old; they've been in Moon class for 15 months. R at first stood out as leader of the duo, always inventive, always relishing what she does. But K seems to be inspired by her to be similarly creative, making things that are distinctive to her, having her own strengths and emphases.</div><div><br />An example, back in September: R's envelope-picture:<span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; height: 211px; overflow: hidden; width: 195px;"><img height="224.61290322580643" src="https://lh3.googleusercontent.com/1jEBTzDtVg2tzaCwRf5PCgzk6LI6XgZEwzDp2Qh072TTUXGzpoA2jgS9hJW5vo7d4IZhzm1DgXLZDpjNGDmUvyC4_QjyfGnEF8fQqRsYgOdd7CLI3R-8ag-uHnbnRdTnv5xKToPM1MnXZGJpTy_UxD4Yq4SGbB1TwRo0SDANHeJJlwu1Mo3EhBOerDre6A" style="margin-left: -67.4184px; margin-top: -6.80645px;" width="300.18893314366176" /></span></span></p></span>What kind of mathematics are present in creating this? An awareness of bringing the corners into the middle of the paper to reorient the square and create triangular flaps. A lot of spatial thinking. An example might be the awareness that when you fold the paper over once, the back of the folded paper faces the same way as the front. She is probably aware that the orientation of the square changes too: first it was in a 'diamond' orientation, now it's in the conventional orientation. She'll be aware that the small square is made up of four triangles. And that there are diagonal lines across the square that meet in the centre. She's aware that some things can be undone, or almost undone. Pencil can be rubbed out. Cuts can be taped together again. And some things can't be undone. The felt pen drawing can't be rubbed out very easily.<br /><br />At the same time, K was doing some folding too:<span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; height: 257px; overflow: hidden; width: 343px;"><img height="257" src="https://lh3.googleusercontent.com/oRGefbM3sSC8umCFYAL9kCy0k6I07183NQdYIPaUQ35Xd9WJQ5dzF5nP5mG-2p5LjODDv_5yPmkDnzyXseZCoWDcHj8f3whdx_BMKk36lIK3yRIYMjciX6xwg2hD6fmRZXHnDr6Tvpa50nUWxp4ge9ma7ugKE3epP42LqGk_um8avVhXPkf5YCeqeEyzkg" style="margin-left: 0px; margin-top: 0px;" width="343" /></span></span></p></span><span><span style="text-align: center;">These paper explorations contrast with art activities that use specifically 'art' materials, painting in particular. There seems to be more of a tinkering feel, more mixing. Take R here, where she’s decided to draw round the scissors, drawn and colored in a pill shape, written a little, filled a rectangle…</span><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="970" data-original-width="1294" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCFqwcGyU15yXBCwd03K1syK2UEsK31FseiGdHJ7ZyAzbCvsFiGGZa5uUcTArsQIlm-RJhKguz15JNaJdrJqyEGiGjEn6JDhAdAup1GQUZb52lNORtzyS77Kw67JAz_E7aeSISvxzfJBY-kRduy0d3puTZ0N2XUlVl1VVfQ9ylXv1VrDCj5IQ6-zmL/s320/HH.png" width="320" /></div></span><p></p>There's a really strong social element in this. There was a group of girls in Star Class two years ago who all tuned into each other with <a href="https://followinglearning.blogspot.com/2021/07/copycats.html">their drawing and colourin</a><a href="https://followinglearning.blogspot.com/2021/07/copycats.html">g</a>, got more and more confident in that, and continued it into Kindergarten.<br /><br />There’s also the sense of self-efficacy, of choosing a project, seeing it through to completion, working alongside others and learning from each other. There’s a kind of joy in the workshop ambience, in having control and making together and separately.<div><br /></div><div>Here's some more, this time involving cut-outs:<br /><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjktNd04q-e8FGQAwxD4FWpIRbfl6ZGQ5pdhPqF9UrrDpFrES77vtSEJivldmRgtRlw7ZnHJRvB0KGZmpTy7qhqW79SwY4jmKIyAotlK-O0KvCVztBGX_uWladDLm-eykJG26XWOp2Vkv5EWlQhV51_KG6rzMEr91ia7yHPVzOVRsRm_kG8MacJVtm0/s320/IMG_3378.JPG" width="320" /></div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-8zYJwGzUcXy-MIOrXiPNIvY4GFANP_JfJUAvLht4Ru4gf4zgv8dziN1VqWOH-aVnd4S0W_SKG3yHj4bhJcR58eGf0fJM_f5BqPeLhXsgez3cRtiRY7gE6N7oijIVJgT5oREgY9xOT77BK6KnVp05A-AnXVr-DBaQ1xShBXG4F0nw6cHy8bQPiwvC/s320/IMG_3380.JPG" width="320" /></div><div class="separator" style="clear: both; text-align: left;">With this must come some sense of how when you fold and cut, the hole you achieve is not like the cut you made. And a developing understanding of the relationship between the two.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">There can be folded-and-cut shapes inside other folded-and-cut shapes:</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRgcUuJAqozEqukLXA4TtdT1bvcPAqnDHFF-dBFSHocJWB-Wzjg_bJH6j_jS6Iq9g73hoaKrL0lnX_2QuTFb6L1eokKqmvRNM4OK2T1Xs6nS-No7xLmquVy3UpX65UfQubstDn-I6j3m81kGv5JxS-WJpMSDIgR7eXJNaF_tLc-_Ep1At8ZpFNnnfr/s3264/IMG_3882.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRgcUuJAqozEqukLXA4TtdT1bvcPAqnDHFF-dBFSHocJWB-Wzjg_bJH6j_jS6Iq9g73hoaKrL0lnX_2QuTFb6L1eokKqmvRNM4OK2T1Xs6nS-No7xLmquVy3UpX65UfQubstDn-I6j3m81kGv5JxS-WJpMSDIgR7eXJNaF_tLc-_Ep1At8ZpFNnnfr/s320/IMG_3882.JPG" width="320" /></a></div><div style="text-align: left;">The smaller shape suggested a watermelon to the girls. It's rare for these creations to be completely abstract; they usually represent something. This is a general feature of a lot of play - mathematics is mixed with creation is mixed with representation is mixed with narrative is mixed is mixed with language is mixed with sociability...</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Another day, a butterfly:</div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrRzoNOEMaOZsTXKy1FEj0cdb2xaYQtcHMbunb7S4nmDp8TxWi9tSP0tpHPbNtJb4GrFIJzZY2QH8vjfMagGzaj_c0prS5IDaqK_EfOnRu4uy5l_QuBY9Ej9UyRnkPai_Pb9Oya1QTHt70gB0olDEg5z5XMBj603rHFlt-F6Hfbz5MBOX5mDyRPfnB/s320/IMG_4261.JPG" width="320" /></div></div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBF8OMHmKTR225amx8qt6yxtb0Bk8X0UYcsS3QdI1gpxp4igjF298J57JsoU7DKNsaXuWlkTxoztHFKvrdpu-YH1paGuSrWLBrIaZw0B096tgwj7PNGSz_QHDTN3PF8gmA-nr6Zd1pU6EMFYir5L5f9UZelLfblnP1-QeYZXAFdgp6dJX2QHpp6iGR/s320/IMG_4266.JPG" width="320" />^</div><div class="separator" style="clear: both; text-align: left;">Another day, a bird:</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC_z49hcchKxM3NIpfbrviTGy0S-wLW8y7GY5BxNkcwm3p3S3i6-xGKqn8kACaJgFeWuTHoX5xUompDxmJQU1Njh8vAQ7msBnTQOp0uc6PwdQPjaSxjwtYMQH6NZ2Z0Oh-BFvOUHFpIgdz35UYuDAOtTPmJCe85etWo2EZHKNlL5ID4slCNakVqpQj/s320/IMG_4628.JPG" width="320" /></div><div class="separator" style="clear: both; text-align: left;">Another day, flowers composed of four punched hearts rotated:</div></div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6g-w2EgR84pDAagmwzu3CZcJPzqqiiXDR3yatymU7yugQUTGpT2WcRmZBCeQ9ueMaHAuZWqhrxv1WAxX_Y6QL7svD3QS0KZsyZm6C2U5Y_a42Tl5D5grtxY6l-12yEdVA1vBFx-K_0QEFeFr4fooCyvApWUoWeRAAdacqEeZWzBe6DYOucK3kcrfX/s320/IMG_4803.JPG" width="320" /></div><div>What is the role of the adult here? Obviously, we keep the table stocked, and help the students to keep it tidy and organised. In the moment, we chat if it doesn't interrupt the flow of the play and conversation. We appreciate what the students are doing, how they're thinking and experimenting, again in a way that doesn't distract from the flow. We document and share with parents on Seesaw, and often with the class in our meeting times. Sometimes we play alongside too; this usually doesn't lead to much in itself, but allows us to be in the workshop too.</div><div><br /></div><div>This time I started playing with R's leftovers (I'd asked if that was OK). I started making little 'windows' with the heart holes. R quite liked what I was doing this time, and together we made a picture, incorporating a bear on a trampoline, and also some of the folded and cut squares that were being made at the table at the same time.</div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMgrT8YqYiTYX7kHinD5_-WdwkyqkrXXlzXOf37Vd1WRUHJs2UMG6xBwuMu_2dDXrLtSrSFbJGBqNRzgH8L0ulkHEhWanzPWtaIbIcUVGeMzXIJkNW1TanD_eYJN7FfQzHJ83v73BGrF-KGOsau2dMS7QOTmSSEOSSZ8jmsFYkJKrhzzzkE1ud_3gw/s320/IMG_4814.JPG" width="320" /></div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="2448" data-original-width="3264" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqUa7-NGxQ1vtJgFyujr2mfhHZIt_dnFoaKtsUHTTQJznmCidFiym4p1jKago5q3mu89RUOTMF1fp9zjnuPZaFBUvhasU0QXEkTaUrbK21SWyLvVjm3iMQD_GEC-FCV2GAQz72qD1CpmvMIFsSU_chrgU-URccjsJ5H2IXjh21mbRBNckgKoDySgb0/s320/IMG_4820.JPG" width="320" /></div><div>But, it's really not necessary for me to be adding anything in to this process: there's so much happening already: theories being refined, interests pursued, skills honed, and much more. </div><div><br /></div><div>We leave approximately the same materials on the table most of the time, and that's its power really. The little squares, the A4 sheets, the scissors, glue, tape and pens are enough for an endless range of operations, and combinations of operations that, the way children use them playfully, become more and more sophisticated.</div><div><br /></div><div>Other things we provide in the class are more one-off. Putting some flowers in a vase to be sketched, along with the sketching materials. This is valid too, but is not a familiar arena that encourages the independence and agency of the students to develop.</div><div><br /></div>In November, R gave a folded-and cut-out character to P, a boy she hasn't had much direct play or conversation with. One of them stuck the character to a sheet of paper, and P added lots of line drawing background. He carried it around with him for half the day.</div></div><div><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="1225" data-original-width="1691" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJQ27tS3U7mPJY1Wld-nn__0xkZg2xWNLutO8Pc4fFFgz95oLazaXAfgKy-Q1jXGE36rvQkECav114sj5zrCxfo7PTDAmol92QZfnqEEtYd9pdgid0KsQitVEY0HDvMsuCu-3uJFPCH2nx_ShOCQzCu-TYWU_Oeg055Ndi_NGtdZVfIqfAbLYyxeWN/s320/for%20P.jpg" width="320" /></div>I was surprised and delighted that this paper play had become a way of reaching out in friendship.<br /></div></div><div><br /></div><div>But maybe I shouldn't have been so surprised. These spaces that the students own, which become for them both a laboratory and a language are the natural places for the real events of the class to happen in.</div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-68137307990562843242022-10-03T08:32:00.007-07:002022-10-03T08:53:06.820-07:00The design cycle, sped up<p><span style="font-family: inherit;">A <span style="font-size: 11pt; white-space: pre-wrap;">(just four) began her time with us with a torrent of paintings. She’s now broadened out, and shows a lot of interest in arranging blocks.</span></span></p><span id="docs-internal-guid-c66d9859-7fff-180e-a911-d672eb422056"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">On Tuesday she got some of the Unit Blocks out and began making little ‘houses’ - combinations of shapes that went together. She was making, knocking down, sweeping them to one side, and remaking anew, again and again. I sat down and tried to add to the houses, but she was mostly not happy with my additions and my adding them only seemed to speed up the sweeping away and remaking!</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; height: 167px; overflow: hidden; width: 1047px;"><img height="102" src="https://lh5.googleusercontent.com/pSCGwXLwUP6Ho4GPydQFgMLYWXk_VEHqccZR442TC05I1C_geNHIZdTxAZShUNQEA2BKtHmGnvvHKK83OH14WhxLySw4MY-xyXvH8Akjm1fWPz-u8q99YDClJD3EAufNf_w3x6_bzGqaqrm2OeFYL94rp4QgcpvEbiKu2Em3Gx2IXFE1st4GdOoCpg=w640-h102" style="margin-left: 0px; margin-top: 0px;" width="640" /></span></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Finally, she had a house shape that pleased her.</span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I was struck anew by something about children’s play that this seemed to exemplify: the rapid movement through iterations, making, destroying, making…</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">If the results weren’t right, pieces were adjusted, rearranged, added or subtracted, up to a point where, if the whole was unsatisfying it was swept to the side and the ground laid bare to build a new thing. It’s like the design cycle, but speeded up:</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; font-family: inherit; height: 187px; overflow: hidden; width: 269px;"><img height="187" src="https://lh6.googleusercontent.com/YQSFU-2mHRnpBhc63GLL2yeZVqLfdiWJIVd-YN8ahbBGeq2zhn42U4XcizTBVAU_abe7fDWdJVRVAjvzXsx1wxcPwu8WOiuTvez1OHrXmnhU_sydHRsciXtqdN1MEb_2oNN2f4Ua7ZFTEuC9o2F2Ccnpsz9NUF1arbBo72jDksIhwSIwa36EtFQpTw" style="margin-left: 0px; margin-top: 0px;" width="269" /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The checking and thinking is so fast, so much during the making, that it doesn’t stand out as a distinct stage, it’s all there in the making. The only other - brief - stage that is separate is the knocking down and sweeping blocks to the side.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; font-family: inherit; height: 243px; overflow: hidden; width: 359px;"><img height="243" src="https://lh4.googleusercontent.com/y0XF6m-To8m6icmRRA5s4Kue8GapH-b3Aip3dcM7u9-E_2U8MTV12FZ5dru2LcgzM8woJkpelI13fK4wpMaBR_ZfxUZ7ehyxtninJdEvdKHYQOjBTt7zwpAJvgYgmfy9POg5VbJF2UUB7gqXhnCSnTQeRKib1tGDGFrASjfCyyE3dpHSs4o96AH8KA" style="margin-left: 0px; margin-top: 0px;" width="359" /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I’m thinking of this, from Alison Gopnick’s great book, </span><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The Gardener and the Carpenter</span><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">: "</span><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">by four, fully 66 percent of calories go to the brain</span><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">". Children are thinking fast, making connections rapidly. And they’re doing a lot of the thinking with their hands. </span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #0f1419; font-family: inherit; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Again, on Friday, this time working with Kapla and little wooden people, A was creating and recreating, remodeling her house again and again to better please her. </span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; font-family: inherit; height: 204px; overflow: hidden; width: 1047px;"><img height="125" src="https://lh6.googleusercontent.com/tE_TcDdeKyrVaoLSZgLBQj2qxvq0Rtqjsnrecfhr0CsSQYt020lE4bRww1A0JVwmnw0M9IgmQPHuBdzPDYwYN2rwr7LtyyAaTI-uxyj5y78heQJfG9YoIO0HLhJTB0BqilMgEqshOGupoybwqlfm7J9BO0MhjczLQ2ehKbooL1isncZ3oybZHOIZUg=w640-h125" style="margin-left: 0px; margin-top: 0px;" width="640" /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #0f1419; font-family: inherit; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">After about twenty-five minutes, the finished house satisfied her. There were bedrooms for all the adults to sleep in, in groups that she found satisfying. The children appear to have some kind of dormitory thing going on:</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; font-family: inherit; height: 264px; overflow: hidden; width: 353px;"><img height="264" src="https://lh3.googleusercontent.com/D3ouOtVtzRWil7jlYxeX36B8HBI8eb1mQLogIgXRB_LKL07ltKTeZoMQE-TFs9Pr5jfteM2dz9cS3liTX6Q2zF7xBK_UX3_Lu7Q2bWdsGhF1v2048yWp__hULVcqUU8gm1Y4mGZeBgp3prBysbQnpaOnZylmy7vYfm9zH1wETEytu3kqIb5b3tK4ZA" style="margin-left: 0px; margin-top: 0px;" width="353" /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #0f1419; font-family: inherit; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">This rapid-fire remodelling is maybe a kind of superpower of the four-year old. While 66% of their energy is going to the brain, they can move quickly between experiences, ‘breaking’ (or leaving) whatever doesn’t seem to work. </span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #0f1419; font-family: inherit; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Though there was a rapid movement in the making, A stuck with the project from 9:52 to at least 10:16 - there’s a time stamp on the photos.</span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">It strikes me that this is characteristic of young children, how they move from one activity to another quickly. Maybe it’s a quick evaluation: is this the optimal possibility now? Could I be getting more from doing something else? We adults might mistake this for an inability to concentrate, or some kind of hyperactivity. But it seems to be just the brain’s optimal learning path. There’s no need to leave a trail, to have a distinct and visible evaluation or planning stage. Both are integrated into the making. There’s no need to document the process. We teachers might see a reason to do this, but children tend to just move on quickly. A doesn’t even seem to care too much about the ‘end’ product being put away. </span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I would propose that A is demonstrating all these <a href="https://www.ibo.org/programmes/primary-years-programme/" target="_blank">IB PYP</a> "attitudes to learning" below, all almost at the same time in the course of her selection and placement of the blocks and people, and the conversation she has as she does it. The separate elements are not visible as separate but they are all present as she places and replaces elements:</span></p><div align="left" dir="ltr" style="margin-left: 0pt;"><table style="border-collapse: collapse; border: none;"><colgroup><col width="86"></col><col width="208"></col><col width="753"></col></colgroup><tbody><tr style="height: 16.5pt;"><td style="background-color: white; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Skills</span></p></td><td style="background-color: white; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Subskills</span></p></td><td style="background-color: white; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: inherit; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">What students do</span></p></td></tr><tr style="height: 16.5pt;"><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Thinking skills</span></p></td><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: bottom;"><span style="font-family: inherit;"><br /></span></td><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><span style="font-family: inherit;"><br /></span></td></tr><tr style="height: 55.5pt;"><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Critical thinking</span></p></td><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Analysing</span></p></td><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Observe carefully.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Find unique characteristics.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Consider meaning taken from materials and events.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Synthesize new understandings by seeing relationships and connections.</span></p></td></tr><tr style="height: 42.75pt;"><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><span style="font-family: inherit;"><br /></span></td><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Evaluating</span></p></td><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Organize information</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Evaluate evidence.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Test generalizations, strategies or ideas.</span></p></td></tr><tr style="height: 42.75pt;"><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><span style="font-family: inherit;"><br /></span></td><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Forming decisions</span></p></td><td style="background-color: #fff2cc; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Revise understandings based on new information and evidence.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Draw conclusions and generalizations.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Apply rules, strategies and ideas from one context to another.</span></p></td></tr><tr style="height: 42.75pt;"><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Creative thinking</span></p></td><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Generating novel ideas</span></p></td><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Use discussion and play to generate new ideas and investigations.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Make unexpected or unusual connections between objects and/or ideas.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Practice some “visible thinking” routines (Ritchhart, Church and Morrison 2011).</span></p></td></tr><tr style="height: 42.75pt;"><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><span style="font-family: inherit;"><br /></span></td><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Considering new perspectives</span></p></td><td style="background-color: #ffe599; border-bottom: solid #cccccc 0.75pt; border-color: rgb(204, 204, 204); border-left: solid #cccccc 0.75pt; border-right: solid #cccccc 0.75pt; border-style: solid; border-top: solid #cccccc 0.75pt; border-width: 0.75pt; overflow-wrap: break-word; overflow: hidden; padding: 2pt; vertical-align: top;"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Seek information.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Consider alternative solutions, including those that might be unlikely or impossible, in play and other situations.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: #333333; font-family: inherit; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">►Ask “what if” questions. Practise some “visible thinking” routines.</span></p></td></tr></tbody></table></div><br /></span>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-79443302283486616952022-09-24T22:40:00.004-07:002022-09-24T22:50:40.231-07:00From back behind them<p> We've got a set of Unit Blocks in Sun Class and a set in Moon Class.</p><p>R and K were playing with them, and also with some of the wooden story figures, and a gorilla.</p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEicf5l119nMl6vn57xBzxvHMdO7gR95bPIJTS1Ndczq-jfllZFnuI42Ri046ZMdmAcKL-V6a8SWmDGmDVYVTgJJuVKDHY1cTgL9ma5Ie2tPQAeTqElnKxRceGoKTeaCn8RXVlH4DgZfWakghiobaz1rzJ45NIMJoCb_5PrQ1CM8bwgx6Bvu-iWzgiq7" width="320" /></div>Sometimes, the building came to the fore.<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiQHqP0PbcHGbSF849k-0jWPTrFhIBxQGgFPg5_5r18UtYtxXZ_V3-_1AyvnBjapQkJVpXrGEHhlL5xePon9f3L0Kh4zoxQJZwYvOYJ8w0TvDVzKQShVxPzgzgXNGgKQ1M46HF9_yz5aYIF5NYP-JoxtvGp_AMsfPgKrXs7FdoAF0t0Wwx0npDPxsMe" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiQHqP0PbcHGbSF849k-0jWPTrFhIBxQGgFPg5_5r18UtYtxXZ_V3-_1AyvnBjapQkJVpXrGEHhlL5xePon9f3L0Kh4zoxQJZwYvOYJ8w0TvDVzKQShVxPzgzgXNGgKQ1M46HF9_yz5aYIF5NYP-JoxtvGp_AMsfPgKrXs7FdoAF0t0Wwx0npDPxsMe" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Sometimes, it was the story telling and acting out with the small-world figures. R's mum later told me that R had watched King Kong in the summer.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Other people, including me, were also contributing to the Unit Block construction.<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg3vd7qTi14DJFHg67FsJrv3WihoHqolhxo8QY7hebjUAq0dfkY_rCKgFSCRknaASrqEDjStHwZqJhRawXLaou06UjIdcUNtz4Zaj_q5ktYZrldOlf5f_zx1sNlFsTC50ieEBeS7g3p9DQJOuxyHg_V84dC4aBkQvAZrFDuhS-tRINoSeNRN3zG8gmO" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg3vd7qTi14DJFHg67FsJrv3WihoHqolhxo8QY7hebjUAq0dfkY_rCKgFSCRknaASrqEDjStHwZqJhRawXLaou06UjIdcUNtz4Zaj_q5ktYZrldOlf5f_zx1sNlFsTC50ieEBeS7g3p9DQJOuxyHg_V84dC4aBkQvAZrFDuhS-tRINoSeNRN3zG8gmO" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">R was kind of telling a story as the characters acted it out.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjI8Xas0m67_39BZyP1hZlPAlR2dk3BuR_-0dAqVrC4H-eupmi95X_cHmm_a2G1uhej1uNDk9reALmeWb61aTEahENk6kHtAzp57N3jZHlxOYURiaw_TjrgQCvwjlZXRHKF38hZCpTwSencmGeMEx93z5NlfLZYo9RhTp40mp3FK2gRZmZ13S353nXb" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjI8Xas0m67_39BZyP1hZlPAlR2dk3BuR_-0dAqVrC4H-eupmi95X_cHmm_a2G1uhej1uNDk9reALmeWb61aTEahENk6kHtAzp57N3jZHlxOYURiaw_TjrgQCvwjlZXRHKF38hZCpTwSencmGeMEx93z5NlfLZYo9RhTp40mp3FK2gRZmZ13S353nXb" width="320" /></a></div>Normally, it's the students who ask me if I can write down stories for them ("helicopter stories"). This time I asked. R and K told this story together, with R leading the way:<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhesUb9kE0qlR-5pQojWaYjEeoIGLMN_ZzQCSbu36m-2LfIAhQIoYlMHkrT3IIDlzA2_IT76bGZaL6j9ogpSMrmoZoMuNNQWJ7bMU6vQdrFQNxhOBIg-REMjy_JShJDM1ZpEuOqt4k311p9xyd_f8q8-DyexML2GoERKbfhnzuwC2Ffds4i-KOY8gbO" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="914" data-original-width="1218" height="480" src="https://blogger.googleusercontent.com/img/a/AVvXsEhesUb9kE0qlR-5pQojWaYjEeoIGLMN_ZzQCSbu36m-2LfIAhQIoYlMHkrT3IIDlzA2_IT76bGZaL6j9ogpSMrmoZoMuNNQWJ7bMU6vQdrFQNxhOBIg-REMjy_JShJDM1ZpEuOqt4k311p9xyd_f8q8-DyexML2GoERKbfhnzuwC2Ffds4i-KOY8gbO=w640-h480" width="640" /></a></div><br /></div><div class="separator" style="clear: both; text-align: left;">"They all heard the noise from back behind them. They turned round. They all jumped when they saw King Kong."</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I was really struck by this part. It describes a moment of surprise in a way that the PK students stories usually don't. And the surprise hinges on a spatial arrangement. At first the character blocks were facing away from King Kong, not conscious of his presence. Then they turn around, and only then do they realise to their shock that King Kong is there.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We often act out our stories together, and acted out this one as I read it out. Again, there was the dramatic moment of all turning round and seeing that King Kong was there.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">And this is what I wonder: Did the small world enactment of the story - the staging of it together - help to introduce this dramatic - and geometric - moment into the story telling?</div><p></p>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com2tag:blogger.com,1999:blog-3071719252136968205.post-83419524806314214402022-07-19T15:16:00.003-07:002022-07-19T23:46:23.101-07:00Block play - an interview with Sofia Wallace<div><span id="docs-internal-guid-533a7c83-7fff-e352-e551-fc3c353d66ae"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i>I am fascinated by our young (3-5 yo) students' block play. So, when <a href="https://twitter.com/SofiaWallace20" target="_blank">Sofia Wallace</a>, who posts delightful and inspiring things happening in her early years class in Milan, posted <a href="https://twitter.com/SofiaWallace20/status/1529186792838246400" target="_blank">this</a>, I wanted to know more:</i></span></p><i><br /></i><div class="separator" style="clear: both; text-align: center;"><a href="https://twitter.com/SofiaWallace20/status/1529186792838246400" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="425" data-original-width="640" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx8n92gSoRYNFXv0DEmJ7_Ru4u9r3EdrvP4xnFgYubM7lJcJrTdqjYq8crCvP4_8trdekemt0cOuY86Z8fljuGh9QwTMo8HRS7YPqATnV9Supy0YR-UnmjrmN_t9TS-vEvaksE8HqQYnuwlul1JDHoBqNryKOfG6SYjQd4ItTm-gR6IOtRUwURfzni/w640-h426/block%20play%201.png" width="640" /></a></div><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i>I asked Sofia if she might be interested, if not in a thesis, at least in a short conversation about block play.</i></span></p><i><br /></i><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i>She liked the idea, and the idea of sharing it with you here. </i></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i><br /></i></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i><br /></i></span></p><div><br /></div></span></div><div><span id="docs-internal-guid-5ecef7a6-7fff-7a83-9b03-21b25a916790"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Simon - Hi Sofia. #justsocool I find block play endlessly fascinating too, so I’m interested! I’d love to talk about it a little more…</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I see already there are some hashtags. They might be good starting points.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">#stories and #structures - It’s amazing how block play brings together engineering and narrative. Can you say a little more about that?</span></p><br /><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Sofia - Hi Simon! Thank you for putting this together! I love block play because it's such an accessible storytelling medium in early years. I’ve found that in my mostly EAL classrooms, children will often get intimidated with more traditional storytelling that requires them to draw or to speak. Blocks are different. All the students I’ve ever taught have been attracted to block play in one form or another. Whether solo exploring, testing how they can use them or sharing in elaborate narratives, there really is something for everyone in block play. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I used the hashtags structure and stories because they seem to be umbrella terms for the two ways I generally see children explore with blocks. Even as young as 1 or 2 children explore structure when they are putting them in their mouths and discovering the texture or shape or physics of how a block drops, or rolls or sounds when it’s thrown. Then as they begin having that ability to use blocks to represent other things they move into being more storytellers. It’s the interplay of stories and structure that allow a child to create these amazing things. </span></p></span><p></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Simon - Yes, it’s amazing how #story and #structure brings so much together! The world of people and the world of things!</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Blocks are such a powerful tool, language, material! I’m struck that you say all the students you’ve taught are attracted to block play! I’m not sure we could say the same, with our 3 to 5 year olds. Let’s take it back a bit… Can you tell me a little more about the actual blocks that your students use in the block play, how they’re stored and accessed, and… how the attraction works? Is it just a matter of the blocks attracting, or is it seeing each other play too? Also, what is the place of the teacher in this? What would you advise early years educators like us who aren’t seeing this attraction in all the students?</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Sofia - Oh great questions! I’ve been really fortunate to work in lots of different settings, all of which had different blocks and building materials available. Currently, my students have access to a combination of Kaplan, Lego, traditional wooden building blocks, Magnatiles and large foam blocks. All year round, a combination of these are stocked in the building area. We have either the shadow of the shape (just paper cut out to match the shape of the block, taped down) or photos posted of what the shelf looks like when put away. For me, a big part of creating a culture that supports exploring with blocks is creating a culture of accessibility. Students have to know that the tools out are there for them to use. For that to work, blocks have to be on a shelf that is at eye level, organised and sorted for easy access. At the start of the year we are pretty selective with what we put out. Slowly, as we develop a culture of care in our classroom, we add more. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We also are mindful to keep the loose parts shelf as near the block area as possible, since loose parts add a lot to the narratives that come with block structures. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Both of these shelves start quite sparse at the beginning of the year, but now have many more materials on them. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Your next question is quite tricky for me to think about. I’m not sure I have a perfect answer for how the attraction works. I know that at the start of the year, we will often play with the students and model what being a good play partner looks like. We ask questions, use polite language to share, offer materials to others, etc. I think this immediately draws in students who are maybe coming to school for the first time and are mostly used to playing with mom, dad, grandma or grandpa in their homes. I found this year more than other years, a lot of my students were initially seeking to play with adults and not other children. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Another way we draw children in is to have some structures made already to spark interest. Almost like a block provocation. We might create a pattern with a structure, an interesting arrangement or add a figurine to suggest a story. We did this more at the beginning of the year. Having the option to add on to something rather than start your ideas from scratch seemed like a good way to encourage children to explore. It also gave us the opportunity to model cooperative building. A lot of our students moved from being more parallel players to partner players this year. To support this we try to give them as many opportunities to collaborate as we can. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We also will add photographs around the block structure area and we change those throughout the year. We started with photos of their homes sent by parents and then went to famous buildings around Milan, pictures of structures families visited, pictures of different architecture around Italy, landscapes, race car tracks, family vacations, etc. We changed these based on what we heard them talk about while playing in other areas in the classroom. Sometimes this inspires and sometimes it doesn’t. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I think the final thing that attracts my groups to blocks is that they feel that their structures are really important. We take lots of pictures, share builds at circle, write stories about creations and allow for things to not get cleaned up. This tells them that their creations are important and valuable and allows them to continue on with their thinking. </span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">More than anything, I believe my students want to be seen as capable. Honouring their work by saying, “Yes! You worked so hard on this creation, tell me all about it” and then taking the time to save what they’ve done and share it with peers and families makes them feel really proud. That pride is what brings them back and gets them thinking in new and creative ways. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">So I suppose to summarise, my advice to an early years teacher who is not seeing a pull to blocks is to…</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">#1 See if the space is inviting and draws you in. </span></p><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px;"><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Make sure pieces are easily accessed on your shelf and that they have a clear place</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Make sure there are not too many options, especially to begin with </span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Have a carpet or foam mat of some kind so that if blocks fall they aren’t alarming or frightening to little learners</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Include pictures of places the children have been, ideas you’re learning about in class or settings from stories the children love to help inspire them</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Include small pictures of students taped on blocks. This allows them to join the narrative</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Make sure your block material match the kind of play your learners and you are ready for</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Start with a provocation:</span></p></li><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px;"><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">An arrangement</span></p></li><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A tower</span></p></li><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A sort </span></p></li><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A photo</span></p></li><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">An odd loose part </span></p></li><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">etc.</span></p></li></ul></ul><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">#2 Adjust the way you think about block play</span></p><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px;"><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Allow structures to be saved, ask if they want to work on it later and create a system where you can do that</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Reflect on how you talk about blocks </span></p></li><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px;"><li aria-level="2" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: circle; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Video or audio record yourself sitting in the block area and notice how you speak about what the children are doing. I am always catching myself inserting my narratives, which might interrupt the thinking. Listening to recording of myself helps me reflect on ways I could have better guided in the future. Being mindful of what you say during the play can really help children go deeper and explore without fear of judgement. </span></p></li></ul><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Take notes of what you see them doing, write down quotes if you hear any, ask if you can photograph things to remember later and then post all of that near your blocks for reflection. It will help you as the teacher notice patterns and them as the students to feel their work is important. </span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">If you want to, try putting blocks in different areas for provocations and introduce them in new contexts (but have your clean up system planned and ready) </span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Determine your rules beforehand with other teachers and figure out what language you are going to use in play to make those expectations clear</span></p></li></ul><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">#3 Give yourself time</span></p><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px;"><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Make sure children get a good 30 minutes of uninterrupted block play time (not including clean up)</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Treat clean up time like a lesson, plan lots of time for it, maybe gather a small group to do a mini lesson on how to clean the area</span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Model, scaffold, don’t rush </span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Don’t clean everything. If you run out of time, honor the work by putting a sign up and saving it for later. The more you do this the more the students will be excited to put in time and energy. (This one bears repeating, because it’s so important) </span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Reflect on exciting things as a group: if there is something they are very proud of, ask them if they want to share it at a group gathering time. </span></p></li></ul><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">#4 Play </span></p><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px;"><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Have a day where you play too, see what it's like to really try and build something that you are proud of and remember what it feels like to create. Remembering the joys, triumphs and frustrations that come with blocks will allow you to better support your students. And it will get you excited about block play, which is then felt by the students. </span></p></li><li aria-level="1" dir="ltr" style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; list-style-type: disc; vertical-align: baseline; white-space: pre;"><p dir="ltr" role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I highly recommend doing this with your team :) </span></p></li></ul><div><span style="font-family: Arial;"><span style="font-size: 18.6667px; white-space: pre-wrap;"><div class="separator" style="clear: both; text-align: center;"><a href="https://twitter.com/SofiaWallace20/status/1463227582980177923" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img alt="" data-original-height="988" data-original-width="936" height="640" src="https://blogger.googleusercontent.com/img/a/AVvXsEjSA8xkzJ4nMx9DmHRXa5HCXY2d2mcOYrLrnc_ZBNdXocayzW5T7m-7IVTDmrZEJmQKmwfN3OOMmOX_7xiQ5xoGu4Xa1dUNKC8cgo5LPp7SfRZi_Ez-ZDmZcaSL9yxSBdpAPKz9L5OB09C-Xp4XhDXb3QWK7N5fJVUgWWAlPykAYOSSqHAjYMEPZ7_E=w605-h640" width="605" /></a></div><br /></span></span></div><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Simon - I’m so glad I asked those questions, Sofia! Yes! I love the way you’ve spelt out the kind of superstructure of influence and inspiration that needs to accompany the blocks being physically there in the classroom! It’s so useful, and practical in its detail! I already feel like you’ve given me a lot to think about and act on… but, perhaps greedily, I want to ask a few more questions…</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">You will be reflecting on what the students have built, and how they built it. Perhaps you’re doing that with colleagues. I’m interested in how you do your thinking about this. Do you have set times together when you do this? Do you think about play schemas? Or how students’ block play is progressing? Are you thinking about students’ interests or their working theories? Do you hone in on particular aspects as you document the building? Perhaps the dramatic, or the mathematical? And how do you select those aspects? How does this reflection feed into the way you re-present the students’ work to them?</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #980000; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">And, on the same theme, whose ideas have influenced your thinking about all this in particular?</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Sofia - Reflecting is always tricky, because the one thing that all teachers never have enough of is time. Reflection (especially with a group of 27 students like we had this year) requires a lot of time. Every Monday, we have one hour of dedicated planning time where we sit and look at photos, notice the patterns and look for opportunities to extend. We put our notes into our planner and use it to come up with action for the following week. Action might look like picking books related to the topics and patterns we saw, finding links to interesting videos or models, asking parents or other staff to come in as “experts”, adding provocations in different spaces, planning for large or small group games to support ideas, and organising pictures and quotes to present to the students for a circle time throughout the week. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">On Friday afternoons, our group attends an hour of gym and Chinese without us. We use that time to write a newsletter and reflect on what the big moments of the week were in play. Our newsletter is a Reggio-inspired document that includes quotes, photos, ideas, narratives and skills presented in parent-friendly-language. This helps us to see where we could go next, and help the parents get involved and keep the conversations going at home. Some weeks, block play would be a big focus, and all the narratives, drawings, games, etc. would connect to their creations. Other weeks it is barely mentioned. It all depends on what is happening in the classroom.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">During the week, we use Seesaw to save pictures and track what is happening. I’m not sure how familiar you are with Seesaw, but it has this great feature that allows you to record over a photo so that even if you don’t have time to talk with everyone in the moment, the children can add comments afterwards (we often did this during Garden time). When helping children create recordings, we are very thoughtful about our questions and the language we use since the point is to gather data on the child's process and thinking. We have a separate document we have been working on that helps guide teacher questions and conversations; it includes a section of block play specific questions we use to guide us. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">In terms of assessing and tracking with block play: those Seesaw posts become key. At the beginning of the year, our Technology lead input all the EYFS standards we have in our yearly curriculum map into the Seesaw Skills for our class, which has made tracking very easy. Basically, once you have listed all the standards or skills you are looking for in the year, you can tag them on a piece of work, a conversation, video, etc. Which is amazing because in early years it allows you to really differentiate. For example: we can track a child's understanding of one-to-one correspondence by seeing how they count the blocks in their structure, animals in small world, pieces of paper glued to a collage or number of times they hit a musical instrument out in the garden. All of these are organic experiences that show the same skill, while still respecting their individual interests and methods of exploring. When we use the app, we are able to upload the data, tag it quickly with a skill, and see how those skills develop in a truly play-based context throughout the year. You can also notice gaps or concepts the child is choosing not to explore and try to create opportunities in their preferred play area for that. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I think you could honestly include anything you are looking to track and it is a great tool. I have heard other people have had great success with different online tracking tools for this. I would be very interested to hear about other tools people have had success with when it comes to documentation, data gathering and tracking.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">This year, we did a systematic reflection on each student 3 times in the year: October, January and March. For this we went through the data we had gathered on Seesaw, in their portfolios and from the small and large group documentation. But to be honest, we didn’t have a rigid system for honing in on skills. Each of us would probably approach a structure or build and notice different skills the children are using. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But I think that is okay. If I come to a block structure and see how the child is developing communication skills and another teacher comes to that same block structure and notices only the maths skills, that’s fine. We aren’t going to get everything, and at the end of the day, that isn’t the point. I’ve had a really good team this year and we have all been on the same page that the thing that comes first is the joy: allowing the child to be a child. To play and wonder and get frustrated and try again without having every detail gone over with a fine-tooth comb by their teacher. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">It’s a bit of a balancing act, because we are always very excited to get inside the thinking and understand. However, as you mentioned, our reflection, questions and perspective will affect the way we record it. By working toward being more mindful, we can avoid losing focus on what's important. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I have been super lucky to have worked with some really amazing teachers, starting with the staff at my university: the University of Minnesota. I got degrees there in both child psych and early childhood education, which gave me a really strong foundation to start from and introduced me to the great minds and amazing science behind play. Since then, I have been very lucky to continue learning from peers in schools, through courses and PD and in places like Twitter! </span></p></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-41187896107266826472022-06-15T10:04:00.004-07:002022-07-28T03:32:07.178-07:00Mathematics is not a "building block" subject<p>I've been reading <a href="https://twitter.com/AlfColes" target="_blank">Alf Coles</a> and Nathalie Sinclair's <i>I Can't Do Maths! Why children say this and how to make a difference</i>. It takes five ideas about teaching maths that they've identified as myths, and explains how the myth works, and what might be done about it.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgM2u94J85z_pEaL85y2l0qF3O_FdtG1g0tQTMx45N_-K9carkqDCZLGqIB7I-zSgD0fCksQCYvE7iw1AGXgbW-DDI-Em64MJECMeAo9Iq3gN_p3g-YR1CL56tvhXLYA0JtnNt1ia5gaWnuIzoKAlkrL7eAu9ekMV0xZL2xL0w9nRkFFr3EEO-bAmWA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="626" data-original-width="400" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgM2u94J85z_pEaL85y2l0qF3O_FdtG1g0tQTMx45N_-K9carkqDCZLGqIB7I-zSgD0fCksQCYvE7iw1AGXgbW-DDI-Em64MJECMeAo9Iq3gN_p3g-YR1CL56tvhXLYA0JtnNt1ia5gaWnuIzoKAlkrL7eAu9ekMV0xZL2xL0w9nRkFFr3EEO-bAmWA" width="153" /></a></div><br /><p></p><p>I'd already seen Alf Cole's TEDx video about the first myth, that mathematics is a building block subject, where we build more complex ideas on top of simple ideas.</p>
<iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/-Gajs_UNItU" title="YouTube video player" width="560"></iframe>
<p>The situation of learning a language by being immersed in a complex whole is of course a really powerful instance of children learning within complexity. My English as an additional language learners learn - fast - by being immersed in the life of the class. They somehow pull out of the messy whole all the grammar and vocab that they need.</p><p>As Alf Coles says, Caleb Gattegno calls this using the 'powers of their minds', and asks why we can't make complex demands on those powers in teaching maths.</p><p>Alf Coles suggests that if you're not succeeding in mathematics class, instead of needing something simpler, perhaps you need something more complex.</p><p>This is the subject of the first chapter of the book: Myth A: Maths is a Building Block Subject. </p><p></p><blockquote>'The idea that in order to learn something, you need to start with the simplest ideas and slowly build upwards - constructing one block at a time - seems to be common sense. The primary maths curriculum in schools in most countries in the West is designed with the tree idea in mind.'</blockquote><p></p><p>But...</p><p></p><blockquote>'...what if our image of learning and mathematics were more like a mangrove forest than a single structure or tree? Mangroves grow as a decentralised network, each part dependent on other parts, growing upward and downward and <a href="http://followinglearning.blogspot.com/2017/07/going-sideways.html" target="_blank">sideways </a>too. If there is a problem, no need to go back to the starting point; no need to find the trunk or the ground floor, since there is no one thing upon which everything else depends.'</blockquote><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="796" data-original-width="1920" height="133" src="https://blogger.googleusercontent.com/img/a/AVvXsEhw8A3eqZ5gW-m2mDKzHSs50_h1cw1XuaQ5yOjwmU4HVkvWX7d-RVQapugWV5suvIHitZLmzbM8z8oADELewrjmw0J7X2pORI-7sOlOSYZFdT8bW6vNEtYhpwkriVrx2vPropcNE5axfRl76a4AOKSzVQXwwe1xuKvyrvEuLv_PJjRNPv2EygEub02n" width="320" /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="color: red;">UPDATE</span> - You can read <a href="https://www.atm.org.uk/write/MediaUploads/Journals/MT282/09.pdf" target="_blank">the authors' piece on this chapter </a>in Mathematics Teaching issue 282.</div><br />This does really seem to go against the usual assumptions about mathematics learning.<p></p><p>And yet I do see it in operation in my students.</p><p>In our learning in Early Years of course, where it is children's play that leads the way, we often see the mathematics embedded in something else - maybe in building a house together. Or some other kind of <a href="http://followinglearning.blogspot.com/2021/10/arranging-things.html" target="_blank">arranging with blocks</a>. Or pretending to run a shop. Or making a pattern of squares. They present their learning to themselves not in the most simplified form but in a complex context in which much of the learning is hidden from easy observation.</p><p>Often the complex task is more satisfying than the simpler one - perhaps in some sense it is more efficient, though it looks much less orderly and logical to us.</p><p>Take that thing of arranging squares. Today I saw this.</p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiQnMvnlMeRjjl9lBrJ1F09Ai0Jk6Eryo5Ex8ft1XHu-ccuvciVzOVxwu0EbaBIMPn7tLENuso-ajEpplBB-_9ORkqYoKn5cgL_00EyNgmc2owIBvsWfHisgveemJVcF7Ormg1QaX0SCSS7EUt3Y5thVoag-7K_oT2bDb2eHyFU3Uy0iWfOH9GFAIGp" width="320" /></div>I've written before about how compelling <a href="http://followinglearning.blogspot.com/2020/10/seeing-mathematical-filling.html" target="_blank">filling a space</a> can be for young children. In terms of motivation, it seems to beat the kind of linear ABAB patterns we teach when we begin pattern. And yet, here we are dealing with a 2D space rather than a 1D space, with a lot more complexity. And yet it is how young students seem to prefer to create their patterns. <div><br /></div><div><a href="http://followinglearning.blogspot.com/2021/12/building-mathematics.html" target="_blank">I've written </a>about how one of my young students (not the only one) likes to build his Numberblocks-inspired numbers out of Polydron, rather than taking the more obvious path of simply using connecting cubes.</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgvjrScDMXwia2INxgAiaYuEsvHdm0Ye1Aqu6bQZspUZoMejBY5Ys3_DgqUMw-9krLcuglVzLFjOdpBOoijgUyn5XZCh7Jx9W5S5wWSI8MY3LB0yn9BeM6s-w5FedFdvRDTEdccqSPDNn22GgcWK5exCM-TY_fkp8snlQ0k-KL71IjfOeQQ5d9UifHJ" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="512" data-original-width="512" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgvjrScDMXwia2INxgAiaYuEsvHdm0Ye1Aqu6bQZspUZoMejBY5Ys3_DgqUMw-9krLcuglVzLFjOdpBOoijgUyn5XZCh7Jx9W5S5wWSI8MY3LB0yn9BeM6s-w5FedFdvRDTEdccqSPDNn22GgcWK5exCM-TY_fkp8snlQ0k-KL71IjfOeQQ5d9UifHJ" width="240" /></a></div><br />I've written a lot about using Cuisenaire rods (<a href="http://followinglearning.blogspot.com/2018/05/multiplication-with-cuisenaire.html" target="_blank">example</a>). The authors too see the power of looking at arithmetic algebraically rather than numerically, and in their chapter on practicalities they go into detail on this. How powerful it is to see that two things are equal so vividly, and to have an easy way of saying it. <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhaqY0p7a8hnIYIsYxmz1NaKCrJ9LtZzigpOMKD5ZLQD5YxWX7PwSfVul3Qgysf63JbMcCIyLtPU6j_pOF5w61A4Aegxv4GwWvj3RBNPBr_VRWUqRsB3YwPJnrvD8Lj_hBzzoaBvIY2awEiEpiF_Vb_zGUR9r0FJ8uG8iCKSqjc6lWm44jsvViA4Q9y" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="334" data-original-width="580" height="115" src="https://blogger.googleusercontent.com/img/a/AVvXsEhaqY0p7a8hnIYIsYxmz1NaKCrJ9LtZzigpOMKD5ZLQD5YxWX7PwSfVul3Qgysf63JbMcCIyLtPU6j_pOF5w61A4Aegxv4GwWvj3RBNPBr_VRWUqRsB3YwPJnrvD8Lj_hBzzoaBvIY2awEiEpiF_Vb_zGUR9r0FJ8uG8iCKSqjc6lWm44jsvViA4Q9y=w200-h115" width="200" /></a></div>Two reds are equal to one pink. 2r=p. Five and six year olds can get a really solid understanding of what equality means. And multiplication becomes counting. Two reds. Just like two apples. This can be a very different route from the counting and number-dependent route children usually follow.</div><div><br /></div><div>I think there's a lot to be said for this mangrove approach - and thanks to Alf Coles and Nathalie Sinclair for articulating it so well! I'm going to be pondering this a lot more.</div><div><br /></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-69511854361090751332022-02-22T11:17:00.002-08:002022-02-22T11:17:38.557-08:00Why play?<p>Here's a nice thing to do. Go down to the Med with your blow-up kayak. Push it out to sea, straight out to avoid the waves rocking it over, hop beaches, admire the mansions along the coast, take pictures, pull the kayak onto a beach and walk across the hot sand to a bar and sip cocktails together, looking out to sea.</p><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="3120" data-original-width="4160" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEj9YRtjRrDBZeb0z7MoejPsLm-hJgQPHB_qG97i6DR9e9UiZpI8IGzHZ06oXCp0Q9Kmi-MheytJEniTaGEQdE_EeZLt15jIMYKqR6SrsZyP79twyl4FUOx5tChAkWNUh9XcdcfjSHm3KjRahKPS8QzFxBR7pPyGlqM_Xfoq7sGRDB7J9-Tg3BGtolqx=s320" width="320" /></div><br /><div class="separator" style="clear: both; text-align: left;">All lovely. To do this, I also need to take my phone, to take pictures, and my card, to pay, and my glasses to see properly. It means we need to be quite careful with waves and water getting in the boat. This is the usual pattern, and it's a lot of fun.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">But one time, I tried something different. I left my glasses, phone, and money with the people on the towels.</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEimEjLDePA_EXRwEv9R1Rbcd2ej_8P2kf4PV42aZ3irXToPvG8KYskbI_bDC0SRpbCvjKurSckquJDcExAtZoCDdCR3MFdYfCE34QS4gfR0Csl6r5o0WCOns5r84OW0FKTi3pGv47aPr9LmI2Q71cJsaGBWImL0PBcksLgvZcz7lEWfYgrTm2WZC-A8=s1911" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1911" data-original-width="1895" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEimEjLDePA_EXRwEv9R1Rbcd2ej_8P2kf4PV42aZ3irXToPvG8KYskbI_bDC0SRpbCvjKurSckquJDcExAtZoCDdCR3MFdYfCE34QS4gfR0Csl6r5o0WCOns5r84OW0FKTi3pGv47aPr9LmI2Q71cJsaGBWImL0PBcksLgvZcz7lEWfYgrTm2WZC-A8=s320" width="317" /></a></div><br /><div class="separator" style="clear: both; text-align: left;">Oh, now there's nothing to get wet, I don't need to worry about water getting in the kayak. I can aim for the waves. I can deliberately capsize it, sit on the upside-down kayak, try, and succeed in, righting the kayak. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This is play. I don't need to get from A to B without getting wet. I don't need to do the correct thing. In fact, I'm going to try out the incorrect thing. I'm going to take risks, try things to the limit. I will get wet, and it will be OK.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">And I learn a lot from it, not that I was setting out to. I feel more connected with the kayak and with the sea. I know better what they can do together. I'm less afraid of what might happen. I know how the boat behaves in the waves at different angles. I know that if we get knocked over, I can sit on top of it, and we can right it. </div></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This play thing seems at right angles to the A to B functionality of the boat. It doesn't get me anywhere, it doesn't keep the boat the right way up, it doesn't keep me dry. And yet, my knowledge is now broader, more reliable, more comprehensive. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">That's what play does.</div><div class="separator" style="clear: both; text-align: left;"><br /></div></div></div><p></p>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-67813784071723758092022-01-01T13:33:00.001-08:002022-01-01T13:33:35.495-08:00Freedom<div>Over the holidays I've been reading David Graeber and David Wengrow's <i>The Dawn of Everything, A New History of Humanity</i>.</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgacujGYppqVt9pb_dYXLZcTBA4BEug42-K0dhyphenhyphenYho6hw9IuIz_YxV67uFmOZQ0WYCYUNpOeparUmpEeCg9QKhYNFg5p3qVHI3cNSITCA2WT8376kZpwXWfPrei1yJmEEnMgxet7uAo7Zc/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="450" data-original-width="300" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgacujGYppqVt9pb_dYXLZcTBA4BEug42-K0dhyphenhyphenYho6hw9IuIz_YxV67uFmOZQ0WYCYUNpOeparUmpEeCg9QKhYNFg5p3qVHI3cNSITCA2WT8376kZpwXWfPrei1yJmEEnMgxet7uAo7Zc/" width="160" /></a></div></div><div><br /></div><div>It's a big book, full of fascinating and momentous ideas about the dawn of civilisation. One of the big things it does is to question evolutionary ideas about a progression from hunter gatherer innocence in small groups evolving to agriculture, to cities, to states.</div><div><br /></div><div>There were huge sites built by hunter gatherers. There were cities all around the world that don't seem to have had kings or queens, but ran their affairs through discussion and deliberation. There were cultures that valued freedom highly and went to great lengths to avoid having that freedom taken away.</div><div><br /></div><div>In fact some of those cultures might have brought ideas of freedom to the fore for Europeans.</div><div><br /></div><div>Father Lallemant, a Jesuit missionary to the Huron in the early 17th century, wrote about the Huron in these terms:</div><div><blockquote>From the beginning of the earth to the coming of the French, the Savages have never known what it was so solemnly to forbid anything to their people, under any penalty, however slight. They are free people each of whom considers himself of as much consequence as the others; and they submit to their chiefs only in so far as it pleases them.</blockquote></div><div>The Jesuits naturally found that this 'wicked liberty of the savages' made it harder for them to submit to their authority.</div><br /><div>Published account of indigenous Americans and their not always favourable view of Europeans were popular reading in Europe. One such account, Louis Armand, Baron de Lahontan's <i>Curious Dialogues with a Native of Good Sense who has Travelled</i><i style="background-color: white; color: #202122; font-family: sans-serif; font-size: 14px;"><b>,</b></i> published in 1703, amounted to a critique of European life, from the point of view of the Huron chief, philosopher-statesman <a href="https://en.wikipedia.org/wiki/Kondiaronk" target="_blank">Kandiaronk</a>.</div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaTaxIasseecA5XBSXfZ6dpGmWNrEwIpJUlJv1wblBu4Q1uaoJTaxLX99458llGP2KwFz0EFrCASXxZRTzASWkiAV_ARfFUCCW9dib3VzuBYrzdpUYdp6fr2r30GMezzo9FeBCeXBZ55U/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="475" data-original-width="261" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaTaxIasseecA5XBSXfZ6dpGmWNrEwIpJUlJv1wblBu4Q1uaoJTaxLX99458llGP2KwFz0EFrCASXxZRTzASWkiAV_ARfFUCCW9dib3VzuBYrzdpUYdp6fr2r30GMezzo9FeBCeXBZ55U/" width="132" /></a></div></div></div><div></div><blockquote><div>Lahontan: This is why the wicked need to be punished and the good rewarded. Otherwise, murder robbery and defamation would spread everywhere, and, in a word, we would become the most miserable people upon the face of the earth.</div><div><br /></div><div>Kandiaronk: For my own part, I find it hard to see how you could be much more miserable than you already are. What kind of human, what species of creature, must Europeans be, that they have to be forced to do good, and only refrain from evil because of fear of punishment? ...</div></blockquote><div></div><div>Kandiaronk saw the Europeans as lacking in both freedom and equality. Graeber and Wengrow propose that views like this from outside Europe helped shape demands in Europe for 'Liberté, Egalité, Fraternité'.</div><div><br /></div><div>Graeber and Wengrow refer to three primordial freedoms - freedoms that are often taken away when a sovereign emerges:</div><div><ul style="text-align: left;"><li>the freedom to move;</li><li>the freedom to disobey;</li><li>the freedom to create or transform social relationships.</li></ul></div><div>Naturally, I think of education in terms of some of the themes of the book, freedom in particular. School can be an institution where all those freedoms are almost completely removed.</div><div><br /></div><div>But - and I'm thinking of the kind of play-based setting that we work in with young children - they can also be places where those freedoms are valued.</div><div><br /></div><div>I was struck by <a href="https://twitter.com/BenMardell/status/586316309706711040" target="_blank">a tweet by Ben Mardell</a> that shows some teacher documentation of some Pre-K students talking with their teacher:</div><div></div><blockquote><div>Ricardo: What does freedom mean?</div><div><br /></div><div>Ms Hannah: That's a good question Ricardo. I'm glad you asked that.</div><div><br /></div><div>Children's responses -</div><div><br /></div><div>- It means you can play!</div><div><br /></div><div>- You can move around and run.</div><div><br /></div><div>- You can finally stop what you HAVE to do.</div><div><br /></div><div>- When someone comes to play and you say yes.</div></blockquote><div></div><div><br /></div><div>The book has made me see freedom more specifically, and also as a value that in various times and places, sometimes in complex societies, in cities even, has been guarded jealously. Some cultures went to great lengths to make sure they could travel and be welcomed elsewhere, and to avoid arbitrary power emerging. These things are well worth guarding with our youngest students.</div><div><br /></div><div>And that last freedom - to create and transform social relationships... I would like to have more situations where the students genuinely, as a group as well as between pairs, have more opportunity to make the most of this freedom.</div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com1tag:blogger.com,1999:blog-3071719252136968205.post-16337753802819094972021-12-20T09:40:00.000-08:002021-12-20T09:40:33.495-08:00Building mathematics<p> One of my students, A, has been with me for over a year now. He was just three years old when he started, and without much English. His favourite thing was to get the Playmobil cars out, fill them with people, and quietly act out stories with them on his own.</p><p>He did lots of other things too. Here he is in the playground, back then in September 2020, with two other students, making a house with the giant Polydron:</p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="1500" data-original-width="2000" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAKFBXyp-fyIMGss45jZ9pJW4FJR4w9wVT6wQtQYPqxvuAk1P2cXg3uHxV2PAD4ZHFm7ig9gfe9O73XDJ5_wUcGST4FokUyqCQCMKPEUJetIFFLDjhG6FGKMlVUcZ9oGOjMw4OS3y_Yqk/" width="320" /></div><div class="separator" style="clear: both; text-align: left;"><span>We've watched lots of Numberblocks (see </span><a href="https://followinglearning.blogspot.com/2021/09/numberblocks.html" target="_blank">my post on this</a><span>), where numbers are represented by blocks.</span></div><div><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="744" data-original-width="1240" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiVowSTK4mc00ffF4-eQRL6ftxq8GHNOINMC0h0Zk5CAEZ526nzcfZfz4_rUwRcSyBZoRSzSm7QyI5GU3xSTU6JOLsVQ9kVN95sYdptRtM9MU6B0zWR80cNwzf1CwCn9EvqztlwCj4rzc/" width="320" /></div>I haven't asked anyone to do this - most of the things that happen in our pre-K (Early Years) classes are child-initiated and developed - but A has been spending a lot of time exploring numbers by building cuboids out of Polydron. While others were content to use our pre-existing interlocking cubes, A wanted to make the cubes himself from squares. He makes other things too, like this house with an interesting floor plan:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm2wsUvqhJQoXQwEcjRKylhxJ4jY5njMSERbgPqO_U9bf9_uqp13iEwYjeyIf8FCs5SmSDQTAo7_7a31wlDrQqUoxZcjBCJcA6koraDtnv_QqFzFkJtcPNbvSLnEjlmjTIOBZUcqX1wsw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm2wsUvqhJQoXQwEcjRKylhxJ4jY5njMSERbgPqO_U9bf9_uqp13iEwYjeyIf8FCs5SmSDQTAo7_7a31wlDrQqUoxZcjBCJcA6koraDtnv_QqFzFkJtcPNbvSLnEjlmjTIOBZUcqX1wsw/" width="320" /></a></div>But here's 8 (called 'Octoblock' in Numberblocks), built by A from individual cubes:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje4Tm_vGrDyedGKxeet6QHyv-3rMr1CurEcM6-b5IcZQLg3j_bLVfKBHAn3QWVJwPbNFCAEJhQ0UPOSopnwo0FGWbwzH8HVqNzFuntdo95zTUGhQnCFvKP-nK71BFMx4ORZKkYTujAxI0/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1080" data-original-width="810" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje4Tm_vGrDyedGKxeet6QHyv-3rMr1CurEcM6-b5IcZQLg3j_bLVfKBHAn3QWVJwPbNFCAEJhQ0UPOSopnwo0FGWbwzH8HVqNzFuntdo95zTUGhQnCFvKP-nK71BFMx4ORZKkYTujAxI0/" width="180" /></a></div><div>There is a Numbrblocks episode called Terrible Twos, where 4 splits into two 2s who tickle the other numbers while they sleep which makes them split into ones. Here is A's version in magnetic Polydron, a 4 made of two 2s.</div><div><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPMKjkIT6cpboryQyvSgMIldhbRpq9fZfGxAebnZdaE4nH66XnpoHzjiUGrur7HASzCCPjdw0g6rPSzIiIUlxUWtCwojmbv4xqH7doXIvZuAJOiz9mScRhJbYCkH8y6cCaaDK35qbob14/" width="320" /></div></div>It even comes into his story writing, which is usually about T. rexes and triceratopses:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM42Qo7grAry6aqfHaO8lvQ4hKf-WMYCYmYiW2cHa-J58JTB7EpfXMuAbbO73AM4DwQq5cXmMl9JDZv0L27y4OJSYtstGc3SignDvQSlB1Q5S4uF6Ysf-lylv4-VhAR5tTnZJASuB0nY4/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM42Qo7grAry6aqfHaO8lvQ4hKf-WMYCYmYiW2cHa-J58JTB7EpfXMuAbbO73AM4DwQq5cXmMl9JDZv0L27y4OJSYtstGc3SignDvQSlB1Q5S4uF6Ysf-lylv4-VhAR5tTnZJASuB0nY4/" width="320" /></a></div><div>The building continues:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii5XlMCDbdAJgDqezLXiDVqD74IwPTZNSnJAFV3bLPmFkldD2hOuEnZtFgDxjXuztWSGCJ2RRF7m84KmRSjJZu51uf0MPhmRNtQHFda59U8MRVtUqTvswCtocTZ-2XuvGL1AzQY8q1dlU/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1440" data-original-width="1440" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii5XlMCDbdAJgDqezLXiDVqD74IwPTZNSnJAFV3bLPmFkldD2hOuEnZtFgDxjXuztWSGCJ2RRF7m84KmRSjJZu51uf0MPhmRNtQHFda59U8MRVtUqTvswCtocTZ-2XuvGL1AzQY8q1dlU/" width="240" /></a></div>Recently he's developed an interest in writing. Here he is practicing writing the numbers:</div><div><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="1190" data-original-width="1522" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghvvWkGWGDeflwhnP30cCKfcXp0kQQ_GXd1NlyYhK6ejI03dCDMM9QAnfMhyD1Z8xT-eBWEx1ukX45RN81oL4IMQyzlRc53ioI0jTuBrDqmHw9cXszg0LXN-1uUL_8IpSHdPQy78FAKJw/" width="307" /></div>Children also play with the Numicon and tell me equations. They've heard a lot of these on Numberblocks. Here's one from A:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIXkLFe0qIvgV5bIZbIIiujQj23PDB7Js-XNtRpk-6KTHLnTb-ixKWNS_DLlT9BmUcepF1MLb1tdFz6VTkEcGtIQ3kucqbTULOVau9lhSL-H0w_GV7v1e09cW6HMt_9ab00QNhwXLum-w/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIXkLFe0qIvgV5bIZbIIiujQj23PDB7Js-XNtRpk-6KTHLnTb-ixKWNS_DLlT9BmUcepF1MLb1tdFz6VTkEcGtIQ3kucqbTULOVau9lhSL-H0w_GV7v1e09cW6HMt_9ab00QNhwXLum-w/" width="320" /></a></div>What I really am pleased about is that all this learning is initiated by him (in a climate of appreciation and encouragement of course). It is very much his own and at his pace. I'm pleased that all the four year old students in my class have also found their own different ways to this, enjoying representing numbers and equations. A has also influenced younger students in the class too. T in particular is a real enthusiast for creating the same kind of Polydron 3D numberblocks.</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioXcs5KS4nBvJO3RBgIpNWbFBTMamw_JSMDHt-p3cmoygCkbYfWEsdd7cX-PwrcUnLAtHjTInkBf4ze4ZDMjsm-nnjBm_elAzmAlYlXkOOeK98VjkHaZKn5AcnK9u_fsPx-UffNe51nac/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioXcs5KS4nBvJO3RBgIpNWbFBTMamw_JSMDHt-p3cmoygCkbYfWEsdd7cX-PwrcUnLAtHjTInkBf4ze4ZDMjsm-nnjBm_elAzmAlYlXkOOeK98VjkHaZKn5AcnK9u_fsPx-UffNe51nac/" width="320" /></a></div>As the students do, T told me some equations linked with what he was doing, and then told me a few more he knew:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2HbO4-Xh3nhpcRHPKSKWyYJZ5I437OatffycGTgpZagJ7sQEVBHU_dBAjg_01hKDpRGhwjoumZ2IPd6z5JXNhl8ifH_wacQGnPkipNlckbZY2QlvucqEnClSkbfpAQu5vuE0GwYaVXTc/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2HbO4-Xh3nhpcRHPKSKWyYJZ5I437OatffycGTgpZagJ7sQEVBHU_dBAjg_01hKDpRGhwjoumZ2IPd6z5JXNhl8ifH_wacQGnPkipNlckbZY2QlvucqEnClSkbfpAQu5vuE0GwYaVXTc/" width="320" /></a></div>I think it's from these landmarks that young students begin to build their number sense, so what he's doing seems just right to me.<br /></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-19493372882316616842021-11-20T10:15:00.007-08:002021-11-21T01:00:44.625-08:00Where mathematics comes from<p> At the moment I'm reading a little about materiality in learning - how physical materials and the physical environment and what they can do are a kind of teacher as we interact with them.</p><p>It made me think about how that is true for learning mathematics. In <a href="http://followinglearning.blogspot.com/2021/10/arranging-things.html" target="_blank">my last post</a>, I pondered what young children are learning as they construct a play house out of bricks together and move into it.</p><p>One of my tentative conclusions is that in arranging matter, they are learning to arrange <i>matters </i>in the broadest sense of the word. They are learning what it is to try things out boldly and get results, what it is to work as a team.</p><p>In <a href="http://followinglearning.blogspot.com/2020/02/natural-powers.html" target="_blank">an older post</a>, I thought about the natural powers that students bring into play when they do mathematics. </p>This is from John Mason and Sue Johnston-Wildery:<blockquote>The kinds of powers that are relevant for learning mathematics are ones that learners will have demonstrated by the time they arrive at school. Learners have innate ability to <b>emphasise or stress some features and to ignore others,</b> enabling them to<b> discern similarity and differenc</b>e in many subtle ways. They can also <b>specialise by recognising particular instances of generalisations</b>, and they can <b>generalise from a few specific cases.</b> In addition, they can <b>imagine things</b> and <b>express what they imagine in words, actions or pictures, together with labels or symbols</b>.</blockquote><p>(my emphasis) </p><p>A couple of things about both agency and these natural powers. First, we learn them by exercising them in the world, interacting with people and things, primarily through play. Secondly, they don't serve us only in mathematics, but in all disciplines and areas of life. </p><p>That second point is important I think. The roots of mathematics are much much broader than the 'trunk' - stretching out into all areas of play and interaction. Squashing playdough, spinning round and round, having a conversation, singing a song, jumping in puddles, listening to a story. And not just because these things have elements of geometry, measure, arrangement and number in them, as they often do - but because <i>all </i>our growing powers are needed for the learning of any discipline.</p><p>I often return to this: </p><div class="separator" style="clear: both; text-align: center;"><img border="0" data-original-height="200" data-original-width="144" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMIb1zJ5BKeNfeJCA2PdkWD1FeOTYcHRyqebsr-KPSFtqd0XkOxgJNNd4uVV8YvVrywoLcDpB9lp6xD9eelaQqRE9xdN52B6g1Yn02OMOuicV8TfRUCfZOLgReb6Gluvf3qBRKrjoUfGo/s0/Maryam_Mirzakhani_in_Seoul_2014.jpg" width="144" /></div><a href="https://en.wikipedia.org/wiki/Maryam_Mirzakhani" target="_blank">Maryam Mirzakhani</a>, the first - and only! - woman to win the Fields Medal, only got into mathematics near the end of her schooling:<div><blockquote>"What are some of your earliest memories of mathematics?"</blockquote><blockquote>"As a kid, I dreamt of becoming a writer. My most exciting pastime was reading novels; in fact, I would read anything I could find. I never thought I would pursue mathematics until my last year in high school."</blockquote><p>(from <a href="https://www.theguardian.com/science/2014/aug/13/interview-maryam-mirzakhani-fields-medal-winner-mathematician#" target="_blank">here</a>) </p><p>Could Maryam Mirzakhani's love of reading have supplied important ingredients that later went into her mathematical work? I think so.</p><p>The foundations of our mathematical learning are in all our learning. </p><p>Maybe - and I'm blundering into unfamiliar territory here - this connects with that old chestnut: 'Is mathematics discovered or invented?'</p><p>The question often seems to be answered without thinking of individual development. As if mathematics were a free-standing thing that wasn't created and recreated each time an individual explores and learns about it.</p><p>I want to say that it is very much discovered - in our first steps and first reaching we encounter magnitude. It's in the world that we learn the agency, the natural powers and all the other building blocks of mathematical thinking. It's in how we arrange the bricks in that play house, how we create an inside and outside, how we space the toy cars on top. And in the logic of how one step leads to another. The material of the world is full of the different logics of mathematics. And when we abstract it away from its inception in the physical world, again and again we return to the world at further points - we have already felt the inflection points of a curve when cycling in figures of eight on the tricycle in the playground. We know what a plane is from the many floors we have moved across well before we meet the Cartesian plane. In algebra, we often get a whiff of the idea of magnitude that lies behind the cat's cradle of manipulations we do with symbols.</p><p>And of course mathematics is invented too. The directions we take are ours. They reflect our economies and social structures. Counting for buying and selling and taxes. Measuring for sowing seeds - and taxes. Another planet would have a very different body of mathematics.</p><p>As usual, my ideas around this are half-formed, rough-draft, and probably too briefly expressed. </p><p>Practically, working with 3-4 year olds, I'm confident that all the story reading and writing, all the conversation, all the art work, messy play, construction, games, roleplay, sensory play, small world play - and of course play with mathematically structured materials and moments - is the best thing, not just for learning in general, but for the learning of mathematics too.</p><p></p><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="914" data-original-width="686" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzvdeRTqPt7TeV2jf-jeyyE0bW1g_L_H1Mnght14C0OlUfEiw-1sJICmVcBdg0t0mkJywUaLDjuvDWiF1eBP0gb-wTxcwgxA3_WAM4Q5lyox497a2_pqwU5c0t37cwJXIyShj-7susmbFh/" width="180" /><img alt="" data-original-height="914" data-original-width="686" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqZfwQyrMoxeXATy5B7BrRtCmDcf6AyeLAAFJvp0bA3P26wA4t9kq_GWtDV53zwjJ3Qxd6bEGdmnwHsnmW5d0cpc8EJ_fSPawT8lCseTtClngDpLyOi__wpj1jJWhqMnhMSpfu3blnRlrH/" width="180" /><img alt="" data-original-height="275" data-original-width="206" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDBHtIr297Fd0FBLFHl6DW4B5ijju0wFq_e5oWYgoCM5hU5xUvHSA5K380iv8mRR9Urq_FoxOf2ND3iGC_AwWFcn12PE9RL9-1Wvl0GMYZVp076TVzc1MN2CZveb8Y85jv60yVPozEgmuu/" width="180" /><br /><div class="separator" style="clear: both;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzXsEeuxmYVHNVeoW-JSJ9u8uU_HfuT84hzh6d7GrHDm-p2d6gp9dI8nLL_tnNfZ8MLsDYCCDk_TuVe3K_LdVUWwLaWYir0mUSRrwNgXOr2TC0bRM60brCK-4tk2SIwSPvJ7M3iHf8jgif/" width="320" /></div></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-19917563586690755362021-10-27T02:30:00.000-07:002021-10-27T02:30:57.405-07:00Arranging things<p><span style="font-family: inherit;"><span style="font-size: 11pt; white-space: pre-wrap;">Three of my new students (aged 3 and 4) have been settling in this half term. They have been doing lots of playing alongside each other, but this was one of the first times they cooperated on a common project, building a house.</span></span></p><p><span id="docs-internal-guid-8bc1aa80-7fff-36db-2bec-8d74984488d4"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; height: 329px; overflow: hidden; width: 438px;"><img height="329" src="https://lh6.googleusercontent.com/cABLGbE3b614SMvWExf6HG8ATk2TJEQF9am2CWB_G84Iw5MFE_hyKZ9NzjxKH3OjB72qU9WoSoMVtW3XXZrhQhfv-L51BzU0kTUdz6YGPWC3qkdKIJVGuUomHYsSkR5QMDnQRVvO=s1600" style="margin-left: 0px; margin-top: 0px;" width="438" /></span></span></span></p><p><span id="docs-internal-guid-70f75a33-7fff-4ede-4695-b643954b7019"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">The conversation was in Spanish, so I couldn’t benefit from it. Once it was built, they had encircled themselves and they enjoyed being in the inside they had created and furnished it with sundry items to make it more of a home:</span></span></span></p><p><span id="docs-internal-guid-890296bc-7fff-bf1f-6986-9d60c91c70a0"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="border: none; display: inline-block; height: 331px; overflow: hidden; width: 441px;"><img height="331" src="https://lh4.googleusercontent.com/PRB2O7qZ13Ua0YR0ac5PkElaodkEzMKrnIKnJOZsPxgYRIZmLGMdhhPs8voQKnyT7ZSNoNyQ0AK4F2Cha727Bc9X717-3TscNwI_-mXVm6RfRLrU4dKPz23ZQ3LmFhMc2QKyIyNl=s1600" style="margin-left: 0px; margin-top: 0px;" width="441" /></span></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">Our early years team have been working with <a href="https://twitter.com/AnnevanDam1966" target="_blank">Anne Van Dam</a>, looking at what ‘working theories’ the children are developing in their play. This follows the work of <a href="https://twitter.com/helenhedges6" target="_blank">Helen Hedges</a>. </span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;"></span></span></p><blockquote><span style="font-family: inherit;">“Working theories are present from childhood to adulthood. They represent the tentative, evolving ideas and understandings formulated by children (and adults) as they participate in the life of their families, communities and cultures and engage with others to think, ponder, wonder and make sense of the world in order to participate more effectively within it. Working theories are the result of cognitive inquiry, developed as children theorise about the world and their experiences. They are also the ongoing means of further cognitive development, because children are able to use their existing (albeit limited) understandings to create a framework for making sense of new experiences and ideas.” (Hedges & Jones, quoted <a href="https://www.nzcer.org.nz/system/files/journals/early-childhood-folio/downloads/ECF%202021_1_032_4.pdf" target="_blank">here</a>)</span></blockquote><p><span style="font-family: inherit;"><span style="font-size: 11pt;">This concept of working theories builds on the work of Bruner, <a href="https://twitter.com/GuyClaxton" target="_blank">Claxton</a>, <a href="https://twitter.com/AlisonGopnik" target="_blank">Gopnik</a>, and Vygotsky. It sees children as actively building their understanding through the thinking and play they do. I like it a lot for its respect of children's thinking, seeing the active way in which children make sense of their worlds.</span></span></p><p><span style="font-family: inherit;"><span style="font-size: 11pt;">And yet... there's something in the fit of this to the kind of loose parts play that doesn't feel quite right. I can't put my finger on it exactly...</span></span></p><p><span style="font-family: inherit;"><span style="font-size: 11pt;">If I were to list some of the ideas and understandings that children might be building in this activity, I might say:</span></span></p><p><span style="font-family: inherit;"><span id="docs-internal-guid-3ee0f5b1-7fff-987b-2425-432eb7ecc953"></span></span></p><p></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;"></span></span></p><ul style="margin-bottom: 0px; margin-top: 0px; padding-inline-start: 48px; text-align: left;"><li><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">'I can make friends playing alongside other children'</span></span></li><li><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">'I can get better at communicating by doing it'</span></span></li><li><span style="font-size: 11pt; white-space: pre-wrap;"><span style="font-family: inherit;">‘I can create a new space by enclosing it’</span></span></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘I can align bricks and build them up to a wall’</span></span></p></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘Here is a place that I belong’</span></span></p></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘I can make this place into one I belong in even more’</span></span></p></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘I can build’</span></span></p></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘I can work together with others on a common goal’</span></span></p></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘We can achieve things together, and it feels good’</span></span></p></li><li aria-level="1" style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline; white-space: pre;"><p role="presentation" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">‘We can bring things into our space’</span></span></p></li></ul><div><span style="font-size: 14.6667px; white-space: pre-wrap;"><span style="font-family: inherit;"><br /></span></span></div><div><span id="docs-internal-guid-48198821-7fff-b5e0-e879-c03d47774fbd"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">These are not once-for-all understandings that are achieved and then we move on, but ones that grow and grow through students’ time at school. That enclosing is a schema, ie a repeated behaviour, seems to indicate that the understanding that is built up doing it is something that needs to grow incrementally and be connected with lots of other thoughts and experiences.</span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">The more experienced children in the class seem to have this understanding much more firmly, and to build and create together with so much more ease. </span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But, like so much of children’s play, it doesn’t seem to be directly pursuing a question (like ‘Where do birds sleep?). Outwardly, it’s more directed towards </span><span style="font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">making</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">, </span><span style="font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">production </span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">than it is to </span><span style="font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">finding out</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. They are, ultimately, finding out, but the immediate impulse is one of </span><span style="font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">creation</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. In this way the play seems to have more in common with the arts than with the sciences.</span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">This is a thought that I’m still mulling over.</span></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixoT_DRDxPN38SB1m1hozGa4qqhihIHZc9vF7hbSmjRgZewdKetKAH6wGyI8Fhebdr4eOInF9NhlklxD3kPYB3L8cPsAIjUQ67_Rv-ibyXJpvInnGRv26l5erfB_D8Fd2dac9C3CbJ7Mo/s554/theories.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="162" data-original-width="554" height="188" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixoT_DRDxPN38SB1m1hozGa4qqhihIHZc9vF7hbSmjRgZewdKetKAH6wGyI8Fhebdr4eOInF9NhlklxD3kPYB3L8cPsAIjUQ67_Rv-ibyXJpvInnGRv26l5erfB_D8Fd2dac9C3CbJ7Mo/w640-h188/theories.png" width="640" /></a></div><span id="docs-internal-guid-4ba48855-7fff-1ce6-4333-65df81336a22"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">And now this sketchy diagram that I’ve drawn is making me think. The impulse to create, to make, to perform, to challenge oneself allows a feedback loop. It puts the results of our action (beige in the diagram) into the world as something that we can observe. A kind of design cycle. We are building up theories about the kinds of achievements we can have in the world.</span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Helen Hedges </span><a href="https://www.tandfonline.com/doi/full/10.1080/03004430.2020.1849169" style="text-decoration-line: none;"><span style="color: #1155cc; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">writes </span></a><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">‘Learning may appear somewhat disorganized, perhaps appear to move around and then return later to topics, questions and ideas, may call on invention and imagination to connect ideas…’</span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">To me, most learning is disorganised, full of imagination and invention. So much of learning, of building theories, is devoted not to how the physical world works or even to social and cultural learning considered as learning what’s already there. A huge amount of learning seems devoted to managing possibility. I have these materials - what could I do with them? How might I deploy them, arrange them? I have this time with my friend? How might I fill it? I’ll learn to wildly invent, to put some unheard-of combination boldly into place - and I’ll see what happens then.</span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">New Zealand’s </span><a href="https://www.education.govt.nz/assets/Uploads/Te-Whariki-Early-Childhood-Curriculum-04-11-low-res.pdf" style="text-decoration-line: none;"><span style="color: #1155cc; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">Te Whāriki Early Childhood Curriculum</span></a><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> has a section called Learning Dispositions and Working Theories. “Dispositions that can be useful for learning include playfulness, whakatoi (daring), persistence, resilience and imagination. Children also develop dispositions towards domain knowledge…”</span></span></p><span style="font-family: inherit;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">What I’m trying to get a grip on doesn’t seem to simply reduce to dispositions though. It is a more disorganised-seeming, less direct way of obtaining knowledge about what daring and playfulness can achieve, what can be done with freedom and within necessity, how the social and physical environment can be remixed. It centres around agency, and uses whatever is at hand to achieve its undefined aims. It achieves its goal of developing capable and skillful being and making in the physical and social world, but its means are more indirect than what comes to mind when we think of theory-building: curiosity -> question -> search -> answers.</span></span></p><div><br /></div><div>This simple house the children make seems to bring so many aspects of learning together. Mathematics is in there too. The straight line of the bricks, the way they are placed in the same orientation, and on top of each other to create layers. The way the lines of bricks are parallel to create the rectangular floor plan, and how the cars are arranged, spaced out evenly.</div><div><br /></div><div>That word arrange. It means both to place things by some kind of design, and also, metaphorically I suppose, though we're no longer conscious of any metaphor, to organise <i>anything</i> in life. </div><div><br /></div><div>Maybe the play follows a similar path to the way the word has travelled? We play at organising loose parts, we learn, ultimately, to organise our lives, whatever the variables it gives us.</div><div><br /></div></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: inherit;">And now I'm curi</span>ous what <a href="https://www.etymonline.com/word/arrange" target="_blank">the roots of that word <i>arrange</i> are</a>:</p></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzqOqZ9di6rSq7tIz0yvItNED69NPpEBEqVpW3zwN9Au7CBOSaSsGfzpRr2f3vfaVCcKKDA9_4TG4hcjZKBEGVSv7bnrnNssiiSgxTEUHWC7gxOYYhUM8OhevLez0oivGcsMWX4Qhn5jw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="451" data-original-width="1845" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzqOqZ9di6rSq7tIz0yvItNED69NPpEBEqVpW3zwN9Au7CBOSaSsGfzpRr2f3vfaVCcKKDA9_4TG4hcjZKBEGVSv7bnrnNssiiSgxTEUHWC7gxOYYhUM8OhevLez0oivGcsMWX4Qhn5jw/w640-h156/image.png" width="640" /></a></div><p>Ah - putting something in a ring. And there's the word rank, like ranks of soldiers.<br /></p><p>It's always fascinating to see the <a href="https://www.etymonline.com/word/*sker-?ref=etymonline_crossreference#etymonline_v_52738" target="_blank">proposed Proto-Indo-European root </a>of a word, and all the offshoots of that:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwpKdqbXrcqmmwi3GKZDFxzyNyakx2Uui-AQSx4UeRvhA_icAxi6qTTQZ44cKgz6Dkmgr2kclkVArB4QjyElK1jPN7VN3lq5DdfiK0o8zGxYEkjCJ3Yl0I9lZaj_CGQ9naxdtLB7Q915g/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="868" data-original-width="1860" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwpKdqbXrcqmmwi3GKZDFxzyNyakx2Uui-AQSx4UeRvhA_icAxi6qTTQZ44cKgz6Dkmgr2kclkVArB4QjyElK1jPN7VN3lq5DdfiK0o8zGxYEkjCJ3Yl0I9lZaj_CGQ9naxdtLB7Q915g/w640-h298/image.png" width="640" /></a></div><p>I find this nexus of related words more than interesting. It's almost as if play recapitulates etymology. We <b><span style="color: #660000;">encircle</span></b> ourselves with loose parts, we line them up in <b><span style="color: #660000;">ranks</span></b>, and doing this we are <b><span style="color: #660000;">researching</span></b>, building working theories about our own agency, our abilities to work with others to build a home, our abilities to <b><span style="color: #660000;">arrange</span></b> matter and matters.</p><p><br /></p><p>(Adapted from notes we each made for our work with Anne Van Dam)<br /></p>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com1tag:blogger.com,1999:blog-3071719252136968205.post-14966446292035173142021-09-14T10:06:00.001-07:002021-09-14T10:06:33.434-07:00Numberblocks<p>In PK, we've been watching the first two series of <a href="https://twitter.com/numberblocks" target="_blank">Numberblocks</a>. These present the numbers zero to ten as different characters who, by the normal rules of arithmetic portrayed dramatically, have the power to transform into one another.</p><p></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="1365" data-original-width="2048" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiewcefFsSZqBgYc4470o1fUPf42hMONy7zJpByjlCIEKXfxl5OqmrdL7wTnzjeLzpokv8qycuPzo2ROdnrZCayZWWi6hvUhkDiX9ZVdSg5z4O_93I3IHe8g5TMawLRle4F2y7vAd0O3rA/" width="320" /></div></div><p>If you're not familiar with Numberblocks, you could watch the first two minutes of this video. (You don't get full episodes on Youtube, you get composites of a number of episodes. We've watched Series 1 and 2 on DVD and on Netflix.)</p><p>
<iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="393" src="https://www.youtube.com/embed/aowUthHmXUM" title="YouTube video player" width="699"></iframe>
<br /></p><p>What do I like so much about it?</p><p style="text-align: left;"></p>Our young three to five-year old children like it so much, want to watch episodes again and again, go home and watch further episodes.<div><br />Numbers are represented as arrangement of cubes. All sorts of things become clear like this. Number as area. Addition as combining, subtraction as splitting. Odd and even-ness à la Numicon. Square numbers. Arrays of numbers. All sorts of interesting avenues for investigation are opened up. For instance in the clip above, the numbers are represented as different polyominoes, different arrangements of squares. What tetrominoes are possible? I'm a fan of figurate numbers, of area-as-number (have I talked to you about Cuisenaire?) because I find it gives children a powerful way into number and arithmetic.</div><div><br />Numbers as character and narrative. We all love a story, and the Numberblocks stories are well thought out and entertaining. They also work <i>because of </i>the mathematics. Again, in the Strampolines episode, the story is about what different arrangements are possible. 'One' is sad because she can only make one arrangement, but is cheered up when she learns that copies of herself make up every arrangement (<a href="https://mathmunch.files.wordpress.com/2015/08/moves-proposal.pdf" target="_blank">polyomino factorisation </a>anyone?). </div><div><br /></div><div>The animation and the music. Yes, we sing along to the songs!</div><div><br />The equations that emerge as numbers transform are represented flexibly. So we don't just see 4+1=5, we see 5=4+1, and also 5-1=4. Children get a sense of what equality means, and they also begin to see how equations relate to arithmetic before having to write them themselves. Often they want to write equations, and it's something we've built on to give the power that writing ones own ideas brings.</div><div><br /><div style="text-align: center;"><img alt="" data-original-height="1500" data-original-width="2000" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIfx63n_Py55MpeiWPsDFAwdO76vETUT79nnDPiEi1UjOjAE3ZfzAdVbszYayGm66x8VnLCR6nKhXY_8IL07Vmb7ueaE8dyaPzEKrP7Dk_z5ZXkNfjTUgXEU5EvVMf8IN_Bjq8BDzTN7o/" width="320" /></div>Students enjoy recreating and exploring what they watch. Here, for instance, a four-year old student observed that 25 is a square.<br /><div style="text-align: center;"><img alt="" data-original-height="1247" data-original-width="1662" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO0Bf4KTDZr7f2opuX36c1J_-94h57nhUIUYdLv4Fproj6seeMw7VJVyg5o_bZanqE7Ewhoyi2quP6erg8tAbj8VfKp6aP8RnI4tH-atlNdqL3zTlNNVxi6glu709IDZLBL6qY0I1zKsM/" width="320" /></div>I pointed out that there seems to be one missing, and he had a good think about that:<br /><div style="text-align: center;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxPY5LJC66Q_bQJVFt4F7EYNgTSxXplxr_AB39Kcx1lcmp3sRFhSFOSaMk5w0W30CVADsaHyK1gOSVKpBtSMKeIWOm1pcI7qFhItaVajhB_PElvQAlbMGqKYpbcDbyxLGNOnWJwEekdpU/" width="320" /></div>One piece of evidence about how well it's worked for the students, is doing 'Number of the Day' with them on the first day of their next year in Kindergarten. I've been able to pop in and work with them on this. In the past, students have been a bit blank when we've asked them what they know about 1, or have commented on what its shape makes them think of, but this year there were equations.<br /><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLJ2-hWgPlvLyUEJ-brh9V1_UgC3gdZnoljXenZVVxzTmbC2rr3i0FH6_APlb55TlAOpGO_uQ1_zf8NORyDvlMg7PM0PTJ_YbK65fvnpJ48UklT7KJnhjv3L26AxikSEFxYFRd3mjR7oQ/s800/number+of+the+day_1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="373" data-original-width="800" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLJ2-hWgPlvLyUEJ-brh9V1_UgC3gdZnoljXenZVVxzTmbC2rr3i0FH6_APlb55TlAOpGO_uQ1_zf8NORyDvlMg7PM0PTJ_YbK65fvnpJ48UklT7KJnhjv3L26AxikSEFxYFRd3mjR7oQ/w400-h186/number+of+the+day_1.png" width="400" /></a></div>By day eight, with a bit of help from Cuisenaire rods, the equations were really flowing.<br /><div style="text-align: center;"><img alt="" data-original-height="914" data-original-width="1214" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3j5ya5ovpc6U2CnvraXy9pXHvdi7uCgZGGOAVZihmXDiV2-2Gl4ENJnEBwRz-amKS3JwSbI0X2t9oBm6bMWvuwzUtVh92kuBwQiMeBOzF4zgJ0jU084pmN5gDSFrr_xP0Sd30wb6357U/" width="319" /></div>And here are the day 9, here are lots of the ideas the Kindergarten students shared:<div><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="470" data-original-width="960" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8CG1yzZi0T_SlaHv4aXvHWYovtDZUtebbSbb6y1q4jNmysZNjrBGagfdT-JahiE9GJ7Sr2rNnFOumUMgK3uvy025_AWargTcHUJFcG8i7UbP83m3_hzUCTqsQsmK9oGIbKA4RDbY3QWw/w640-h314/image.png" width="640" /></div><div class="separator" style="clear: both; text-align: left;">So, a big thank you to the Numberblocks team, and also to <a href="https://twitter.com/ThinkingMaths" target="_blank">Debbie Morgan</a> who has been their chief mathematical advisor.</div></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-54505913810664814242021-08-01T00:52:00.002-07:002021-08-01T01:06:12.136-07:00Sleeper effects<p>There are two studies I keep thinking about. Both involve large numbers of students. Both concern 'sleeper effects' - effects that don't appear straight away, but emerge later.</p><p style="text-align: center;">😴</p><p>The first is a study in Boston Massachusetts, and I heard about it via <a href="https://twitter.com/AlisonGopnik" target="_blank">Alison Gopnik</a>. Public preschools had been made available to everyone, but there was such demand that places had to be decided by lottery. Effectively this produced a very large randomised trial, involving more than 4000 students.</p><div style="text-align: left;"><span style="background-color: #fafafa; font-family: inherit;">The study, <a href="https://seii.mit.edu/research/study/the-long-term-effects-of-universal-preschool-in-boston/" target="_blank">The Long-Term Effects of Universal Preschool in Boston</a>, produced some very interesting results. Preschool attendance did not improve test scores in elementary school. It did however have a sleeper effect that emerged later in high school. More students who'd been to preschool finished high school, and more went on to college.</span></div><p><span style="background-color: #fafafa;"></span></p><div class="separator" style="clear: both;"><div class="separator" style="clear: both; font-family: Georgia, serif; font-size: 15px; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh1Rg71sySFk3-rNexLtptAuAiFjjq44w8yZpCjJSTdoFl22cFZ6qE67y4lFZZYZmkjj3pEXVwxi-XWDbPOnE4_jWyn7nrqWVbuvSoie7G0ncKlB0BkQJ-YBMQ8uFjhcn1aGv7ZHD4YaU/s960/boston+study+fig+1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="960" data-original-width="951" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh1Rg71sySFk3-rNexLtptAuAiFjjq44w8yZpCjJSTdoFl22cFZ6qE67y4lFZZYZmkjj3pEXVwxi-XWDbPOnE4_jWyn7nrqWVbuvSoie7G0ncKlB0BkQJ-YBMQ8uFjhcn1aGv7ZHD4YaU/w396-h400/boston+study+fig+1.png" width="396" /></a></div><div style="text-align: left;"><span style="font-family: Georgia, serif; font-size: 15px;">That's fascinating, isn't it? Four-year olds going to preschool didn't effect their test scores in the immediate years following, but it did have a significant positive effect much later. </span></div><div style="text-align: left;"><br /></div><div style="text-align: left;">What would be your guess about how this works?</div><div style="text-align: left;"><br /></div><div style="text-align: center;">😴</div><div style="text-align: left;"><br /></div><div style="text-align: left;">The second study was conducted with an even larger number of students, more than 12,000 this time. They are at the other end of their formal education, at a four-year college. <a href="https://twitter.com/profkeithdevlin" target="_blank">Keith Devlin</a> writes about it in <a href="https://sumop.org/2019/09/27/why-straight-as-may-lead-to-poor-learning-report-from-an-unusual-study/" target="_blank">this piece</a>, </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Students are randomly assigned to different teachers, and their test results are collected over a long period of time. There are two really interesting results, and I'll just touch on one of them here.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">As Devlin puts it:</div><blockquote>But here is the first surprising result. Students of professors who as a group perform well in the initial mathematics course perform significantly worse in the (mandatory) follow-on related math, science, and engineering courses. For math and science courses, academic rank, teaching experience, and terminal degree status of professors are negatively correlated with contemporaneous student achievement, but positively related to follow-on course achievement. That is, students of less experienced instructors who do not possess terminal degrees perform better in the contemporaneous course being taught, but perform worse in the follow-on related courses. </blockquote><div style="text-align: left;">Or, in <a href="http://faculty.econ.ucdavis.edu/faculty/scarrell/profqual2.pdf" target="_blank">the words of the authors of the study</a>:</div><div style="text-align: left;"><blockquote>We find that less experienced and less qualified professors produce
students who perform significantly better in the contemporaneous
course being taught, whereas more experienced and highly qualified
professors produce students who perform better in the follow-on related
curriculum.</blockquote></div><div style="text-align: left;">Isn't that interesting! Students of more experienced and better qualified teachers get poorer test results that year - - - but better results in subsequent years!</div><div style="text-align: left;"><br /></div><div style="text-align: left;">What a fascinating sleeper effect! What would be your guess at an explanation for that?</div><div style="text-align: left;"><br /></div><div class="separator" style="clear: both; font-family: Georgia, serif; font-size: 15px; text-align: center;">😴</div></div><br /><p></p>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-47839004302442259822021-07-31T07:26:00.004-07:002021-07-31T07:26:33.929-07:00Copycats<p>As an EY team we look back at 'Moments in the Day' together - times when something in the children's play and learning strikes us. We share documentation and discuss. In our last time doing this in the school year, Estelle shared this photo with us:</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAa4vjukJhr85z1Cm9gBEZOQv4j1xGGNymUN5xVgwo9_7BpvqcC4fn5_vCoQ_xJRxsoTx3P3P_eV1aRpL_1Iyn0lmPd0p1z4hCrDIl_lSBDzBgHpwerrVMRoZ3dOXj5IdbfKQs-EbH0rsU/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="614" data-original-width="856" height="230" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAa4vjukJhr85z1Cm9gBEZOQv4j1xGGNymUN5xVgwo9_7BpvqcC4fn5_vCoQ_xJRxsoTx3P3P_eV1aRpL_1Iyn0lmPd0p1z4hCrDIl_lSBDzBgHpwerrVMRoZ3dOXj5IdbfKQs-EbH0rsU/" width="320" /></a></div><p></p><p></p><div>She wrote:<br /><i></i></div><blockquote><div><i>I’m still puzzled about this activity that S., G. and M. engage in regularly.<br /><br />It is often initiated by M. but not always (I think). I’m not sure I’ve watched closely enough at the right moment. I wonder what skills they are using here and that makes me think that I almost need to try it myself to find out. Perhaps they will allow me to quietly join in…. Otherwise I could have a conversation with them.<br /><br />There is definitely a quality to this play that is ‘safe’, mindful and we can assume that it is good for their well-being based on the repetition. Maybe for the artist no. 1 there is a feeling of being the leader, being ‘seen’ and valued. For artist no. 2 perhaps the feeling of making a connection in this way has meaning.</i></div><div><i><br />Perhaps I can join in and see what is happening; it all happens so fast.</i></div></blockquote><div>I've notice<span>d children doing things in unison a lot too, and I'm interested. What do we derive from this? </span></div><div><span><br /></span></div><div><span>As teachers, we think of our jobs as being about building individual creativity, individual agency, so where does this leading and following, this doing (almost) the same thing fit in?<br /><br />Questions like this are quite hard to get a handle on. We have hunches, but they don't feel like the complete story.<br /><br />Perhaps we should take up Estelle's suggestion and just draw the same thing together, and see what it feels like 'from the inside'. There's no guarantee that we'll feel the same as the students do of course, but it might help.<br /><br />What else does copying look like in our classes?<br /><br /></span></div><div><span>Here's some more examples.</span></div><div><span><br /></span></div><div>At a certain count, friends are jumping off chairs in unison:</div><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="914" data-original-width="686" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYTV8VuJjg_se3IokW7o9wo5cSOEZtvJDRs3PjNPBiZCTLHZl0gTeRHzADelCJsYn0smPhmeDcrL51kpcCJJb8WdOxKW_Cq8dCXucHfkfrk65Ud1a44DubO3ckaxkmzsXi8MgpJmPMj0yV/" width="180" /></div><span>Pairs of students making the same as - or here, the reflection of - each other's designs with the square tiles in trays:<div><span style="font-family: Arial;"><span style="font-size: 14.6667px; white-space: pre-wrap;"><i><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="676" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrY5v_OTMqBDui5c-E3geeYMqJxRgqctGsCS9ci2BLIlcVt8e_RmH18n5vMQ3FBBzv0Qhyphenhyphens7Ff9RFXndmus7N6csI7hAF1BDIJD1Nh70mFU9mz1F1IZ-QZgAGa6k6qaXPG948HpR8QYh9W/" width="320" /></div></i></span></span></div></span><div style="text-align: center;">We're at the pattern block table and a student says. 'Simon, let's play I make something and you copy it.<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPaSOZh1NUI2iYt4OSgAgFUeltYUFAH7Bqq2z0MxF11KVioQFmoyJZhvPCIMe-CCY5ngEd1ctYM44WUpni_361EetSQhyphenhyphenfavjktsu8Pi_guhVs1eI4j-Xl3BBzirCDaelvuzm5_V2W-A8U/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="680" data-original-width="510" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPaSOZh1NUI2iYt4OSgAgFUeltYUFAH7Bqq2z0MxF11KVioQFmoyJZhvPCIMe-CCY5ngEd1ctYM44WUpni_361EetSQhyphenhyphenfavjktsu8Pi_guhVs1eI4j-Xl3BBzirCDaelvuzm5_V2W-A8U/" width="180" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><img alt="" data-original-height="680" data-original-width="510" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc3nyXLzpRLPMSZfFCZ78YzD4FgWBt6lhFI0NZGXbcpuuDfgCVFFshYx7ySCAj021OnL-6nH3qFz4xHmvh4F7usbg_Xw-OhP9yoca_AUKCCwn_-02EUIy5cWVNjDbYQ81M4bD1Nf7utELC/" width="180" /></div><div style="text-align: left;">Using large foam pattern blocks to make rockets together:</div></div><div class="separator" style="clear: both; text-align: center;"><img alt="" data-original-height="675" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoSw0xm3O5uZVfalnDVanB0lHwMhuV6M1CaeVMOud-3UgLJq15ft1wIaDzj1tqzDMUvj9CYj-cOatMLn9q9q9-ZiR35NWp2pXIos09wTqtmkqaGgqSw7MFKIGzNo4AgrWkX_ESbBucPz-4/" width="320" /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhroY4F5ABBlb0QiQu1kocvu0hFWJxRsfRoFgs0TX9CqvAI5Zd83yzvM0rTboMIYfa-ksnmlrNYudQfzHNlnSa62F7kPv41TYFeyBwTyLdNxXoWGbMIe8ajonAyeJp5yJlUScShiUqrjhwK/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="675" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhroY4F5ABBlb0QiQu1kocvu0hFWJxRsfRoFgs0TX9CqvAI5Zd83yzvM0rTboMIYfa-ksnmlrNYudQfzHNlnSa62F7kPv41TYFeyBwTyLdNxXoWGbMIe8ajonAyeJp5yJlUScShiUqrjhwK/" width="320" /></a></div>Painting together:</div><div style="text-align: center;"><img alt="" data-original-height="830" data-original-width="946" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8RhKAZOm2aWJaWTcPODCCdmrwzPSyRvMBxMFWzWH1774wKODXVKxx4BXCDLD6acgK0YfThf-HxuHkChe-q-73Ay14vXIDCqcxCr7maxJtyumWf_dp3eoFD0-hGyZUbNBrgUGNT64PkEkN/" width="274" /></div><div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvPSz_yRVXKRmRRaHcjWLz8aMERtdg2yitomaVTgXHHNFEoWLyH_fGaHkXxPlEZdNlVK1Lv6fT6ENcFhL9lnPbFgbvyqFZha9HNkTiQVK3wberuli0RSIw_XNyPSa_T-TgQ7HjP4a5kz1T/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="914" data-original-width="1218" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvPSz_yRVXKRmRRaHcjWLz8aMERtdg2yitomaVTgXHHNFEoWLyH_fGaHkXxPlEZdNlVK1Lv6fT6ENcFhL9lnPbFgbvyqFZha9HNkTiQVK3wberuli0RSIw_XNyPSa_T-TgQ7HjP4a5kz1T/" width="320" /></a></div></div><div class="separator" style="clear: both;">Tap-a-shape:</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOBh8NY08qHSSvgNY8wZS9fSxiO_Nlm2DVbf-ZJ8YcYNOnDIUxu_Kt7OruQgYLFDWrRTZXZ7um8jC5A-AxspNTIxpeLL3aOB7wQFoKz4vVuXXmyipegGpMTWQXFWRL4ia_T8MBLsl21QeP/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="860" data-original-width="1134" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOBh8NY08qHSSvgNY8wZS9fSxiO_Nlm2DVbf-ZJ8YcYNOnDIUxu_Kt7OruQgYLFDWrRTZXZ7um8jC5A-AxspNTIxpeLL3aOB7wQFoKz4vVuXXmyipegGpMTWQXFWRL4ia_T8MBLsl21QeP/" width="316" /></a></div><div style="text-align: left;">And of course, the <a href="https://playandpk.blogspot.com/2021/06/wild-things-in-forest.html" target="_blank">playing music in unison in the forest in the previous blog post</a>.</div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5aSptBS7y1HVAn0nGJm6mi9odSOsgfQeKCSanqsRda8sNIR7r5q_jqNCYn19lWmV6LGjMvMGBFIeOfLIHDZzFDSffQE42JXwxCILVfYdLVuDHZLqYNC5OUGG-CSBQohtZZp6kNFyDhvIq/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="249" data-original-width="332" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5aSptBS7y1HVAn0nGJm6mi9odSOsgfQeKCSanqsRda8sNIR7r5q_jqNCYn19lWmV6LGjMvMGBFIeOfLIHDZzFDSffQE42JXwxCILVfYdLVuDHZLqYNC5OUGG-CSBQohtZZp6kNFyDhvIq/" width="320" /></a></div><br /></div></div>So what's going on?</div><div><br /></div><div>I can't say, but there are certain things I sense might be going on. This passage from Sloman and Fernback's <i>The Knowledge Illusion</i> might help orient us:</div><div><p></p><p></p><blockquote><p>Sharing attention is a crucial step on the road to being a full collaborator in a group sharing cognitive labor, in a community of knowledge. Once we can share attention, we can do something even more impressive—we can share common ground. We know some things that we know others know, and we know that they know that we know (and of course we know that they know that we know that they know, etc.). The knowledge is not just distributed; it is shared. Once knowledge is shared in this way, we can share intentionality; we can jointly pursue a common goal. A basic human talent is to share intentions with others so that we accomplish things collaboratively.</p></blockquote>Let's make a list of some of the things happening: </div><div><ul><li>Feeling comfortable with each other,</li><li>Feeling comfortable with an activity,</li><li>Being in the same space with each other,</li><li>Somehow having an idea of doing things in unison,</li><li>Understanding the proposal,</li><li>Accepting the idea together, sharing the intention, having a joint project,</li><li>One leading, other(s) following (how flexible is this?),</li><li>Monitoring each other's actions,</li><li>Recreating each other's creation,</li><li>Comparing the results,</li><li>Completing the project.</li></ul></div><div>That's part of what happens, and it's a lot. But there's also the significance. What does it mean to do the same thing together? </div><div><br /></div><div>That time the children synchronised themselves jumping off the chairs, was such a moment of joy. It seemed like a celebration of friendship and of feeling great in their bodies, in the classroom and together! Not all the examples are so exuberant, but there's a pleasure and significance in not just being in the same place and time, but in the same self-chosen project.</div><div><br /></div><div>As an adult, I can appreciate this too. In fact, teaching together with the PK team, we plan our activities together. We then, mostly, work in our separate places. But there's a tremendous affirmation in having the same understandings and objectives, in approving of the same resources, environment, activities. And, of course, bringing our stories of what happened back to each other. Our work together is so intertwined that what we do with our students isn't usually the idea of any one of us, it's a kind of team thing.</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLrzmpwL_Hvw-edlIVAJ-f29aqJykw2tKauS3lDFaQOzk8qYXpXtfRwm2eOo-Aor7UOb3F27Q06J6PiOREoIMZFZ9NuJK_qPFsmax0Pv0K53wN7h5CF24LqJAXyN-52S7yt7U0r-hzyJFP/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="770" data-original-width="678" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLrzmpwL_Hvw-edlIVAJ-f29aqJykw2tKauS3lDFaQOzk8qYXpXtfRwm2eOo-Aor7UOb3F27Q06J6PiOREoIMZFZ9NuJK_qPFsmax0Pv0K53wN7h5CF24LqJAXyN-52S7yt7U0r-hzyJFP/" width="211" /></a></div>Then there's singing Beatles songs with friends. We're not exactly doing the same thing: one of us plays piano, another guitar, another ukulele, but mostly we sing the same melody and words. What is it that's so satisfying about it? There's something in there about the whole being more than the sum of the parts.</div><div><br /></div><div><br /></div>In our 'Moments' meeting, Nick mentioned that humans succeeded where Neanderthals didn’t because they shared ideas; they didn’t have bigger brains, it was just that they shared their ideas.This is part of what it is to be human, and what has given us our success.<div> </div><div>I first came across this idea in Rutger Bregman's great book <i>Humankind</i>. Bregman has this chart:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0x8BtVVx9x1h_zh_3GDpyg7HNBmp41yZLQtYVUHM_hQJdtJ6_YqHXRNvgIuRMq8XDu-Ob32inkbVEIoqppJmVsHzi9PPGNxLJ5GpJjUhEEf-WTUjAIyVtstNL4_NrCZwawkG_U89_7xay/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="828" data-original-width="1080" height="491" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0x8BtVVx9x1h_zh_3GDpyg7HNBmp41yZLQtYVUHM_hQJdtJ6_YqHXRNvgIuRMq8XDu-Ob32inkbVEIoqppJmVsHzi9PPGNxLJ5GpJjUhEEf-WTUjAIyVtstNL4_NrCZwawkG_U89_7xay/w640-h491/image.png" width="640" /></a></div>Following anthropologist Joseph Henrich's modeling, Bregman invites us to think of a planet with two tribes. One tribe, the Geniuses, are great at inventing things, but not so good at sharing their ideas; the other, the Copycats are not such great inventors, but do share. The Geniuses are a hundred times better at inventing. The Copycats on the other hand are ten times better at sharing. Which tribe do inventions spread through most?</div><div><br /></div><div>The Copycats. <br /></div><div><br /></div><div>So, I'm coming round to valuing these times when children get into total synch with each other.</div><div><br />And next year, I'm going to copy Estelle's idea, and try to catch more of what is happening as children copy each other. </div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-10880608389374883502021-04-23T12:21:00.003-07:002021-04-23T12:22:38.882-07:00Rulers<p>Dan Meyer tweeted </p><blockquote class="twitter-tweet"><p dir="ltr" lang="en">My toddlers are convinced that as they get older they'll get bigger (true) and that I'll get smaller and turn into a baby (mostly false). They talk about taking care of me when I'm a baby. I'm in no hurry to correct any of this.</p>— Dan Meyer (@ddmeyer) <a href="https://twitter.com/ddmeyer/status/1385341174471266307?ref_src=twsrc%5Etfw">April 22, 2021</a></blockquote><p>and Kassia tweeted:</p>
<blockquote class="twitter-tweet"><p dir="ltr" lang="en">At 4, my son told me he had figured out “why oceans have big waves.” “Whales jumping!” Its was such a lovely theory I couldn’t correct it. My first mom (on on better days, teacher) move for wrong theories is to say nothing. Which is not the same as doing nothing.</p>— Kassia Wedekind (@kassiaowedekind) <a href="https://twitter.com/kassiaowedekind/status/1385361676724211713?ref_src=twsrc%5Etfw">April 22, 2021</a></blockquote><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMxf8flqgb6ck1k2Ll4gHtEQLUvaIDCd0Qo2KMoiF8Wnp2gFy4EId8yu5eZCnS57OG98JgkL9ndgNXIG39C3yIWngdKn1MkCYe0EwJg7CphVJkevWv3L0JzCW_1SI6gaomZGe1UdaSpDc/s340/Wally-s-Stories.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="340" data-original-width="340" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMxf8flqgb6ck1k2Ll4gHtEQLUvaIDCd0Qo2KMoiF8Wnp2gFy4EId8yu5eZCnS57OG98JgkL9ndgNXIG39C3yIWngdKn1MkCYe0EwJg7CphVJkevWv3L0JzCW_1SI6gaomZGe1UdaSpDc/s320/Wally-s-Stories.jpg" /></a></div>And I have just read this in <i>Wally's Stories: Conversations in the Kindergarten</i> by Vivian Gussin Paley . It's a lovely example of how Paley is able to write against herself, to document her growing points as a teacher, alongside the learning of the children:<p></p><p><b><i>Rulers</i></b></p><p>Rulers were another example of the wide gulf separating my
beliefs from those the children demonstrated whenever they
were allowed to follow their ideas to logical conclusions. I
had not realized that "rulers are not really real." We were
about to act out "Jack and the Beanstalk" when Wally and
Eddie disagreed about the relative size of our two rugs.</p><p></p><p>Wally: The big rug is the giant's castle. The
small one is Jack's house. </p><p>Eddie: Both rugs are the same. </p><p>Wally: They can't be the same. Watch me. I'll
walk around the rug. Now watch: walk, walk, walk, walk, walk, walk,
walk, walk, walk - count all these
walks. Okay. Now count the other rug.
Walk, walk, walk, walk, walk. See?
That one has more walks. </p><p>Eddie: No fair. You cheated. You walked
faster. </p><p>Wally: I don't have to walk. I can just look.</p><p>Eddie: I can look too. But you have to measure it. You need a ruler. About six
hundred inches or feet.</p><p>Wally: We have a ruler.</p><p>Eddie: Not that one. Not the short kind. You
have to use the long kind that gets
curled up in a box.</p><p>Wally: Use people. People's bodies. Lying
down in a row.</p><p>Eddie: That's a great idea. I never even
thought of that.</p><p>Wally announces a try-out for "rug measurers." He adds
one child at a time until both rugs are covered-four children
end to end on one rug and three on the other. Everyone is
satisfied, and the play continues with Wally as the giant on
the rug henceforth known as the four-person rug. The next
day Eddie measures the rugs again. He uses himself, Wally,
and two other childen. But this time they do not cover the
rug.</p><p>Wally: You're too short. I mean someone is
too short. We need Warren. Where's
Warren?</p><p>Teacher: He's not here today.</p><p>Eddie: Then we can't measure the rug.</p><p>Teacher: You can only measure the rug when
Warren is here?</p><p>Jill: Because he's longer.</p><p>Deana: Turn everyone around. Then it will fit.</p><p>(Eddie rearranges the measurers so that each is now
in a different position. Their total length is the
same.)</p><p>Eddie: No, it won't work. We have to wait for
Warren.</p><p>Deana: Let me have a turn. I can do it.</p><p>Jill: You're too big, Deana. Look at your
feet sticking out. Here's a rule. Nobody
bigger than Warren can measure the
rug.</p><p>Fred: Wait. Just change Ellen and Deana
because Ellen is shorter.</p><p>Jill: She sticks out just the same. Wait for
Warren.</p><p>Fred: Now she's longer than before, that's
why.</p><p>Teacher: Is there a way to measure the rug so we
don't have to worry about people's
sizes?</p><p>Kenny: Use short people.</p><p>Teacher: And if the short people aren't in
school?</p><p>Rose: Use big people.</p><p>Eddie: Some people are too big.</p><p>Teacher: Maybe using people is a problem.</p><p>Fred: Use three-year-olds.</p><p>Teacher: There aren't any three-year-olds in our
class.</p><p>Deana: Use rulers. Get all the rulers in the
room. I'll get the box of rulers.</p><p>Eddie: That was my idea, you know.</p><p>Deana: This isn't enough rulers.</p><p>Eddie: Put a short, short person after the
rulers - Andy.</p><p>Andy: I'm not short, short. And I'm not playing this game.</p><p>Wally: Use the dolls.</p><p>Teacher: So this rug is ten rulers and two dolls
long? (Silence.) Here's something we
can do. We can use one of the rulers
over again, this way.</p><p>Eddie: Now you made another empty space.</p><p>Teacher: Eddie, you mentioned a tape measure
before. I have one here.</p><p>(We stretch the tape along the edge of the rug, and
I show the children that the rug is 156 inches long.
The lesson is done. The next day Warren is back in
school.)</p><p>Wally: Here's Warren. Now we can really measure the rug.</p><p>Teacher: Didn't we really measure the rug with
the ruler?</p><p>Wally: Well, rulers aren't really real, are
they?</p><p><br /></p><p>I recognise this kind of thing from my own teaching: the children are thinking about things a certain way, and I'm eager to present my ready-packaged solution to all their needs. But it's not time yet. The value of a transcript like this is that it puts our teacher noses in it! Are you really wanting to replace this brilliant conversation and thinking with your pale version of progress?</p><p>It's interesting here how the children's thinking around measuring the rugs with each other is so rich - there's debate, there's problems, resolutions, ad hoc rules, modifications and concensus. The teacher's tape measure solution is relatively meagre. It may be 'right' from our adult perspective to use a tape measure, but where the children are now, 'Well, rulers aren't really real, are they?'</p><p>Young children are learning incredly fast, learning more than we adults are able to. But they don't necessary learn in the chunks of time we would like them too. And they don't necessarily learn in the 'efficient' way we would like them to. They repeat things again and again, seeming to need to do this to realise something or some things. Here they need people lined up on the carpet. That's a lot more interesting to them, a lot more what they need than any next step.</p><p>What could the teacher do here if not be the supplier of the answer, the next piece of information? I'd say, enter into the moment without itching for the next step. I'd say, take a picture of it and put it up on the wall. And, document it, to discuss what the learning and theory building is with other teachers, And of course, share it with the parents. A transcript like this is precious. Even a remembered summary of it is something that can help us to think about real learning.</p>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-91670726381005215432021-03-21T06:04:00.002-07:002021-03-21T08:53:11.324-07:00Listening <div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6EI7jIEK1PBwMKoDakZT7db_T5zO8IpC4qhy57HWLg7ic3040RhhEsllYfq60YC8EhqHMmmwcFub9pcYfY-JQUnvi-2BbjTQVAaXar5Htx1ZOYu4tS1BhBgz0K_MOVKcX79bABfQxKbMU/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6EI7jIEK1PBwMKoDakZT7db_T5zO8IpC4qhy57HWLg7ic3040RhhEsllYfq60YC8EhqHMmmwcFub9pcYfY-JQUnvi-2BbjTQVAaXar5Htx1ZOYu4tS1BhBgz0K_MOVKcX79bABfQxKbMU/" width="200" /></a></div></div><p></p><p><i>Simon writes:</i></p><p>Back in 2015, Estelle and I ran <a href="http://followinglearning.blogspot.com/2015/10/valuing-talk-in-classroom.html" target="_blank">a workshop on talk in the classroom</a>. I was in Grade 3 (Year 4), Estelle was in Grade 1 (Year 2), and we were sharing ways we encourage students to talk more in our classrooms. To prepare for it we visited each other's classes, watched some established ways, and tried some new ideas too. </p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOUnX7nxgaKTjXDLGB2y6JPwv82Ur9paFcShjXlc8uVCVKLot0onvzrVxfVHzZYYjq-Dj0CE2yg5mSi-AzPB63T2Okn2E86Huk1gylJlGv29Wgv2Rj915uVU6vWPmMZofku38VQIt15IY/s2048/Estelle+1.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOUnX7nxgaKTjXDLGB2y6JPwv82Ur9paFcShjXlc8uVCVKLot0onvzrVxfVHzZYYjq-Dj0CE2yg5mSi-AzPB63T2Okn2E86Huk1gylJlGv29Wgv2Rj915uVU6vWPmMZofku38VQIt15IY/s320/Estelle+1.JPG" width="320" /></a></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both; text-align: left;">Estelle, as well as being a wonderful friend, is a fellow edu-geek. We read, we discuss, we even go to see the odd French education film like <a href="http://followinglearning.blogspot.com/2017/11/play-and-manipulatives.html"><i>Le Maître est l'Enfant</i></a> and <a href="http://followinglearning.blogspot.com/2018/03/etre-plutot-quavoir.html"><i>Être plutôt qu’avoir?</i></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Some things were working against student conversation in class back then. We teachers have some tradition behind us, and a lot of curriculum to get through. We end up <i>listening for </i>rather than <i>listening to</i>.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This distinction, <i>listening for </i>rather than <i>listening to</i> is one Helen Williams uses lots, but it seems to have had multiple origins. Max Ray-Riek was one of them, and if you have five minutes to think about this a bit more, this is a now classic talk of his:</div><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="394" src="https://www.youtube.com/embed/h00Ux1qx2zw" width="525"></iframe><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I'm not sure how much we were thinking about<i> listening to</i> at that point. We <i>were </i>thinking about 'What do you notice? What do you wonder?' to hear what the students actually have to say, but we were very much orchestrating what lessons were all about and the kinds of things that might be talked about in them. I had discovered people in the mathematical Twitter world who were guiding me towards close listening to students. Estelle was and is a brilliant listener. But we were still listening mainly <i>for</i> the matter in hand, the curriculum content.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">In June 2016, Estelle and I knew we were moving down into Early Years, Estelle as the coordiantor. We went off to Prague for a great few days on play. Estelle would be leading the Early Years through a lot of change, but I'm not sure if she knew how much change there would be.</div><div class="separator" style="clear: both;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8ttQO2qnazk4r1F4QbIBnXFPW_tz3Qcq8df_UdvKn3tY_6YRbGZR7HhGApH-gAkD0B7tQhrRI1KVkruJl-4z3FJddF6GcQWUCB8QIT_dKpK3UBls4T1HVBhyaJBzFEGGjFBhklYu4jOE/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="768" data-original-width="1024" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8ttQO2qnazk4r1F4QbIBnXFPW_tz3Qcq8df_UdvKn3tY_6YRbGZR7HhGApH-gAkD0B7tQhrRI1KVkruJl-4z3FJddF6GcQWUCB8QIT_dKpK3UBls4T1HVBhyaJBzFEGGjFBhklYu4jOE/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Loose parts play in Prague</td></tr></tbody></table><br /></div><div class="separator" style="clear: both; text-align: left;">That September, and for the next few years, I taught in K (5 and 6 yos). We still had specific mathematics lessons, for 45 minutes each morning. At the time, I <a href="http://followinglearning.blogspot.com/2017/07/looking-back-looking-forward-few.html" target="_blank">blogged about</a> the some maths aspects of this:</div><div class="separator" style="clear: both; text-align: left;"><blockquote>'There was a lot of space for the students own creations and explorations. I was keen to keep a sense of agency, and tried to respond to any initiative. This was as important, I feel, as the exact direction we went in. That sense of 'this is an inquiry we're following because B started us off with this; let's see where it goes' is something I really want to nurture again, and even more so, next year.'</blockquote></div><div class="separator" style="clear: both; text-align: left;">Last year, Estelle and Rachel were in K and I was popping in, especially for maths lessons, in my role as STEAM coach. From September, they changed the mathematics so that there was a lot more choice in the range of activities available. Then in November, Rachel went off to Ljubljana for a play-based learning course, and when she came back she said they were recommending moving away from specific subjects at specific times of day and onto a continuous provision where children could choose what they engaged in for long periods of time. Estelle listened and was really responsive to the idea and Rachel's enthusiasm for it. In January, the K classes became more truly play-based, with children having a lot more choice.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">As STEAM coach, I wanted to keep some record of the changes, so at the end of the month I asked Estelle about the changes. Here's a few minutes taken from that conversation:</div><div class="separator" style="clear: both;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwc6Nf8knHlGRl3ZunK5InGsJsdOoo_IKCazy3X6YoqESBq8JWDvBPSAIlTwd37sBg5CDTK3Jn1P8_M17YEpg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: left;">It was not easy for me, this change. I had really enjoyed having a time with the K students each day where we would be exploring maths together. But of course, there had been a cost in terms of student autonomy and agency. Now children would choose more how to spend their time, and it would be our job to make sure the mathematics offer was atractive and just right!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The PYP (Primary Years Program of the International Baccalaureate) was changing too. In 2018, the PYP document <i>The Learner</i> described a major shift towards play for young children. Here's part of a table that describes the changes:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><table class="tei-table2 c-table-pure" style="background-color: white; border-collapse: collapse; border-spacing: 0px; color: #333333; font-family: myriad-pro, Helvetica, Arial, sans-serif; font-size: 16px; margin: 0px 0px 18px; min-width: 100%;"><tbody id="id-39f917bc-6475-4561-a1ab-8da72c2b5ca9" style="box-sizing: border-box;"><tr class="tei-row3" id="N1_6_2_4_7_9_5_3" style="box-sizing: border-box; font-weight: bold;"><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Move away from</p></td><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Move towards</p></td></tr><tr class="tei-row4" id="N1_6_2_4_7_9_5_5" style="box-sizing: border-box;"><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Predetermined time structures and routines</p></td><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Flexible timeframes and routines that are responsive to the needs of the students</p></td></tr><tr class="tei-row4" id="N1_6_2_4_7_9_5_7" style="box-sizing: border-box;"><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Pedagogy that centres around instructional processes for students and is teacher-led</p></td><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Play that is co-constructed between students and teachers</p></td></tr><tr class="tei-row4" id="N1_6_2_4_7_9_5_9" style="box-sizing: border-box;"><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;"><p class="tei-p26 ib-paragraph" style="box-sizing: border-box; margin: 0px 0px 12px;">Repeated large-group experiences as the basis for all learning</p></td><td class="tei-cell6 ib-table-cell" style="border: 1px solid rgb(228, 228, 228); box-sizing: border-box; font-size: 14px; padding: 12px 18px; vertical-align: top;">Whole-group experiences at pertinent learning moments</td></tr></tbody></table></div></div><p>Actually, we were already well on the way to the right hand side, but there was more travelling to be done.</p><p>We've been thinking a lot about our pedagogy. During lockdown, we zoomed about Kath Murdock's <i>Power of Inquiry</i>. And when it was over, we met in peron after reading Anna Ephgrave's <i>Planning in the Moment</i>.</p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc1VcU69x2NAWlbFFEackUqQuk6LSprSl-SAbe8vK8OiHbv4Hvr1XGfpOopyBeUOVWsrUxwFfipaK5aCr-F_i2Z4tPsVtYt9bs3Qie_uPykqkad6fBWa4U4bJsFKqNg0BUz4RMQXFH5I0/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc1VcU69x2NAWlbFFEackUqQuk6LSprSl-SAbe8vK8OiHbv4Hvr1XGfpOopyBeUOVWsrUxwFfipaK5aCr-F_i2Z4tPsVtYt9bs3Qie_uPykqkad6fBWa4U4bJsFKqNg0BUz4RMQXFH5I0/" width="320" /></a></div><div style="text-align: left;">This year, we've been doing Saturday morning sessions with Anna Van Dam, debriefing afterwards to apply all the things we'er learning to our classes:</div></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVXhtMF3uAraMmWapsb8Q8gELaRcnSyD4fBaGN3bNj84ZmIf0KA_Rdoc6bgsWgz6I6_smGdruyPp7WHl2o3CW_BaKsSYImSzSOJY8FDBQqTviKtvwxkoMNRKqpUlq3mkOFE1Vnx1h9uz8/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="900" data-original-width="1718" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVXhtMF3uAraMmWapsb8Q8gELaRcnSyD4fBaGN3bNj84ZmIf0KA_Rdoc6bgsWgz6I6_smGdruyPp7WHl2o3CW_BaKsSYImSzSOJY8FDBQqTviKtvwxkoMNRKqpUlq3mkOFE1Vnx1h9uz8/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">We've also discovered, and are loving, Vivian Gussin Paley's books.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">And Rachel, Estelle and I are together in PK, with 3-5 year olds - in Sun, Star and Moon class! It's a kind of homecoming in some ways - finally the choice and playfulness that I tried hard to allow space for in lessons is the actual stuff of our time!</div></div><p></p><p>We're becoming more and more interested in listening to children. And finding out that our questioning is often not helping. Julie Fisher's <i>Interacting or Interfering: Improving Interactions in the Early Years</i> crystalised for us how some of the tools we might use in adult conversations, such as questioning, are often actually a hindrance with young children.</p><p>And as <a href="http://mcs.open.ac.uk/jhm3/Selected%20Publications/Effective%20Questioning%20&%20Responding.pdf" target="_blank">John Mason writes </a>in the context of teaching mathematics:</p><p></p><p><i>"The secret of effective questioning is to be genuinely interested not only in what learners are thinking, but in how they are thinking, in what connections they are making and not making. Genuine interest in the learners produces a positive effect on learners, for in addition to feeling that they are receiving genuine attention, you can escape the use of questions to control and disturb negatively. Instead of asking for answers, which in most cases you probably already know, you can genuinely enquire into their methods, their images, their ways of thinking. In the process, you demonstrate to learners what genuine enquiry is like, placing them in an atmosphere of enquiry which is, after all, one view of what schooling is really intended to be about."</i></p><p></p><p>Especially as most of our young students don't have English as a first language, we're finding that <i>watching</i> can be an important part of listening. Seeing what our students do, trying to guess their lines of thiking.</p><p>Slowing the pace down, giving students our attention for longer periods of time.</p><p>Here's Estelle in the forest the other week. I managed to video part of a much longer conversation. </p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dxR-ggMPLvunpvR_MM5QqB1KA_V5TY3ou0rcbF53vtU7x48KMi-GIWjrt6_OsWDbKe8voGxvnAT6ZO1KGUUbA' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><p>Young students like this don't usually respond well to the direct approach, to questioning. It's more about creating the conditions for relaxed conversation. Here Estelle establishes a slow pace, peeling open acorns, seeing that some of them have turned to powder inside, seeing that there are holes in those ones, talking about worms. It's a comfortable situation, and sure enough, a student begins sharing his knowledge about worms. </p><div>After this, Estelle starting delving for acorns that were beginning to grow. </div><div><div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoGgScwuAr9x0FPLZUBHnv2mLx1m-bmPJJJiUAJ1NmEzCRx-ndERcJyVinvdpwNAKh3tT9OrKyF7UF65VzXr7_mxCR-qSlHVSfUWahlu2Kqn2She_vaiIG24b0NPQ8MESJYbApAOxxslE/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoGgScwuAr9x0FPLZUBHnv2mLx1m-bmPJJJiUAJ1NmEzCRx-ndERcJyVinvdpwNAKh3tT9OrKyF7UF65VzXr7_mxCR-qSlHVSfUWahlu2Kqn2She_vaiIG24b0NPQ8MESJYbApAOxxslE/" width="320" /></a></div>(We took some back to the classes, and there are some seedlings now!)<br /><br /></div><div>There's a quality to the listening which we sometimes get. There's a giving attention to whatever the student wants to say, in their own time.</div><div><br /></div><div>Estelle, Rachel and I have been documenting 'Moments in the Day' - times when we watch a student at play, document it, try to see what learning is happening, and bring it to the EY group for discussion.</div><div><br /></div><div>An example:</div><div><br /></div></div><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px;"><div><span id="docs-internal-guid-1ea282d0-7fff-757a-d86c-e744846eaa3d"><i>Estelle writes:</i></span></div><div><span><div class="separator" style="clear: both; text-align: center;"><span style="color: #800180;"><i><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwaONXgg3rCvMzI8Vh8cRAZSnPunZrSB7U2eegrs738I-2tto92lYET7xCn9CumzAIoI7v9iiyvmzzcIJ2W6g' class='b-hbp-video b-uploaded' frameborder='0'></iframe></i></span></div></span></div></blockquote><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px;"><div><span><i>"G is sitting in the sun and holding up a jelly digit. What catches my eye is his quietness and his gaze on the object. I go over and ask what he’s noticed. I try to go carefully and softly with my interactions wanting to avoid taking over.</i></span></div><div><span><i><br /></i></span></div><div><span><i>G says these things at different points in the play and conversation.</i></span></div><div><span><i><br /></i></span></div><div><span><i>“I just cut it in half and it did that.</i></span></div><div><span><i><br /></i></span></div><div><span><i>What is this? (holding up the digit zero)</i></span></div><div><span><i><br /></i></span></div><div><span><i>Every time I do this it does that (points to two bubbles as they move in opposite directions when he presses his finger down.</i></span></div><div><span><i><br /></i></span></div><div><span><i>I made four now (bubbles).”</i></span></div><div><span><i><br /></i></span></div><div><span><i>Observations, sharing, trial and error, comparing across objects that are similar but not exactly the same. Counting the number of bubbles. Thinking about letters and numbers. It was G on the number hunt who was asking about the zero and saying it was an o.</i></span></div><div><span><i><br /></i></span></div><div><span><i>A joins us:</i></span></div><div><span><i><br /></i></span></div><div><span><i>“It’s broken into more!” Bashing it and making loads of tiny bubbles.</i></span></div><div><span><i><br /></i></span></div><div><span><i>...There is a quality of being in the moment, attention and pause which was noticeable."Documenting together (and thanks to Anne Van Dam for encouraging us in this) is making us more keen to listen. Reflecting together on what we've documented is making us realise how much there is in what we hear.</i></span></div></blockquote><div><div><span id="docs-internal-guid-1ea282d0-7fff-757a-d86c-e744846eaa3d"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="color: #9900ff; font-family: Arial; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i><span style="font-size: x-small;"></span></i></span></p><p style="text-align: center;"></p></span><span><p></p></span><span></span><span><p></p></span></div><div>We're all still learners in this art. We have to tell ourselves to leave space, to not do all the work. <br /><p></p><p>It's kind of odd that it's hard for us. Estelle, for one, has listening as a superpower. I know how good she is at listening to me and other friends, and to colleagues at school. But, the challenge is harder now. Making space for students who, at 3, 4 and 5 years old, and are still building up the confidence to speak in English. Making our interactions carry little weight, to not swamp their tentative beginnings at expressing themselves.</p><p>Now at least, and at last, our antenae are twitching, waiting to hear what our students want to say, trying to read in their play the theories they are building. (Thanks again to Anne Van Dam for that emphasis. See <a href="http://followinglearning.blogspot.com/2021/02/dinosaurs-and-thinking.html">the previous post </a>for more on this.) </p><p></p><blockquote>"In listening to others, accepting them in their irreducible difference, we help them listen to themselves, to heed the speech of their own body of experience, and to become, each one, the human being he or she most deeply wants to be." <i>from D M Levin, The Listening Self, quoted in <a href="http://www.maxvanmanen.com/files/2014/03/Listening-in-a-mathematics-class-Brent-Davis.pdf" target="_blank">this piece by Brent Davis</a>.</i></blockquote></div></div><div><div><p></p></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com1tag:blogger.com,1999:blog-3071719252136968205.post-68140227599476662012021-02-20T01:45:00.003-08:002021-02-20T01:45:22.873-08:00Dinosaurs and thinking<p> Rachel, Estelle and I have been on a great course with <a href="https://twitter.com/AnnevanDam1966" target="_blank">Anne van Dam</a> on Saturday mornings in January. </p><div>One of the things she asked us to consider was the theory building that we see in children’s play and conversation, and to use this intentionally as the basis for planning. <br /></div><div><div><br /></div><div>I wondered about some of the times play doesn’t seem to be theory building - for instance when some of the students like to get the dinosaurs and bash them together in dinosaur fights. Maybe I needed to look closer, Anne suggested. So I did. I recorded a little of U and V playing with them.</div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: 11pt; margin-left: 1em; margin-right: 1em; white-space: pre-wrap;"><img height="240" src="https://lh4.googleusercontent.com/z8QeWeD6Bpw-8hqDwG9B2CBLxZpmGJQy_W9k22KutezZXbPXsVUJ-pnQ2FjCFYFsfPDy_aHfhFSpPJM1auJMwxo9QwMMKBGynPXJEqFpuXw-aY5RVKTsDsIBeYOBkDNCDt-m8kNq=w320-h240" style="margin-left: 0px; margin-top: 0px;" width="320" /></span></div>After bashing for a while they say:<br /><br />U: Le he apretado el cuello.<br />V: Todos los dinosaurios son fuertes pero este es el mas fuerte, a que si?<br />U : Vamos a ver los cuellos. Son los mismos?<br />V: No, el con la boss, el mio es mas grande.</div><div><br /></div><div>I don't speak Spanish (yet - I'm puting in some Duolingo time on it!) so I asked our colleague Irene to translate from the video, and she kindly sent back:</div><div><br />U: I held his neck.<br />V: All dinosaurs are strong but this one is the strongest, am I right?<br />U: Lets see how tall the necks are. Are they the same?<br />V: No, the one with the hump, mine, is the strongest.<div><span id="docs-internal-guid-af8c4b05-7fff-dcac-9376-c4bc8a451e3a"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC1_E7N5N-9BeTszVCLZ-66N4W6gW8QfH7SaSOWSnpSU3bK-JSDZUhY3lnqLL0QMWF1Z4eMtSgDdiNJdwsxNPvegOma1A749klqIjvxzfC1y4EGkKqFkMZZII2xoo0rgEufv09JS8Y436s/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="506" data-original-width="900" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC1_E7N5N-9BeTszVCLZ-66N4W6gW8QfH7SaSOWSnpSU3bK-JSDZUhY3lnqLL0QMWF1Z4eMtSgDdiNJdwsxNPvegOma1A749klqIjvxzfC1y4EGkKqFkMZZII2xoo0rgEufv09JS8Y436s/" width="320" /></a></div></span>So... thinking about strength, where the strength is, comparison, anatomy… lots going on!<br /><br />More specifically, they seem to be considering the features of the dinosaur that might contribute to strength, and beginning to measure those features. They are interrogating each other and seeking evidence: ‘Let’s see...Are they the same?”<br /><br />Anne encouraged us to think about next steps, and as it seemed both to be fascinating to some of the students, and to be a place where they were thinking critically and theory building, I thought it was maybe worth building on. What could the next steps be, I wondered?</div><br />I showed this image, and asked what is strong here:<br /><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1tc_zECa03gd9Y2n0-BDQdbJs44j_6lQyHRmf1c5K08Bipnpm-Dn_z_J9ApwPBAUWpUp9lewCB0HkPjHarCuV3DZyEPAGFre6FQSNQ-HxtKBjsM6_7gQUF4ruF0AnZyJIRhSt1YWXi6OQ/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="473" data-original-width="800" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1tc_zECa03gd9Y2n0-BDQdbJs44j_6lQyHRmf1c5K08Bipnpm-Dn_z_J9ApwPBAUWpUp9lewCB0HkPjHarCuV3DZyEPAGFre6FQSNQ-HxtKBjsM6_7gQUF4ruF0AnZyJIRhSt1YWXi6OQ/w400-h236/image.png" width="400" /></a></div>I was very pleased that T wanted to contribute lots. Though he’s 3 and beginning with English, he knows a lot of dinosaur names and has a lot of interest in them.<div><div class="separator" style="clear: both; text-align: center;"><br /></div>Alongside this, a question about the relative strength of two pyramids came up. Which is the stronger?</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9Cv464_3NfmWaT2YwD_3xPX9vOCWt7SaDB7Y_CBL9NpzdkvW0TDz9tgTFW-cQKq8-GUAgYjkBC_NpeAL6MIX_E3vWsLOibV_UV__W1oEcAwfyMVFKlSt5-q-MXh1oQ1nVjG1DKXGLAL5f/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="388" data-original-width="852" height="146" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9Cv464_3NfmWaT2YwD_3xPX9vOCWt7SaDB7Y_CBL9NpzdkvW0TDz9tgTFW-cQKq8-GUAgYjkBC_NpeAL6MIX_E3vWsLOibV_UV__W1oEcAwfyMVFKlSt5-q-MXh1oQ1nVjG1DKXGLAL5f/" width="320" /></a></div>We tried it out with our dot stones, which have graded weights, to see how much each pyramid could support.</div></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhljKGVxRJrUcS8LvjHvmeN_3LM7SxF1VtYXPLYGwQAZsaOL2q772pIcC_YDbMZ8okUwTiN2DtcFVcGQ9NBHdr_lkSdvoL5twrxw45MDpbbySlbrsnVAIh_wuKBAtP4ifGj9jEhysevZgSi/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1536" data-original-width="2048" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhljKGVxRJrUcS8LvjHvmeN_3LM7SxF1VtYXPLYGwQAZsaOL2q772pIcC_YDbMZ8okUwTiN2DtcFVcGQ9NBHdr_lkSdvoL5twrxw45MDpbbySlbrsnVAIh_wuKBAtP4ifGj9jEhysevZgSi/" width="320" /></a></div><div class="separator" style="clear: both;">It turns out the square-based pyramid is stronger:</div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2bnMBSADGTDu9FGr2DJ_JYUQY4Yc59z7ontuSSZ-lPa3F_dUtvUsdlhmt53JCbRmkekw3lp5icdQAx1xVe7OppIQ8fvtmDtNZCQNY-1efzOTcq1DL7YOrrRrqBjF_3EZWmPlw2-5-0mpY/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="675" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2bnMBSADGTDu9FGr2DJ_JYUQY4Yc59z7ontuSSZ-lPa3F_dUtvUsdlhmt53JCbRmkekw3lp5icdQAx1xVe7OppIQ8fvtmDtNZCQNY-1efzOTcq1DL7YOrrRrqBjF_3EZWmPlw2-5-0mpY/" width="320" /></a></div>Back to dinosaurs...</div><div class="separator" style="clear: both;"><br /></div>At some point I tried playing one of the many simulations of triceratops facing up to a tyrannosaurus. Children started asking to watch more of these, and I found some that could work. I was stopping the video at various points and getting lots of observations and conversation.<br /><div class="separator" style="clear: both;"><span><span face="Roboto, sans-serif" style="color: #0f1419; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></span></div>I also wrote this up and shared it with Estelle and Rachel and the team in our regular Monday meetings where we look back at specific moments of play and learning. Afterwards, I wrote:</div><div><br /></div><div><span id="docs-internal-guid-32224fa1-7fff-f711-a3f2-38bfc35206a2"><span face="Roboto, sans-serif" style="background-color: #fff2cc; color: #0f1419; font-size: 11.5pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I’m finding putting this down and sharing it with colleagues is helping me think of next steps. It’s bringing it into focus for me - I don’t really see the way ahead, but I feel like there are enough clues in what’s happened already, and in our shared knowledge, to come up with some ways forward. It helps to have detailed evidence to work on, and might give us pointers to more general matters about pedagogy too. </span></span></div><div><br /></div><div>Then I saw on Twitter a story about palaeontologist <a href="https://twitter.com/gsciencelady">Dr Elsa Panciroli</a> who had stumbled over a fossil Stegosaurus bone on the Scottish island of Eigg. If we could talk to her, it might help us to see that people - scientists - do the work of finding out about these creatures. It might also show the students that they could ask questions and get answers. And of course, tell us more about dinosaurs. I tweeted to her - and she agreed to Zoom with us! </div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3bZMAfw0soTFQUOhxXDw6SBPMvBUv6SnYzSCrKW012u31UuuZb-cNLt-5e8QUNFi8fEnSdVRpcVQ47pwG9BN0cl_-RGVn_sXzkh5sDY24Sq6Owa_MDmWRL5s3mZtDd8ZsA9JvUVeY2E3T/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="939" data-original-width="1252" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3bZMAfw0soTFQUOhxXDw6SBPMvBUv6SnYzSCrKW012u31UuuZb-cNLt-5e8QUNFi8fEnSdVRpcVQ47pwG9BN0cl_-RGVn_sXzkh5sDY24Sq6Owa_MDmWRL5s3mZtDd8ZsA9JvUVeY2E3T/" width="320" /></a></div>She became our 'Dr of Dinosaurs' and answered the questions brilliantly. It was great to see children that were just beginning to feel confident at school put whole sentences together in English asking their questions and getting answers.</div><div><br /></div><div>If I was in any doubt about the impact this had, one of the parents shared how her son had been so animated about our meeting that she'd written down what he'd said:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5wCVUoTa19kQ2Y7uQTFhJW2c1Iwqic_NqyQvHsXUkXCbB13Zk8f3MjnX8tvGZKNqYCfr9qMFfCsX0Y5jZ_UhKm7ThkQBoMk81NiAFlK36amYM4ur8wbkGP7vOba9JdTcBslxmfvNO9ET5/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="900" data-original-width="675" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5wCVUoTa19kQ2Y7uQTFhJW2c1Iwqic_NqyQvHsXUkXCbB13Zk8f3MjnX8tvGZKNqYCfr9qMFfCsX0Y5jZ_UhKm7ThkQBoMk81NiAFlK36amYM4ur8wbkGP7vOba9JdTcBslxmfvNO9ET5/w480-h640/image.png" width="480" /></a></div>And when I asked about favourite dinosaurs, Stegosauruses were now the most popular.</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhr5mpF_IRpZ-cqgSyEA45CLgvLfQlw1icMO0l2QYCWvUurz4huBq_hmNvYQkLX2Hwi1p_kXcnrSk6Ztd_1eoK6qhaLfFap6gO0dCa_0CP5SgAqEOIgu_1fyf9LGcbAFI6dPcB9hsPwyN4A/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="675" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhr5mpF_IRpZ-cqgSyEA45CLgvLfQlw1icMO0l2QYCWvUurz4huBq_hmNvYQkLX2Hwi1p_kXcnrSk6Ztd_1eoK6qhaLfFap6gO0dCa_0CP5SgAqEOIgu_1fyf9LGcbAFI6dPcB9hsPwyN4A/" width="320" /></a></div>I don't know where this will go next. But it feels good to be following up on not just one on the things that interests some of the students, but on their thinking about that interest, and to be making connections outwards from there.</div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-57171078805919427162021-02-15T05:30:00.001-08:002021-02-15T05:30:05.886-08:00Number books<p> <i> Simon writes:</i></p><p></p><div class="separator" style="clear: both;">Estelle has tried helicopter stories before - hearing children's stories, writing them down for them exactly as they tell them, and then giving the class the chance to act out the stories on a classroom 'stage'. (We've discovered Vivian Gussin Paley, who made great use of this approach. We've read her brilliant <i>Mollie is Three</i>, and are moving onto <i>The Girl with the Brown Crayon</i>.)</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Z (4 yo) sat down to begin a book. Like this. She tells me what to write in my story book, and wants it on the page too.</div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcbopb_tNFOrbYnKZyeo0xXKm3YQdLr6G2_Af3MSva2pnGBFSsX9XZl_HlDE5ixc0q3FHSj5uUnyHGFfrfeKja2JhrFybo8_gBBmN_UgpDAtqAJSMq1044LBfcVXljc8vgingxsDRl_0Kz/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="912" data-original-width="1222" height="239" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcbopb_tNFOrbYnKZyeo0xXKm3YQdLr6G2_Af3MSva2pnGBFSsX9XZl_HlDE5ixc0q3FHSj5uUnyHGFfrfeKja2JhrFybo8_gBBmN_UgpDAtqAJSMq1044LBfcVXljc8vgingxsDRl_0Kz/" width="320" /></a></div><div class="separator" style="clear: both;">The second page followed:</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuKq1TPWPjHUneq3Ya3VVf1WmlLIq3rVB7h2YsIZACMAX2ib3qrLrbJgqlYf0aHbkJi-KqdKLaiFUg9LnmUMb1LpXYeEt45VWNWpCq8K3tlZCiIj8LyoXul1ZDR9DXB0fUnnvrqoEVLVsD/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1222" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuKq1TPWPjHUneq3Ya3VVf1WmlLIq3rVB7h2YsIZACMAX2ib3qrLrbJgqlYf0aHbkJi-KqdKLaiFUg9LnmUMb1LpXYeEt45VWNWpCq8K3tlZCiIj8LyoXul1ZDR9DXB0fUnnvrqoEVLVsD/" width="320" /></a></div>Two other children had joined her:</div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmZisRDtiRalv5A1lVfHXBZ2ZvFkkAXSVgsKdXwEIlXnvRBLIZuiJyMQPMnDnTFswMGrzEXUAEvBlCsIGKhF6F5UbZxZMgpypD4yL2PaEyQbxYvbA7hKTUWvRH2vEzL8QQQ-_KLtttX-2G/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1222" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmZisRDtiRalv5A1lVfHXBZ2ZvFkkAXSVgsKdXwEIlXnvRBLIZuiJyMQPMnDnTFswMGrzEXUAEvBlCsIGKhF6F5UbZxZMgpypD4yL2PaEyQbxYvbA7hKTUWvRH2vEzL8QQQ-_KLtttX-2G/" width="320" /></a></div>At some point, W decided this was going to be a number book. There was one cat on the first pages, and two cats on the next pages. It would carry on like that.<br /><br /></div><div class="separator" style="clear: both;">She wrote out the numbers, copying them from the wall.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM_nyyP1WlyxNaT89yIWW6dwAtwdPY-ucu5561Gopog9TDkVbDZAlSwj8Ka6nel6iroQ5KFoONZPQ0Ls4ACt4Kl6MtrDInRLyYasqpfSz0syTwyl7o8to5OuNA9fWcAdle76zrkr7RAXaF/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM_nyyP1WlyxNaT89yIWW6dwAtwdPY-ucu5561Gopog9TDkVbDZAlSwj8Ka6nel6iroQ5KFoONZPQ0Ls4ACt4Kl6MtrDInRLyYasqpfSz0syTwyl7o8to5OuNA9fWcAdle76zrkr7RAXaF/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; text-align: start; white-space: pre-wrap;">'I've just learned to write five!'</span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf4UmW84-dK-TXGoa-2ioYnzdytdnYt_j6vAVCL81lDBQfQ4mMl9iH16t0r54tiZrLRy9mJrsnWsJEjFWECB1OsTiQ4V8MOBgMuOs3ler2f_9tuoJ5dloUH5Tq8OKfcHDBtmU7NxlN_cFA/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf4UmW84-dK-TXGoa-2ioYnzdytdnYt_j6vAVCL81lDBQfQ4mMl9iH16t0r54tiZrLRy9mJrsnWsJEjFWECB1OsTiQ4V8MOBgMuOs3ler2f_9tuoJ5dloUH5Tq8OKfcHDBtmU7NxlN_cFA/" width="320" /></a></div></div><div class="separator" style="clear: both;">And into the afternoon:</div><div class="separator" style="clear: both;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigW6_fwXFZbpsk156elF0H3l3vrUZz6SRtrqPJ1v-7uO13psWEWUhLtD7v6UcabnWZh6QE4fnZc8iIgzr863ACiUw_Q7NB22aqFz1Hh8oHfX2cfWhp4ltZ1mxCndJ1LYrIOje9HrkstKxq/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="722" data-original-width="1222" height="189" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigW6_fwXFZbpsk156elF0H3l3vrUZz6SRtrqPJ1v-7uO13psWEWUhLtD7v6UcabnWZh6QE4fnZc8iIgzr863ACiUw_Q7NB22aqFz1Hh8oHfX2cfWhp4ltZ1mxCndJ1LYrIOje9HrkstKxq/" width="320" /></a></div>From seven onwards, there was a lot of counting and checking the numbers:</div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzEn0Kz10ZN2zkWCw3m22RYbLFFengRDCwMCGHeLe-cA3HsTbQh1j7mBO-A2BEYEghXnjiY_MjoNwf-MsmCTQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><div class="separator" style="clear: both;">Z was really pleased with her book, smiling and laughing at how much she was writing and drawing, and loving her creations! The whole group spent about an hour on it in the morning and another in the afternoon. It was also a leap forward with writing numbers. Perhaps she needed the reason to use the numbers to be motivated enough to try and write them.<br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">A week later, Z made a little book with some pretend writing. Estelle had been talking to me about encouraging her class that it was OK to do this, but, without a word from me, Z knew this was a good thing to do.</div><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dxcdZ-b8h-mqTFAeOVfLky6_FVQruauoBJhSOsh185-RUiP_THOUCQb8466SqBZbXmMNdK6XMZ2IMPaIYelVQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div>The book grew to be up to ten. Later she read her writing to me:</div><ol><li>All about the number 1, because 1 is a tiny number and zero is nothing.</li><li>2 and 2 equals 4.</li><li>Number 3 is big enough to be a monster.</li><li>Number 4 is big enough to be a zombie.</li><li>I feel so alive. You know that you've arrived when you're with number 5.</li><li>Look what you do. You look good.</li><li>Let's say number 7. Look how I work with this information book.</li><li>I'm 8 always. And you can see 5. This number likes 5 because they're friends.</li><li>This number is very tricky, but more easy than paint.</li><li>And then, let's look at number 10. 10 is big enough to be a dinosaur.</li></ol><div>I wrote it all down in my story book, and read it back to her. Later she asked Steph to copy it all into her book. Again, she was really pleased with her book, and keen to take it home.</div><div><br /></div><div>It's very interesting to me how different people's paths to loving numbers are. Counting is really working for some children, with our How Many? images going well, Pass it On and Numicon games are good with others, Numberblocks episodes are doing it for others (Numberblocks pop into Z's book at number 5, with a line from the number 5 song). For Z, a way in is being an author, and finding out that she could make substantial books that had an integrity of their own and would be exciting to share with others.</div><div><br /></div><div>Since then, I've shared her work with the class, making some blank zigzag books available with numbers 1-7 on pages. I'm going to get some blank stapled books out on the table too.</div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-68746580744362647822020-11-21T05:31:00.003-08:002020-11-21T23:17:49.771-08:00fascinating water play<p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3pzwEC2mJkRCKZSqzH-L4jn1by3bLCsF61StiZLfeZ9Y_IHkY1IHDElFo_9QA4wrFHIYm2KH57GeupxCrTgj36iqbiuZZ-a2srhabXE3vU0IuutdV4qmNkqwiXZpZQZ3DGBsmbi_g34Q/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="913" data-original-width="1217" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3pzwEC2mJkRCKZSqzH-L4jn1by3bLCsF61StiZLfeZ9Y_IHkY1IHDElFo_9QA4wrFHIYm2KH57GeupxCrTgj36iqbiuZZ-a2srhabXE3vU0IuutdV4qmNkqwiXZpZQZ3DGBsmbi_g34Q/" width="320" /></a></div><p></p><p>A short while back I was talking with Estelle and - I can't remember what the subject was - was it play schemas? - anyway, the subject of water play came up. It was something we both wanted to look into a little more.</p><p>We put water out, because it fascinates children. We think they must be learning if they're so active and so fascinated. Children will spend half an hour or more pouring and filling and emptying and much more. But what kinds of things are they investigating? What is interesting them in the water play?</p><p>I've been watching students play, asking myself what's going on, sometimes asking students but not getting much reply, and asking my colleagues.</p><p>If you haven't thought about this already, you might like to stop and think about what the fascination is with water play, before you've read other people's answers.</p><p>I thought I'd try Twitter too. I posted a photo of a student playing, and asked, 'What is it about playing with water that makes it so fascinating?'</p><blockquote class="twitter-tweet"><p dir="ltr" lang="en">What is it about playing with water that makes it so fascinating? <a href="https://t.co/VqzyMLooGQ">pic.twitter.com/VqzyMLooGQ</a></p>— Simon Gregg (@Simon_Gregg) <a href="https://twitter.com/Simon_Gregg/status/1328654421153226752?ref_src=twsrc%5Etfw">November 17, 2020</a></blockquote> <script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script>
<p></p><p><a href="https://twitter.com/scharlescole/status/1328656489469390848" target="_blank">Syreeta </a>answered the call: </p><p><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #14171a; font-size: 15px; white-space: pre-wrap;">We enter the world via the amniotic sac of fluid. Perhaps it reminds us of our beginning.</span></p><p>It's true, we are water creatures. Not only that, but we come from a <i>very</i> long line of water creatures.</p><p>Once I'd <a href="https://twitter.com/Simon_Gregg/status/1328762970906701824" target="_blank">made clear</a> that this wasn't a rhetorical question, answers came flowing in.</p><p><a href="https://twitter.com/kassiaowedekind/status/1328764578285621253" target="_blank">Kassia tweeted</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: white; color: #14171a; font-size: 15px; white-space: pre-wrap;">Filling and pouring seem to interest kids (and adults!) of all ages.</span></p><p>(Filling and emptying had been my first though too: satisfying to get to the end points - full and empty - and then to reverse the process. Maybe satisfying to so easily change the state of something into its opposite. Also, it doesn't have to be water: it can be rice or sand or wood pellets .)</p><p><a href="https://twitter.com/Trianglemancsd/status/1328766043179933698" target="_blank">Christopher replied</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #14171a; font-size: 15px; white-space: pre-wrap;">True. At least 40% of fun of home brewing is playing with water. Which, by the way, involves siphoning. Do these children have access to a siphon? </span><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #14171a; font-size: 15px; white-space: pre-wrap;">Cuz if you're gonna make a tremendous mess, a siphon is a SUPER fascinating way to do it.</span></p><p>Must siphon!</p><p><a href="https://twitter.com/AstenAstensmith/status/1328847968393437185" target="_blank">Aston too was clear</a>, adults have the same pleasure: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">It’s not just children- I’m 38 and been working on our rink in the back yard. Nothing more satisfying then watching the water spread out and freeze. </span></p><span class="css-901oao css-16my406 r-4qtqp9 r-ip8ujx r-sjv1od r-zw8f10 r-bnwqim r-h9hxbl" face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline-block; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; height: 1em; line-height: inherit; margin: 0px 0.075em; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap; width: 1.2em;"><div aria-label="Face with tears of joy" class="css-1dbjc4n r-xoduu5 r-1mlwlqe r-1d2f490 r-1udh08x r-u8s1d r-h9hxbl r-417010" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 1.2em; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; width: 1.2em; z-index: 0;" title="Face with tears of joy"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-x3cy2q r-1p0dtai r-xoduu5 r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://abs-0.twimg.com/emoji/v2/svg/1f602.svg"); background-position: 50% 50%; background-repeat: no-repeat; background-size: 100% 100%; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 17.9977px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;"><br /></div></div></span><p><a href="https://twitter.com/jack_m_brown/status/1328764875598860288" target="_blank">Jack wrote</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #14171a; font-size: 15px; white-space: pre-wrap;">I think in part it hits a sweet spot between something that acts on its own and thus gives a sense of mystery and something that is controllable and thus reassuring. Also their is the slight drag of moving through it which is wonderful tactile feedback from the world.</span></p><p>The tactile feedback links in with what Steph had said: it's a sensory experience in a way that most of the day isn't. Estelle's impression too, putting her hands into the water, was about the sense of touch: how we felt the cold of the water entering it, and the warmth coming out.</p><p><a href="https://twitter.com/DavidKButlerUoA/status/1328766216819806208" target="_blank">David also commented</a> on the meeting of opposites in water: </p><p><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #14171a; font-size: 15px; white-space: pre-wrap;">Maybe it’s because water is so paradoxical:</span></p><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #14171a; font-size: 15px; white-space: pre-wrap;">You can see it’s there, but you can see *through* it.
You can feel it, but not grasp it.
You can make mess with it, but the mess disappears.
You can carry it, but it can carry things too.</span><p></p><div class="separator" style="clear: both; text-align: left;"><a href="https://twitter.com/mpershan/status/1328851681472339972" target="_blank">Michael too saw an opposition</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">It is solid enough we can shape and change it but only for a moment, sending us back over and over again to try again. </span></div><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">
Also it makes really satisfying sploosh sounds.</span><div><p><a href="https://twitter.com/Cukalu/status/1328765568271441920" target="_blank">Westley thought</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">It's magical, like fire. We can control it but it also has a life of its own.</span></p><div class="separator" style="clear: both; text-align: left;"><a href="https://twitter.com/j_lanier/status/1328959417312808964" target="_blank">Justin also had a word</a> about fire: <span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: left; white-space: pre-wrap;">It burns less t</span><span class="css-901oao css-16my406 r-1qd0xha r-b88u0q r-ad9z0x r-bcqeeo r-qvutc0" face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; font-weight: 700; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: left; white-space: pre-wrap;"></span><span class="css-901oao css-16my406 r-1qd0xha r-ad9z0x r-bcqeeo r-qvutc0" face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.3125; margin: 0px; min-width: 0px; overflow-wrap: break-word; padding: 0px; text-align: left; white-space: pre-wrap;">han fire.</span></div><span class="css-901oao css-16my406 r-4qtqp9 r-ip8ujx r-sjv1od r-zw8f10 r-bnwqim r-h9hxbl" face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #0f1419; display: inline-block; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; height: 1em; line-height: inherit; margin: 0px 0.075em; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap; width: 1.2em;"><div aria-label="Face with tears of joy" class="css-1dbjc4n r-xoduu5 r-1mlwlqe r-1d2f490 r-1udh08x r-u8s1d r-h9hxbl r-417010" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 1.2em; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; width: 1.2em; z-index: 0;" title="Face with tears of joy"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-x3cy2q r-1p0dtai r-xoduu5 r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://abs-0.twimg.com/emoji/v2/svg/1f602.svg"); background-position: 50% 50%; background-repeat: no-repeat; background-size: 100% 100%; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 17.9977px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;"><img alt="Face with tears of joy" class="css-9pa8cd" draggable="false" src="https://abs-0.twimg.com/emoji/v2/svg/1f602.svg" style="bottom: 0px; height: 17.9977px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;" /></div></div></span><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZ8mzogaJt6ZA_Ru2rrNf3b_EJAiykT1jZFreS6QnY3DQsqMlMSAClCV-VYi85KNa00ZKs405PU3aL4R424pu0Wrx6l22ncF6ygEkSqUMHbIur2lxp4jyyfTUhopx6P1y4JyjeLTDoeds/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="653" data-original-width="489" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZ8mzogaJt6ZA_Ru2rrNf3b_EJAiykT1jZFreS6QnY3DQsqMlMSAClCV-VYi85KNa00ZKs405PU3aL4R424pu0Wrx6l22ncF6ygEkSqUMHbIur2lxp4jyyfTUhopx6P1y4JyjeLTDoeds/" width="180" /></a></div>Watching students play should provide some of the answers. One of the things that seemed to fascinate this student, was how you could tilt the container just a little and the water would swill to the other end and start pouring. Shake it, and it comes out in all sorts of ways! <p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD5_MEhbLPRQ1o9sHM4aYcAb_Eu5jH7uM3K6bXnPfTzh4xAc9g7RdBwOR2ltkRgCytvGBDqmBHRxwgKdDXTz3LCPMHLkGeOaHnEHGtsm1SsKFNCZ87JrjXXcH8YCOctayWubqvyBpfoFw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="686" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD5_MEhbLPRQ1o9sHM4aYcAb_Eu5jH7uM3K6bXnPfTzh4xAc9g7RdBwOR2ltkRgCytvGBDqmBHRxwgKdDXTz3LCPMHLkGeOaHnEHGtsm1SsKFNCZ87JrjXXcH8YCOctayWubqvyBpfoFw/" width="180" /></a></div>He spent about 40 minutes with this water. He liked the bubbles too. Sometimes, the bubbles made a kind of noise. Here's Estelle listening to it.<p></p><p>When I got home, I showed Pam some photos from the day, and asked her too what the fascination is in water play. She had a lot to say:</p><blockquote>Water is just the most fantastic material. The way it has so many interesting properties, shapes, colours. The way the light passes through it. The way it twists as you’re pouring it. It doesn’t just go from one place to another. When you pour it, it catches the light, it sometimes has a smooth bent surface, it cascades, it’s in drops, it might fall in zigzags through the air.<br /><br />You can hold it, but you can’t hold it. You can scoop it, but you can’t control it. If you put your hand in to pick something up, it’s not where you think it will be.<br /><br />There’s something mysterious about it.<br /><br />If it’s in a transparent container, it’s different according to what side you put it into. There’s nothing boring about water.<br /><br />And then there’s bubbles! Even in water without squeezy in, there’s a bubble when you drop something in.<br /><br />It’s funny as well. You splash it, and it goes on your clothes but there’s no harm – it will dry out. Maybe a bit of water on the floor. But it’s just fun. <br /><br />You’ve got something floating and then it sinks, you can experiment with it just by playing and having a laugh. It’s fun.</blockquote><p>Meanwhile, more tweet answers were washing in.</p><p><a href="https://twitter.com/danbrow93953917/status/1328771255349207041" target="_blank">Dan suggested</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">I wonder if asking why might not get to the heart of what it's *like* to play with water? </span><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">What’s it like to ... might get closer to the experience?</span></p><p><a href="https://twitter.com/amanda_renard/status/1328768840671510528" target="_blank">Amanda wrote</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">It's the one substance besides air that we have a lot of regular contact with, but it acts differently than air, in very interesting ways. When we go to the beach, it seems like access to a totally different world. It's incredibly powerful.</span></p><p><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">We don't think much about air because for the most part it's not visible or tangible to us. But water does cool stuff!</span></p><p><a href="https://twitter.com/PolyPantelides/status/1328771319572299777" target="_blank">Poly tweeted</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">I am totally with this little one: watching water move is fascinating! Might be interested <a href="https://www.wallacejnichols.org/122/bluemind.html" target="_blank">in this book</a> by a marine biologist, all about our fascination with all things water and why it makes us happy. </span></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia9MHkPjuV_6wgGyEZH3k-wgKAhqi42Hmt1MYpJSqr2TPCBaOHUieftshkDvsqCnAz8U3Rwdjqkqk-dGj9bJoiZk6nhNklQACzzN-OiNtW0-uzaeWYtbwv5XXbC5LLt6FFZsqhDtUt2Ec/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="499" data-original-width="333" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia9MHkPjuV_6wgGyEZH3k-wgKAhqi42Hmt1MYpJSqr2TPCBaOHUieftshkDvsqCnAz8U3Rwdjqkqk-dGj9bJoiZk6nhNklQACzzN-OiNtW0-uzaeWYtbwv5XXbC5LLt6FFZsqhDtUt2Ec/w213-h320/image.png" width="213" /></a></div><br /><div style="text-align: left;">I am interested! It seems to me that the exploration of water, the experimenting and contemplating is carried by a comfort with water, the pleasure in being close to it. While we're enjoying water, waves of learning splash over us too!</div><div style="text-align: left;"><br /></div><div style="text-align: center;"><div>maggie and milly and molly and may</div><div>went down to the beach(to play one day)</div><div><br /></div><div>and maggie discovered a shell that sang</div><div>so sweetly she couldn't remember her troubles,and</div><div><br /></div><div>milly befriended a stranded star</div><div>whose rays five languid fingers were;</div><div><br /></div><div>and molly was chased by a horrible thing</div><div>which raced sideways while blowing bubbles:and</div><div><br /></div><div>may came home with a smooth round stone</div><div>as small as a world and as large as alone.</div><div><br /></div><div>For whatever we lose(like a you or a me)</div><div>it's always ourselves we find in the sea</div><div><br /></div><div>e.e. cummings</div></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><a href="https://twitter.com/MargKelpi/status/1328782716121341952" target="_blank">MB talked about</a> our attraction to water: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">And as well as all it does, it’s really good for us to touch the elements of nature. Water, sand, Earth, wood, pebbles etc. Think we are intrinsically drawn to it.</span></div><p></p><p><a href="https://twitter.com/mini_lebowski/status/1328774447935987714" target="_blank">Sarah also spoke about</a> the emotional power of water: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">When my son was born,he was always unsettled and barely slept. He didn't sleep through the night for four years. Water was the one thing that calmed him.He would immediately relax and was soothed. He's now 19 and still loves water. Water can be restorative as well as fascinating</span></p><p><a href="https://twitter.com/guidedlearning2/status/1328787770916016128" target="_blank">Maria</a>: <span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;">It's splishy, splashy fun! </span></p><p><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif" style="background-color: rgba(0, 0, 0, 0.03); color: #0f1419; font-size: 15px; white-space: pre-wrap;"><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif">"From one million miles away our planet resembles a small blue marble; from one hundred million miles it’s a tiny, pale blue dot. “How inappropriate to call this planet Earth when it is quite clearly Ocean” Arthur C. Clarke</span></span>, <a href="https://twitter.com/NMedina5/status/1328818326965989376" target="_blank">quoted by Nicole</a>. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7baKXIU4xHnzn3OMLUcC7odXIFXM2jbyXazqHQU3lPLP6CW6UHT0lNnn3qtqNv0EXgaokVfJS7-wJNUKLtc8yjXPGLsy9X2dMzam-36T445l4eIs6kE9FRWzUtSETKFYtBCOsY0_HZVA/s2048/446281366_f232d677b1_o.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="1536" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7baKXIU4xHnzn3OMLUcC7odXIFXM2jbyXazqHQU3lPLP6CW6UHT0lNnn3qtqNv0EXgaokVfJS7-wJNUKLtc8yjXPGLsy9X2dMzam-36T445l4eIs6kE9FRWzUtSETKFYtBCOsY0_HZVA/s320/446281366_f232d677b1_o.jpg" /></a></div><p>All this has of course made me only more keen to have water play as a big part of our provision for our 3, 4 and 5 year olds. This week we've had red strawberry-scented water, (a bit too) blue peppermint-scented water</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7eyx79pJjNXjSMpL9Y0O6rqKynlIYfl8zeDuA5TxCkuLJ80a1icP74H5ZM_o1vk56vshaHgY1nGxYvZlu_YgSgLaftWyfrdgDYxEwhYuM4Cwo4R74eXjKL-POp_CHAyTbmLD0bSY_xA8/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="510" data-original-width="680" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7eyx79pJjNXjSMpL9Y0O6rqKynlIYfl8zeDuA5TxCkuLJ80a1icP74H5ZM_o1vk56vshaHgY1nGxYvZlu_YgSgLaftWyfrdgDYxEwhYuM4Cwo4R74eXjKL-POp_CHAyTbmLD0bSY_xA8/" width="320" /></a></div><br /> and yellow lemon-scented water.<p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBzePw5o2hlt0AXs6_KsX679G73Ki7jQ8g_9BkjlUX8zajn96Ahuot-fkbvXxchyphenhyphen-CbPpt5emSAeZ5JaJ94TG4Sg9ZbDK-ic2L1Pd5XyB2MzF5O-2ZMuZ3fRv_7AVpSyQSoujQEp6wJ-4/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="510" data-original-width="680" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBzePw5o2hlt0AXs6_KsX679G73Ki7jQ8g_9BkjlUX8zajn96Ahuot-fkbvXxchyphenhyphen-CbPpt5emSAeZ5JaJ94TG4Sg9ZbDK-ic2L1Pd5XyB2MzF5O-2ZMuZ3fRv_7AVpSyQSoujQEp6wJ-4/" width="320" /></a></div>It's also made me want to watch closely, an see what it is that children are attending too, and experimenting with. </div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com1tag:blogger.com,1999:blog-3071719252136968205.post-91930187775505943162020-11-13T13:46:00.004-08:002020-11-13T13:46:47.234-08:00Mathematical joy!<p>Y is the youngest three year old in my class. Though she's becoming more comfortable at school each day, she is still tentative about joining in activities with other children, still holds back from lots. The other day she and I were in front of the big tin cans that hang so they can be hit with bamboo beaters. She watched as I beat out a rhythm on a can - and when I then held the beater out to her, she ran away.</p><p>But, when it comes to mathematics, she is in her element. She has a kind of exuberance, of joy playing with numbers and shapes.</p><p>I first noticed it when I'd put some Numicon out back in September. Steph - always upping the opportunities for mathematics! - added some jelly numbers. I was amazed when Y quickly matched up the Numicon pieces and the numbers, and seemed to be really enjoying it too!</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_KqRyzzYA0qC6_6WcJOo9rMvbnIyY7ILSMymbMeqToSm_JwpIygTUU_hWj0NNxMc0yMYynaEH4eQ-Vz_mxKsR2AjciFcjpz_zBcfzunqXG7zjV3JPcu-9xZCzGwnBLQQxXhZ9MknWawd4/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_KqRyzzYA0qC6_6WcJOo9rMvbnIyY7ILSMymbMeqToSm_JwpIygTUU_hWj0NNxMc0yMYynaEH4eQ-Vz_mxKsR2AjciFcjpz_zBcfzunqXG7zjV3JPcu-9xZCzGwnBLQQxXhZ9MknWawd4/" width="320" /></a></div><br />Doing some mathematics is one of the places Y seems to feel really comfortable alongside other students. Here she is on the left, arranging some of the dot stones:<p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dz1fVi2O9ZU-vXvSW3C3bFTrVYDyYQz4He1TlS378DvfHSITd5n8glHC-l6-Hjsfx8_NGmnesRAncaa42O_Uw' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div>And here she is in October with the same student, sorting the magnetic Numicon-type shapes:<div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHAuRM3imRV3mo3OY00xIyWW_YZzgXnwcI_keh4LJ6G6mIYEhR02oBOpbMc-XMmjpdGrVQkrMUBqfC_AdBYUr-5dm0Is3qxpZB0sZcn04JhJ03ofUldEUvfiYmH3LPpA8Jkxa9s7fhNWxt/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="830" data-original-width="1107" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHAuRM3imRV3mo3OY00xIyWW_YZzgXnwcI_keh4LJ6G6mIYEhR02oBOpbMc-XMmjpdGrVQkrMUBqfC_AdBYUr-5dm0Is3qxpZB0sZcn04JhJ03ofUldEUvfiYmH3LPpA8Jkxa9s7fhNWxt/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">I'm really pleased that she is happily sociable in her mathematical play. For her, but also for the others - to spread the mathematical joy!</div><div class="separator" style="clear: both; text-align: center;"><br /></div>Later in the day, she was at the board with another student, this time putting the pieces up and calling out the numbers as they did. Steph suggested they add the word 'Splat' which seems to give it a bit more drama, making it into more of a game:<br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dyiWNQRg_BslrB6nIweSQXN0srQXfmt03DdI42ckYtgHXBvDgVgUR28TQf9ZuU8DUGqyVHE-twtRbsXeNrKRQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><div>We've played this game quite a lot. Now, in November, she's changed it to be 'Splat, two fives!' as she puts a pair of pieces up with both hands. When it's 'Splat! Two twos!' it makes her laugh.</div><div><br /></div><div>It's evolving all the time. I brought a pen out and wrote some of the numbers yesterday, and she took the pen from me and enjoyed doing that too:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1yzoFT3yKYblQ8vb4Trg3KLrpdxt_JL_ATHqAWnaxGzE2QtwcvI_AhdnqJCsVXTWvf9GhhFiuWU7EFJj01my4Vdgy8-I0Mztp_uKZxcRKJIsVPsSYvAqjN6gWt6YR1shkyg64ZFSqEhC5/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1yzoFT3yKYblQ8vb4Trg3KLrpdxt_JL_ATHqAWnaxGzE2QtwcvI_AhdnqJCsVXTWvf9GhhFiuWU7EFJj01my4Vdgy8-I0Mztp_uKZxcRKJIsVPsSYvAqjN6gWt6YR1shkyg64ZFSqEhC5/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYaWRnfik0QRBMoh_dULVNK_P-04CnsFbE2zQLuj0s_SjQhOsxWct4ZqQ6-W6fPe6rYQheQIMtWPHH0fdeRi5w2csYydWr4KPLvSKIhHdNt6CTGv-LPHwE98vWY3YZ-bXlfxuxoKp-jVX7/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYaWRnfik0QRBMoh_dULVNK_P-04CnsFbE2zQLuj0s_SjQhOsxWct4ZqQ6-W6fPe6rYQheQIMtWPHH0fdeRi5w2csYydWr4KPLvSKIhHdNt6CTGv-LPHwE98vWY3YZ-bXlfxuxoKp-jVX7/" width="320" /></a></div></div>The idea of equality came up in the Numberblocks episode we watched, and as she was doing this, I was saying how the six and the four together are the same as, are equal to the ten. This might be something we develop more, depending how much it interests her.<br /><br /></div><div>Some thoughts:</div><div><ul style="text-align: left;"><li>Y's joy in all this is something precious. I don't want it to be dampened by taking any of this out of her hands. She is leading the way, sharing what she's doing with me, and I want to keep it that way.</li><li>Like I said, the sociability of her enthusiasm is a real asset for the whole class. In these mathematical moments she forgets any diffidence and is happy to take turns or work together with a partner. </li><li>I don't think it's important to go too much into the written symbols for numbers at this stage, but Y clearly has an interest in this, and I'm happy to respond to that too.</li><li>I'm really interested to see how her pleasure and understanding grow, and how it spreads through the class.</li></ul></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-74122578619211307062020-10-24T08:53:00.005-07:002020-10-24T10:49:28.243-07:00Seeing the mathematical: Filling<p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivg2IbsNL2bKot2SFHyMmMjSNMdObPWzpTRWHXsCdMfWBCn6tdp_YfkJTMvUo2Ea-rWxWO3PZwmoxWZlYjymwwBiyDJDts4MLhW_75KmdEP40wsm0F4oEGjzKcbC0wotbCpO6kzuJDEEs/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivg2IbsNL2bKot2SFHyMmMjSNMdObPWzpTRWHXsCdMfWBCn6tdp_YfkJTMvUo2Ea-rWxWO3PZwmoxWZlYjymwwBiyDJDts4MLhW_75KmdEP40wsm0F4oEGjzKcbC0wotbCpO6kzuJDEEs/" width="320" /></a></div></div></div><p></p><p>I'm teaching in PK this year. It's my first year teaching the 3 and 4 year olds! Luckily, I've got a wonderful team to work alongside, who I'm learning so much from, and who do a lot to compensate for gaps in my knowledge.</p><p>One of the things that intrigues me is what mathematics looks like at this age.</p><p>I don't know the full answer to this - does anyone?? - but I do know it doesn't look like it does later on. Here are some of its characteristics, from my point of view.</p><p>It's:</p><p></p><ul style="text-align: left;"><li>woven into all sorts of other activities - art, building, role play, small world play, block play;</li><li>not mainly about numbers or counting;</li><li>mostly expressed through spatial means, often with physical objects;</li><li>hardly ever symbolic (for instance, using the names and written symbols for numbers);</li><li>often something that happens for a few minutes and then it's over for now;</li><li>not about trying to remember anything;</li><li>difficult for us to see, or recognise as mathematics.</li></ul>We may not even recognise that we're not recognising it. It's a little like the way the substance of what becomes a tree enters the tree - not only are the roots underground, but the tiny root hairs where the uptake happens are hardly visible to us even when we dig. And, that's not all: most of what becomes trunk, branch, leaf, flower, fruit comes from the <i>air</i>, entering the tree through tiny holes in the leaves. It certainly doesn't arrive as wood in any way! And what does enter the tree - the carbon dioxide, the water, the minerals - doesn't enter in any obvious way - it enters through a million invisible doorways.<p></p><p>What are the tiny mathematical doorways for young children?</p><p>I came across an interesting list <a href="https://www.hbook.com/?detailStory=five-questions-for-grace-lin-2020" target="_blank">in an interview with author Grace Ling</a>:</p><blockquote>'I think the biggest challenge was to get out of the mind frame that “math is numbers.” I kept thinking it had to be kids counting, but after many talks with Marlene Kliman, a senior scientist and math specialist at TERC, she really opened my eyes to how we use math without even knowing it — sorting, sharing, comparing, finding, waiting.'</blockquote>I was particularly struck by a couple of those items. <i>Finding </i>for instance - how does that link to mathematics? When I tweeted her that as a question, <a href="https://twitter.com/pacylin/status/1316504716168364037" target="_blank">Grace answered</a>, 'I mentioned finding because in “What Will Fit?” Olivia finds something to fit her basket.'<div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFPpHItxhrg1WnTI1y6BUkJPxDJNa3-oo_Uo76KLbpnLZbln7QXYikGU5ijVmOJG_0ha0oK1PT_NkbGuHwEsYLqO1sz45BkLWsNJrHTGYhceTZULAG0sjTNTEPCytrS-E5QDKvJQGmrCE/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="1064" data-original-width="1052" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFPpHItxhrg1WnTI1y6BUkJPxDJNa3-oo_Uo76KLbpnLZbln7QXYikGU5ijVmOJG_0ha0oK1PT_NkbGuHwEsYLqO1sz45BkLWsNJrHTGYhceTZULAG0sjTNTEPCytrS-E5QDKvJQGmrCE/" width="237" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>What Will Fit?</i> - one of Grace Lin's <i>Storytelling Math </i>books</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzW0nHEXIpfoK8t2TxXzr9_QgwOKllAtyp2jj88c_1CwGZC7I3WqR7-f2lJti8w15NAMk_B6HfWdbC3TcDAM-Mrb92kJ7BJt-htMj_G3YkBPtPh9T7Dky5hlYDRBDzz-30znJ9_Xsfptw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="427" data-original-width="861" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzW0nHEXIpfoK8t2TxXzr9_QgwOKllAtyp2jj88c_1CwGZC7I3WqR7-f2lJti8w15NAMk_B6HfWdbC3TcDAM-Mrb92kJ7BJt-htMj_G3YkBPtPh9T7Dky5hlYDRBDzz-30znJ9_Xsfptw/w400-h199/image.png" width="400" /></a></div>Yes, and <i>finding</i> because:</div><div><span class="css-901oao css-16my406 r-4qtqp9 r-ip8ujx r-sjv1od r-zw8f10 r-bnwqim r-h9hxbl" dir="auto" face="system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Ubuntu, "Helvetica Neue", sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #14171a; display: inline-block; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; height: 1em; line-height: inherit; margin: 0px 0.075em; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap; width: 1.2em;"><div aria-label="Basket" class="r-xoduu5 r-1mlwlqe r-1d2f490 r-1udh08x r-u8s1d r-h9hxbl r-417010 css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 1.2em; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; width: 1.2em; z-index: 0;" title="Basket"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-x3cy2q r-1p0dtai r-xoduu5 r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://abs-0.twimg.com/emoji/v2/svg/1f9fa.svg"); background-position: 50% 50%; background-repeat: no-repeat; background-size: 100% 100%; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 17.9977px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;"></div><img alt="Basket" class="css-9pa8cd" draggable="false" src="https://abs-0.twimg.com/emoji/v2/svg/1f9fa.svg" style="bottom: 0px; height: 17.9977px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;" /></div></span>She has set herself a task;</div><div><span class="css-901oao css-16my406 r-4qtqp9 r-ip8ujx r-sjv1od r-zw8f10 r-bnwqim r-h9hxbl" dir="auto" face="system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Ubuntu, "Helvetica Neue", sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #14171a; display: inline-block; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; height: 1em; line-height: inherit; margin: 0px 0.075em; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap; width: 1.2em;"><div aria-label="Basket" class="r-xoduu5 r-1mlwlqe r-1d2f490 r-1udh08x r-u8s1d r-h9hxbl r-417010 css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 1.2em; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; width: 1.2em; z-index: 0;" title="Basket"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-x3cy2q r-1p0dtai r-xoduu5 r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://abs-0.twimg.com/emoji/v2/svg/1f9fa.svg"); background-position: 50% 50%; background-repeat: no-repeat; background-size: 100% 100%; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 17.9977px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;"></div><img alt="Basket" class="css-9pa8cd" draggable="false" src="https://abs-0.twimg.com/emoji/v2/svg/1f9fa.svg" style="bottom: 0px; height: 17.9977px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;" /></div></span>She has set herself constraints;</div><div><span class="css-901oao css-16my406 r-4qtqp9 r-ip8ujx r-sjv1od r-zw8f10 r-bnwqim r-h9hxbl" dir="auto" face="system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Ubuntu, "Helvetica Neue", sans-serif" style="background-color: rgba(0, 0, 0, 0.03); border: 0px solid black; box-sizing: border-box; color: #14171a; display: inline-block; font-size: 15px; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; height: 1em; line-height: inherit; margin: 0px 0.075em; overflow-wrap: break-word; padding: 0px; position: relative; white-space: pre-wrap; width: 1.2em;"><div aria-label="Basket" class="r-xoduu5 r-1mlwlqe r-1d2f490 r-1udh08x r-u8s1d r-h9hxbl r-417010 css-1dbjc4n" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; border: 0px solid black; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 1.2em; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; overflow: hidden; padding: 0px; position: absolute; width: 1.2em; z-index: 0;" title="Basket"><div class="css-1dbjc4n r-1niwhzg r-vvn4in r-u6sd8q r-x3cy2q r-1p0dtai r-xoduu5 r-1pi2tsx r-1d2f490 r-u8s1d r-zchlnj r-ipm5af r-13qz1uu r-1wyyakw" style="-webkit-box-align: stretch; -webkit-box-direction: normal; -webkit-box-orient: vertical; align-items: stretch; background-color: rgba(0, 0, 0, 0); background-image: url("https://abs-0.twimg.com/emoji/v2/svg/1f9fa.svg"); background-position: 50% 50%; background-repeat: no-repeat; background-size: 100% 100%; border: 0px solid black; bottom: 0px; box-sizing: border-box; display: inline-flex; flex-basis: auto; flex-direction: column; flex-shrink: 0; height: 17.9977px; left: 0px; margin: 0px; min-height: 0px; min-width: 0px; padding: 0px; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;"></div><img alt="Basket" class="css-9pa8cd" draggable="false" src="https://abs-0.twimg.com/emoji/v2/svg/1f9fa.svg" style="bottom: 0px; height: 17.9977px; left: 0px; opacity: 0; position: absolute; right: 0px; top: 0px; width: 17.9977px; z-index: -1;" /></div></span>She has a way of measuring whether what she finds will fit the constraints.</div><div>This is especially mathematical in my view, because she has her own inquiry that she is following through on.<br /><div><br /></div><div>In this case, the finding has to do with the size of the pumpkin - that it fits in the basket. There are no numbers involved. Here it's continuous magnitudes that are important, and these manifest themselves by a kind of comparison - does it fit in the basket? (My post on continuous magnitudes is <a href="http://followinglearning.blogspot.com/2019/03/magnitude.html" target="_blank">here</a>.)</div><div><div><br /></div><div>Do we recognise this kind of fitting as mathematics?</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKgmoT13cXQxG9b4lQ0Up4XvGBufzjfGwJ8iUDGdmYj26enat7BtX5aYKYa7t9q7ePpTtGlDP7M_0R9L7LQ9lYVqAp87DkzNuQU3_rblAfp-n3vlUSlUZyBO_EAzTykD1h7zDpE9xM5_Y/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKgmoT13cXQxG9b4lQ0Up4XvGBufzjfGwJ8iUDGdmYj26enat7BtX5aYKYa7t9q7ePpTtGlDP7M_0R9L7LQ9lYVqAp87DkzNuQU3_rblAfp-n3vlUSlUZyBO_EAzTykD1h7zDpE9xM5_Y/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">I like blogging about this, because it helps me to get my thinking clearer - to focus in on the mathematics. Fitting in the pumpkin-in-basket case is about filling. <i>Filling</i> seems to link closely with the play schema of <i>enclosing</i>. There's a boundary and you put things inside it. With filling, we often want to completely fill up to the boundary, to fit in as much as possible. Sometimes, we dispense with the boundary, and just try to cover the space without leaving any gaps.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We do a lot of filling in our classes:</div><div class="separator" style="clear: both;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDRzUSTJbAbS6r68OifCaIUUuNHeG2iK-u08SGgx71WIV3U9QvMl5rU7FlmiNf0JzLDs3ECsozGc4eVEUvkAY7Py9xX7m_nCS9zUyO7cDY_jhpqWSAtW8Xwe1rMyUMBzUNT4QbT64TkiA/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="830" data-original-width="1107" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDRzUSTJbAbS6r68OifCaIUUuNHeG2iK-u08SGgx71WIV3U9QvMl5rU7FlmiNf0JzLDs3ECsozGc4eVEUvkAY7Py9xX7m_nCS9zUyO7cDY_jhpqWSAtW8Xwe1rMyUMBzUNT4QbT64TkiA/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling a peg board<br /></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCjsN1e3AOEbajfN4b-syi6vHnxrDjF77BP9-YSz3ppLdTPL_cGeyWsqQRndfkYwinOZAd90JGA_tTXCFPN266F24yNpjsj0v4dwq3OUqOCq273CVo1qU4hdiVxyK_c9SrNZLdyvHkjrM/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="686" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCjsN1e3AOEbajfN4b-syi6vHnxrDjF77BP9-YSz3ppLdTPL_cGeyWsqQRndfkYwinOZAd90JGA_tTXCFPN266F24yNpjsj0v4dwq3OUqOCq273CVo1qU4hdiVxyK_c9SrNZLdyvHkjrM/" width="180" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling containers with water</td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaL9jTrA4tufdcW6lxMxgqvF-iFizYiCAhmQPe9r_jVwZF7DcW37VP3BFcUnRk2w-C4n_C0xClcF92G7wGkijVlb06BjEEWRCATGz2nAS3OuvqMdPS4oEYqq93k4J4R-nhVFSRhzGlhA4/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaL9jTrA4tufdcW6lxMxgqvF-iFizYiCAhmQPe9r_jVwZF7DcW37VP3BFcUnRk2w-C4n_C0xClcF92G7wGkijVlb06BjEEWRCATGz2nAS3OuvqMdPS4oEYqq93k4J4R-nhVFSRhzGlhA4/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling 20 cm square trays with square tiles</td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe8gTqvTACrSQdb0aeskntvpXdZbY2_eRIub0J58E7jmafrimlhyphenhyphen0NvxF1rrAfL2cazJPrdDjGoPKlWfQuEbxSwyB7z4EWjWHg6i6L-Q3XwE9Z1fm_3PZ7i1vy32nE4-BbJejbdgrxY5U/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe8gTqvTACrSQdb0aeskntvpXdZbY2_eRIub0J58E7jmafrimlhyphenhyphen0NvxF1rrAfL2cazJPrdDjGoPKlWfQuEbxSwyB7z4EWjWHg6i6L-Q3XwE9Z1fm_3PZ7i1vy32nE4-BbJejbdgrxY5U/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling space without gaps with magnetic Polydron triangles</td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXz0hoqyjZCTH9VcQbByMzNmedsjNiXWM-oSFRHUNHRIb2Se2CYioyvKe174dPPMn4qIVKJw42ILP7YzlLKdZy5d4vTuHlku9OZcJJpnQboBhKuis5GEMU03LtTB9T2bML5uC6PP7zCOI/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXz0hoqyjZCTH9VcQbByMzNmedsjNiXWM-oSFRHUNHRIb2Se2CYioyvKe174dPPMn4qIVKJw42ILP7YzlLKdZy5d4vTuHlku9OZcJJpnQboBhKuis5GEMU03LtTB9T2bML5uC6PP7zCOI/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling triangular holes with pattern blocks<br /></td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjq-mHNEdNr9sTJptS-ztAoISlYgkjGoedLD5UX2iBsEmmO2ExKblqGYwOTenfbiJqUcFH2ni9AqFP8SSwrNpOySRQcjWdHwbc1BCpALq7MT-5iwZfUDB-J2gCHlzor35IArUNMaxYYgA/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjq-mHNEdNr9sTJptS-ztAoISlYgkjGoedLD5UX2iBsEmmO2ExKblqGYwOTenfbiJqUcFH2ni9AqFP8SSwrNpOySRQcjWdHwbc1BCpALq7MT-5iwZfUDB-J2gCHlzor35IArUNMaxYYgA/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling a square tray with Tangram pieces<br /></td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQOxIwI1ua73YEeOCGxEsDmXQAaWb5xfb1vrGZSqzZMbqKNla0TWBG_WtLIeFP86s7jKEBA6Wxykz3qDl0CCJKSHtdLeKfHTUj4_SBDMztSSmfAru8MKzar_g41KOB7kScjp_Nr2sbe_Y/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQOxIwI1ua73YEeOCGxEsDmXQAaWb5xfb1vrGZSqzZMbqKNla0TWBG_WtLIeFP86s7jKEBA6Wxykz3qDl0CCJKSHtdLeKfHTUj4_SBDMztSSmfAru8MKzar_g41KOB7kScjp_Nr2sbe_Y/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling a chessboard with glass pebbles<br /></td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK5f8EncwqbbdYsWOvGF8TSVSgMwRCYa8fMIB9JgUyETrLhh3LN3CVra5AuFNSrmMAo1VRpCobDliHB2XhGvEZ8zE7bMvcJjgU2Dp8FBQSQ_kpsnxEpOuuUqH3wvf5jKCO9ku21cq-GRY/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="915" data-original-width="1220" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK5f8EncwqbbdYsWOvGF8TSVSgMwRCYa8fMIB9JgUyETrLhh3LN3CVra5AuFNSrmMAo1VRpCobDliHB2XhGvEZ8zE7bMvcJjgU2Dp8FBQSQ_kpsnxEpOuuUqH3wvf5jKCO9ku21cq-GRY/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Filling a Numicon board<br /></td></tr></tbody></table><div style="text-align: left;">What are some of the qualities of the mathematics here? </div><div style="text-align: left;"><ul style="text-align: left;"><li>There's a rigidity in the frame, just as there was to the basket that had to fit the pumpkin, or sometimes in the way the pieces fit together - that is: there are <i>constraints</i>;</li><li>There is also <i>freedom </i>- the space can often be filled in a variety of ways. Take this last image of the Numicon. The student chose to try and fill with the light blue "2" pieces and the orange "1" pieces (we talked about them as 2s and 1s) until these ran out. Another time she tried with other pieces. She's also thinking a little about symmetry;</li><li>There's often a kind of beauty to the finished product;</li><li>The activity is often quite abstract - it doesn't have to link with a narrative. Children get used to abstraction;</li><li>The activity is about equivalence, equality - all the parts add up to the whole; and the different ways of filling are equivalent to each other;</li><li>There are discrete or continuous magnitudes involved - for instance the number of holes in the Numicon pieces or the space they occupy;</li><li>As well as the final product, there's a process, and the process could be different for the same end product - for instance in the way pegs are added to a pegboard: some students go round the edge first, some start in the middle, some fill randomly. There's time during the process for conversation, and comment on what's being done;</li><li>Where there's a boundary, there's usually a clear end point - when it can be seen there's no more space. The product, or a photo of it, is an object that can be celebrated, discussed and reflected on. Is there a pattern, symmetry? How is the student's work developing?</li></ul></div><div style="text-align: left;">At the moment, it's hard for me to do the conversation part much. Most of my children have English as second or third language. Sometimes I'm talking to Spanish speakers in French. But a lot is communicated about the students' intentions in the choices they make during the fitting and filling.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">There's probably a lot more to this than I've listed, but already that's quite a lot. A look at the overarching concepts referred to in the Diploma Program (for the 16-18 year olds) of the International Baccalaureate shows surprising links. Or, perhaps they shouldn't be surprising, since the more conceptual we get, the more generality:</div></div><ul style="text-align: left;"><li>approximation, </li><li>change,</li><li>equivalence,</li><li>generalisation,</li><li>modelling,</li><li>patterns,</li><li>quantity,</li><li>relationships,</li><li>representation,</li><li>space,</li><li>systems,</li><li>validity</li></ul><div>Which ones might crop up in <i>filling</i>?</div><div><br /></div><div>The ones that jump out to me are equivalence, patterns, quantity and space.</div><div><br /></div><div>Children aren't necessarily articulating anything about these yet, but they are nevertheless thinking mathematically as they construct examples, thinking for instance implicitly about equivalence. When we ask 5 year olds to make this more explicit, the background they've had of experiencing equal areas filled makes this a small step:</div><div style="text-align: center;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_o0IN_cbT599vjVEK1ozRf5pldlnlzd4rNqzMHqwOJ5eBEwSb3B6RpRyE4gysvMnSlOYpRWJna4mhVHwvtmpCsSf67mbEXdi5MOKYAqZpF7LDeKPGqbK4wcKzex3MUxnJE2hfH9GoPaY/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="600" data-original-width="800" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_o0IN_cbT599vjVEK1ozRf5pldlnlzd4rNqzMHqwOJ5eBEwSb3B6RpRyE4gysvMnSlOYpRWJna4mhVHwvtmpCsSf67mbEXdi5MOKYAqZpF7LDeKPGqbK4wcKzex3MUxnJE2hfH9GoPaY/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Equal-area Cuisenaire rods<br /></td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3rRjxyKdeUoPhYXzUbb4f5uZzYWeCpF6SvVUa3bLB9OSHbNgNjbyHEQ5TqVf-xfHAsOSJQBB9dvP_J3f39rFyA-4zvFMiFKRcSixy3FeghU4Kr-EHE0lChdmlvGQSbFFggbJgYRgNmJo/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="505" data-original-width="900" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3rRjxyKdeUoPhYXzUbb4f5uZzYWeCpF6SvVUa3bLB9OSHbNgNjbyHEQ5TqVf-xfHAsOSJQBB9dvP_J3f39rFyA-4zvFMiFKRcSixy3FeghU4Kr-EHE0lChdmlvGQSbFFggbJgYRgNmJo/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Equal area pattern blocks<br /></td></tr></tbody></table></div></div></div></div></div></div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com7tag:blogger.com,1999:blog-3071719252136968205.post-64270955531643805322020-10-20T13:03:00.002-07:002020-10-21T02:14:46.822-07:00Positioning and enclosing<p>I often find it hard to fit the play and creation of my students into an overall map of development. Is this not something that's possible? Perhaps we have to trust that a rich ecosystem of experiences, play and creation will provide the environment for all the learning that needs to take place? In all this, can we identify thresholds, turning points, key moments? I don't know. Perhaps it's best to try and document and ponder certain things students are giving time to, having success with?</p><p>Here's a kind of success story. Though I'm not sure if I can discern a story arc in it, we could call it a months-long high point:</p><p>One of my 3 year old students is finding it hard to get used to life in school. One of her 'safe spaces' is to sit and paint or draw a picture. Here are some of her drawings:</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2G3vG_Wr5lAUVvkcySss-o1GTVG2_BZUsuSnrXmM2ZQHqXOTB8zAJ3Dc3qhcsgVcjwONzCCp1Y1msQovUwyZ7VpFBEg73jZgL6Bh4aUdBwoNm0fb7JdNPbpQ4lLZNiLuMemGNSipIrZM/s512/drawing.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="387" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2G3vG_Wr5lAUVvkcySss-o1GTVG2_BZUsuSnrXmM2ZQHqXOTB8zAJ3Dc3qhcsgVcjwONzCCp1Y1msQovUwyZ7VpFBEg73jZgL6Bh4aUdBwoNm0fb7JdNPbpQ4lLZNiLuMemGNSipIrZM/s320/drawing.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">She takes her time with them, often watching what's happening in the classroom from the vantage point of her creation. This one above is an early example. To me it's fascinating: how she has divided up the paper into sections with the orange lines and then experimented with dots in lines, dots in circles, circle parts, dots in groups, scribbly lines. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiY725NW-QYneL8xDiRs39JP1I7CKGeWKNpPPpuFsu2dax1v3S25pNNf7imjZ7hM1GZ53zUkyxJs7qFUL_FO3ZEA7cXgQruZLgp77CVe2tTXDhYTB0IqOcRnG_HCa5Y3aBc8KF5T6cddgs/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1247" data-original-width="1661" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiY725NW-QYneL8xDiRs39JP1I7CKGeWKNpPPpuFsu2dax1v3S25pNNf7imjZ7hM1GZ53zUkyxJs7qFUL_FO3ZEA7cXgQruZLgp77CVe2tTXDhYTB0IqOcRnG_HCa5Y3aBc8KF5T6cddgs/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">She has a stencil here and she's adding areas of black using the stencil, on top of the orange and black lines and areas that she's already laid down.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhni2rpWDp_RAGEFDChCHjTX0sc9pXARFUpb5Zl3K7-8pgIHFqk0leZygDWCTDlZrt3q_ZMsL-9qPBhlyh_2xan0hKM1db4TwDbhFAUbDKXNZrUkjLH1EiyHt5WxFFr0EBxnP0BdK8_UZY/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="976" data-original-width="1548" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhni2rpWDp_RAGEFDChCHjTX0sc9pXARFUpb5Zl3K7-8pgIHFqk0leZygDWCTDlZrt3q_ZMsL-9qPBhlyh_2xan0hKM1db4TwDbhFAUbDKXNZrUkjLH1EiyHt5WxFFr0EBxnP0BdK8_UZY/" width="320" /></a></div><div style="text-align: left;">There's a discipline in her investigations. This one has stuck to roughly oval areas of colour each separated from the other.</div><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMemJAppX3cPPZdlS0QWjanyLEJjPyh_6NzE1GHUk7sOsiXa_umhTPZUUpiWqX40vWUKEuhwkFjTjAzLk1WZcX6SUcXPoIXkY1nTv3MlCupY5PrsEsdfqy93iQ1H3tpQQMKAvbs9zrgk/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="810" data-original-width="1080" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUMemJAppX3cPPZdlS0QWjanyLEJjPyh_6NzE1GHUk7sOsiXa_umhTPZUUpiWqX40vWUKEuhwkFjTjAzLk1WZcX6SUcXPoIXkY1nTv3MlCupY5PrsEsdfqy93iQ1H3tpQQMKAvbs9zrgk/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Here she has created her circular areas with dramatic movements of the pen, and then has carefully filled them with red.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMIrbFnHVLgEQf8kj_VXQ2l9nD1ZT9NFa0p1KNpDGqccQ9HojROC9IZPsnjW00pGidoWqDLZOFj97D4mO9eVXLkzAd1DZe-LG50swEt9JKlwhIVH255-xES_EIKnDp_fCyAF-x434xRMw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="979" data-original-width="1305" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMIrbFnHVLgEQf8kj_VXQ2l9nD1ZT9NFa0p1KNpDGqccQ9HojROC9IZPsnjW00pGidoWqDLZOFj97D4mO9eVXLkzAd1DZe-LG50swEt9JKlwhIVH255-xES_EIKnDp_fCyAF-x434xRMw/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">More wild movement and careful colouring. I wish I could ask her about her pictures but we only share a few words of English. I'm left to interpret them myself, and, who knows? I'm likely to be missing things. But I see a concern with positioning elements, with spacing them out on the paper. Also a balance of wild and careful, of pen stroke and filled colour.</div><div class="separator" style="clear: both; text-align: center;"><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw3Vkba2g4rHbXxLVLV7g42LGSyegRTSxAQvluJ_J5774GrBk0ZZ_lrPsYgMkTlvA2_KMLOTHuanGltgmNAtCi1QtG4kOGzVdpouQaNg15tP7ds03OiWNnLReHdJD8vCi3uuJUonRGVSc/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="675" data-original-width="900" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw3Vkba2g4rHbXxLVLV7g42LGSyegRTSxAQvluJ_J5774GrBk0ZZ_lrPsYgMkTlvA2_KMLOTHuanGltgmNAtCi1QtG4kOGzVdpouQaNg15tP7ds03OiWNnLReHdJD8vCi3uuJUonRGVSc/" width="320" /></a></div><div style="text-align: left;">This one surprised me - hands! She'd done this after I'd been cutting out outlines of my hands to record ways that we could hold up three fingers.</div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQrIR-oha81v1_wlwxJJ6h3qHEB_v22RsRAwImAgZ76NRN8VNFkla9YiTW2-CrBv_C5ftXX75aolO6h7ig6epU2Mis53v63QluIml3QBiTLXOE6sieUSbpRA7twM9dAibhnJ-f6sfCgHA/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1536" data-original-width="2048" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQrIR-oha81v1_wlwxJJ6h3qHEB_v22RsRAwImAgZ76NRN8VNFkla9YiTW2-CrBv_C5ftXX75aolO6h7ig6epU2Mis53v63QluIml3QBiTLXOE6sieUSbpRA7twM9dAibhnJ-f6sfCgHA/" width="320" /></a></div><div style="text-align: left;">She and another student caught the offcuts as I cut and made sure they went in the bin! I didn't imagine she would take the idea into her drawings.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">How do I "assess" this? What development is there?</div><div style="text-align: left;"><br /></div><div style="text-align: left;">I think the answer is that I'm in no hurry for any development. This exploration seems so beautiful, so complete as it is. I wish it was all in one book. I'd love to be able to talk about the images. I'm glad I've got photos of many of them, before she folded them so that they'd fit in her bag to take home.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">How do we analyse work like this? I'm not sure. The play schemas give us some small handle:</div></div></div></div></div></div><ul style="text-align: left;"><li>Transporting</li><li>Enveloping</li><li>Enclosing</li><li>Trajectory</li><li>Rotation</li><li>Connecting</li><li>Positioning</li><li>Transforming</li></ul><div>Which do you see in these drawings? I see a lot of concern with positioning, and some with enclosing. Add in a little rotation and connecting. But this hasn't taken me a lot further. It does help me to see how drawing links with other learning, opens my eyes to possible connections.</div><div><br /></div><div>I'm pretty sure there will be development. I don't expect it to follow an obvious path - I can't predict how it will go. Will she keep that fine balance between the wild scribble and the careful positioning and filling? Will she continue to take her time on each piece? I hope so. </div>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0tag:blogger.com,1999:blog-3071719252136968205.post-54150591107169189752020-09-24T02:08:00.008-07:002020-09-24T02:12:53.781-07:00The Gardener and the Carpenter<p>I've just discovered the work of Alison Gopnik, and it's very interesting. These two paragraphs from<a href="https://www.theguardian.com/books/2016/aug/17/gardener-and-the-carpenter-by-alison-gopnik-review" target="_blank"> a review of her book</a> <i>The Gardener and the Carpenter</i> jumped out at me:</p><p style="color: #121212; font-family: "Guardian Text Egyptian Web", Georgia, serif; font-size: 17px; font-variant-ligatures: common-ligatures; margin: 0px 0px 1rem; padding: 0px; text-align: left;"><span class="drop-cap" style="box-sizing: border-box; color: #6b5840; display: inline-block; float: left; font-family: "Guardian Egyptian Web", Georgia, serif; height: 5rem; margin-right: 0.3125rem; padding-top: 0.0625rem; text-transform: uppercase;"><span class="drop-cap__inner" style="background-color: #fff2cc; display: inline-block; font-size: 6.8125rem; font-weight: 700; line-height: 4.6875rem; vertical-align: text-top;">I</span></span></p><span style="background-color: #fff2cc; color: #121212; font-family: "Guardian Text Egyptian Web", Georgia, serif; font-size: 17px; font-variant-ligatures: common-ligatures;">n 2011, a team of psychologists did an experiment with some preschool children. The scientists gave the children a toy made of many plastic tubes, each with a different function: one squeaked, one lit up, one made music and the final tube had a hidden mirror. With half the children, an experimenter came into the room and bumped – apparently accidentally – into the tube that squeaked. “Oops!” she said. With the other children, the scientist acted more deliberately, like a teacher. “Oh look at my neat toy! Let me show you how it works,” she said while purposely pressing the beeper. The children were then left alone to play with the toy.</span><br /><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><aside class="element element-rich-link element--thumbnail element-rich-link--upgraded" data-component="rich-link" data-link-name="rich-link-1 | 1" style="clear: left; color: #121212; float: left; font-family: "Guardian Text Egyptian Web", Georgia, serif; font-size: 17px; font-variant-ligatures: common-ligatures; margin: 0.3125rem 1.25rem 0.75rem -10rem; text-align: left; width: 8.75rem;"><div class="rich-link tone-news--item rich-link--pillar-news" style="margin: 0px; overflow: hidden; position: relative;"><div class="rich-link__container" style="position: relative;"><div class="rich-link__header" style="box-sizing: border-box; font-family: "Guardian Egyptian Web", Georgia, serif; font-size: 0.875rem; line-height: 1.0625rem; min-height: 2.25rem; padding: 0.125rem 0.3125rem 0.5em;"><h2 class="rich-link__title" style="font: inherit; margin: 0px; padding: 0px;"><br /></h2></div></div></div></aside></blockquote><p style="color: #121212; font-family: "Guardian Text Egyptian Web", Georgia, serif; font-size: 17px; font-variant-ligatures: common-ligatures; margin: 0px 0px 1rem; padding: 0px; text-align: left;"><span style="background-color: #fff2cc;"><br /></span></p><p style="color: #121212; font-family: "Guardian Text Egyptian Web", Georgia, serif; font-size: 17px; font-variant-ligatures: common-ligatures; margin: 0px 0px 1rem; padding: 0px; text-align: left;"><span style="background-color: #fff2cc;">In the “accidental” group, the children freely played with the toy in various random ways. Through experimenting, they discovered all the different functions of the tubes: the light, the music, the mirror. The other group, the children who had been deliberately taught how to use the toy by the teacher, played with it in a much more limited and repetitive way. They squeaked the beeper over and over again, never discovering all the other things the toy could do.</span></p><aside class="element element-rich-link element--thumbnail element-rich-link--upgraded" data-component="rich-link" data-link-name="rich-link-1 | 1" style="clear: left; color: #121212; float: left; font-family: "Guardian Text Egyptian Web", Georgia, serif; font-size: 17px; font-variant-ligatures: common-ligatures; margin: 0.3125rem 1.25rem 0.75rem -10rem; text-align: left; width: 8.75rem;"><div class="rich-link tone-news--item rich-link--pillar-news" style="margin: 0px; overflow: hidden; position: relative;"><div class="rich-link__container" style="position: relative;"><a aria-label="Tears, tantrums and other experiments" class="rich-link__link u-faux-block-link__overlay" href="https://www.theguardian.com/education/2000/jan/26/parents.familyandrelationships" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; bottom: 0px; cursor: pointer; left: 0px; opacity: 0; overflow: hidden; position: absolute; right: 0px; text-decoration-line: none; text-indent: 200%; top: 0px; touch-action: manipulation; white-space: nowrap; z-index: 0;"></a></div></div></aside><p>For us teachers, this is momentous. Just by the act of 'being a teacher', in the sense of demonstrating something, we can close something down.</p><p>Here's another similar experiment <a href="https://youtu.be/lUl0EG3hDVU?t=2754" target="_blank">from a talk</a> by Alison Gopnik. (I suggest you just watch to the end of the part about the Thingamibob experiment and variations, or maybe carry on a bit to listen to implications.)</p>
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<div><br /></div><div>Two things come out of this: the impressive causal reasoning of three and four year old children, and how the stance of the adult ('clueless' or knowledgeable) influences whether children bring their powers to bear on the subject.</div><div><br /></div><div>I'm still trying to work out what this means exactly for us teachers, especially us teachers of young children, but teachers of all ages - and I'd be interested in your thoughts.</div><div><br /></div><div>So - I haven't read the book yet - I think the distinction between the gardener and the carpenter, is that a gardener creates conditions for the shaping of the garden (the plants themselves will create the garden), whereas the carpenter does all the work on the wood, shaping it themselves.</div><div><br /></div><div>This reminds me of Socrates, who said his mother was a midwife and his father was a sculptor, and that he aimed in his conversations to be more like the midwife, to help his conversation partners to bring to birth their own ideas.</div><div><br /></div><div>There's this thing called Socratic Ignorance. Partly it seems to be a genuine understanding of the limits of our knowledge, partly a device for getting back to the 'clueless' way of operating in a conversation. For instance this, edited for brevity from the beginning of the <a href="http://classics.mit.edu/Plato/meno.html" target="_blank"><i>Meno dialogue</i></a>:</div><div><br /></div><div><b style="background-color: #ffffcc;">Meno: </b><span style="background-color: #ffffcc;">Can you tell me, Socrates, whether virtue is acquired </span><a name="16" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">by teaching or by practice; or if neither by teaching nor practice, then </span><a name="17" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">whether it comes to man by nature, or in what other </span><a name="18" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">way?</span></div><div><span style="background-color: #ffffcc;"><br /></span></div><div><b style="background-color: #ffffcc;">Socrates (edited to keep the quote short):</b><span style="background-color: #ffffcc;"> </span><span style="background-color: #ffffcc;"> ...</span><span style="background-color: #ffffcc;">And I myself, </span><a name="35" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">Meno, </span><span style="background-color: #ffffcc;">confess with shame that I know literally nothing about </span><a name="37" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">virtue...</span></div><div><br /></div><div><b style="background-color: #ffffcc;">Meno:</b><span style="background-color: #ffffcc;"> No, Indeed. But are you in earnest, Socrates, in saying </span><a name="42" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">that you do not know what virtue is? And am I to carry back this report </span><a name="43" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">of you to Thessaly?</span><a name="44" style="background-color: #ffffcc;"></a><br style="background-color: #ffffcc;" /><br style="background-color: #ffffcc;" /><b style="background-color: #ffffcc;">Socrates:</b><span style="background-color: #ffffcc;"> Not only that, my dear boy, but you may say further </span><a name="45" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">that I have never known of any one else who did, in my </span><a name="46" style="background-color: #ffffcc;"></a><span style="background-color: #ffffcc;">judgment.</span><a name="47" style="background-color: #ffffcc;"></a><br style="background-color: #ffffcc;" /><br style="background-color: #ffffcc;" />So, lots to think about.</div><div><br /></div><div>I recommend this TED talk by Alison Gopnik too:</div><div><br /></div>
<iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="394" src="https://www.youtube.com/embed/cplaWsiu7Yg" width="700"></iframe>Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.com0