As my teaching evolves to start with students' thinking and talking, I'm usually beginning my hour long maths lessons with routines that encourage these things. Here are five favourites:
Quick Dot ImagesSee this by Steve Wyborney. I show an image quickly, then show it a second time; the idea is that almost all students should be able to have seen how many dots there are. But the interesting thing is not how many, but how. Students really like sharing their ways. And the message is: this is something you can do your way; you didn't need to be told how to see this. And - your way is worth sharing.
|Students like to do the annotating themselves.|
Often I do it: to speed things up, and to model revoicing.
Which One Doesn’t Belong
Christopher Danielson got the ball rolling with this. Since then, Mary Bourassa has done a great job of collecting WODBs together at wodb.ca . I've blogged about them a while back, and recently.
The idea is that you can justify the choice of any of the four items as the odd one out.
EstimateStudents write three numbers on a blank number line on their whiteboard, one too big, one too small and as close as you can (Graham Fletcher has some; these can be extended into whole lesson activities which are great modelling activities - and then of course there’s our regular, estimation180).
Estimation is such a key skill that we've also devoted some blogging time to it, with each student making their own estimation challenge.
See, think, wonder
Last year it was notice and wonder, but I like the differentiation of notice into see and think, and feel it's worth distinguishing the two. (Both are brilliant though!) I'm reading Making Thinking Visible, and this is one of their routines.
The point is just to present an image and see what people see, preferably recording it all.
|This one developed into a really interesting debate|
I've also adapted this to be what equations do you see, often presenting an image of Cuisenaire rods:
Counting CirclesI've blogged about this before. The idea is to count from different starting points, with different jumps. We do it round in a circle. Then we stop, and think about what the number three or four jumps on would be. Students share how they know.
I haven't used these yet, but this is a great idea, and Nat Banting is developing a really useful site with lots of images: fractiontalks.com - watch this space!
Simon, I love that you have collected all these routines here in this one post, and shared how they've worked in your classroom. They all have the power to engage students and get them talking, thinking, and sharing without the fear and anxiety that so many associate with what normally happens in a math class. It's exciting to be a part of a community that is creating, exploring, and experimenting with these routines.ReplyDelete
Thanks Joe. One of the things I should have said about these routines in how portable they are. Just like a lot of the activities you’ve shared recently – like Fill the Stairs, Number Grid Tic-Tac-Toe, How Close to a Hundred? and Five Boxes. They will fit into any curriculum, they are easy to understand, they don’t need a lot of setting up, they don’t even have to take up much classroom time. So they’re easy to slip into whatever way of working a teacher has. And, once in, they work on the teacher as well as the students, giving him or her the chance to listen in on students’ thinking and see how far that can take the learning. There’s the option of taking them further, for instance by getting maths journals out and recording what’s happened, and thoughts about it. Or the way Graham takes an estimation activity and extends it to be a 3-Act.Delete
Absolutely brilliant Simon. This is top drawer stuff!ReplyDelete
Love this post. Thanks for sharing. I love the emphasis on using Counting Dots for the "how" and listening to students.ReplyDelete
I haven't seen does like these. Would be more appropriate for my middle schoolers. I will try these tomorrow for Number Talk Tuesday! Thanks!ReplyDelete
Did you try them Shannon? Wonder how it went...?Delete
Thank you for sharing! What I love about these routines is how easy they are to begin implementing, even for a teacher just beginning to lean into change! They are easy to plan to routines that can pack a big punch! Thanks again!ReplyDelete
I like that, Jamie: lean into change! Yes, they're low-floor, high-ceiling for us teachers too, aren't they!Delete
Thank you so much for these routines all in one place, plus the links to the resources. Great stuff for encouraging math thinking and dialogue.ReplyDelete
This is an excellent post, Simon! I plan to share this with educators not only online, but also at several upcoming conferences. I really like your attention to detail. For example, in the first picture, I think it is very important to have multiple copies of the same image all on one page (or display) so that students can compare the variety of representations of thinking. That one small detail really opens up the power of that activity. Excellent post. Thank you for sharing!ReplyDelete
Steve - thank *you* for all your work for us on the Quick Images - and all your other great resources!Delete
If I could have more images up there, I would. Whiteboards need more definition!
Great direction of travel Simon.ReplyDelete
It is, Mick - and great to be travelling that way with you too!Delete
I missed this one in March. Glad I caught it now though as it is great!ReplyDelete
Can you say more about your preference for "see, think, wonder" rather than "notice, wonder"?
Both are great. But they're interesting to compare...ReplyDelete
"See" maybe doesn't have to be as significant as "notice" - maybe there's a hint of it being a little important in "notice". Seeing is just asking for what is there, without any further thought at all.
"Think" then gets processing the observations after seeing has been given time.
Especially with images, sometimes it's good just to let the eye wander. Also, in a class of sighted children, it opens it up more; everyone can contribute: just say what you see.
If I want it briefer, I'd be more inclined to go with notice/wonder.
Plus, I can't help but feeling if we ask the same questions the same way all the time, students might get a bit jaded.
What do you think?
I had to give your comment some time to marinate. Your reasoning is clear and you make good points about "see, think, wonder" yet there was still something I instinctively preferred about "notice/wonder."ReplyDelete
I narrowed it down to the words "see" and "think" and their history in the American classroom. As I pondered those words, I realized "think" was one word that is thrown about by teachers often. "Think harder", "just think about it", etc. I had a conversation a few years back with, I believe Nina, and we talked about the uselessness of phrases like that for students. It's beyond meaningless to tell a kid to "think harder" if they don't have any idea what cognitive process(es) you're hoping they do. "Think" has thus become a word of little meaning in most classes I have experienced.
"See" is not quite the offender as "think" in American classrooms but I believe it still holds some negative cultural connotations from traditional classrooms. "What do you see Mark? Come on, think!" Yes, I'm drawing from past experiences.
Notice/Wonder was, for me, fresh. Notice and see don't differ much in definition in the verb form so there's no case there. But notice/wonder seemed to resonate with the students (and teachers!) that had engaged with it.
I do wonder though, after reading your account, if 1) I am missing clues from participants that "notice" might be asking too much and 2) if my own experiences with "see" and "think" might be overly biasing my preference for notice/wonder.
Regardless, thanks for the exposition of your thoughts.