tag:blogger.com,1999:blog-3071719252136968205.post1098362557941227019..comments2017-09-16T05:02:10.617-07:00Comments on Following Learning: Cardinality, ordinality and developments with the Cuisenaire rods in K3Simon Gregghttp://www.blogger.com/profile/07751362728185120933noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-3071719252136968205.post-31512712029887339882017-01-26T14:17:26.082-08:002017-01-26T14:17:26.082-08:00Thank you Michelle! That Mr Gregg was me too, just...Thank you Michelle! That Mr Gregg was me too, just another account! Great to hear from another C rod fan - and one who understands that just having the tool isn't enough!<br />The ones we use are wood too. I think they work better. ;-)Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-13931753428962479922017-01-25T15:35:51.131-08:002017-01-25T15:35:51.131-08:00I love C-rods. They are the one manipulative that ...I love C-rods. They are the one manipulative that I most remember from my own early mathematics learning. They were wooden back then! They offer a powerful visual cue that not only enhances counting concepts (including conservation, which isn't talked about very much) but also addition/subraction, mult/div and fractions and early algebraic thinking. In senior classes I've used them (with a metre ruler) for modelling decimals as well. <br /><br />Mr Gregg raises a very good point: without professional development for teachers that focuses on the underlying cognitive and pedagogical concepts the manipulatives lose their power. I've been training teachers for a number of years and found that I can demo the use of C-rods, 10s frames, PV blocks - you name it, we've done it - till the cows come home but it has very little impact on student learning if the teacher doesn't understand WHY they are using them. <br /><br />It's all about maintaining what I call the Knowledge Triangle - models + symbols + words. All three are shown in your above example. Models are vital to the development of internal constructs (imaging) and number sense, and the symbols and words are vital to the communication (socialisation) of mathematical concepts for the student. <br /><br />I really enjoy your blog, by the way, and regularly share them with my teachers. Keep up the good work!Michele Kirehttps://www.blogger.com/profile/16748229359986007277noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-73486203600016667692017-01-23T03:21:04.843-08:002017-01-23T03:21:04.843-08:00We use all the manipulatives you'd expect - pr...We use all the manipulatives you'd expect - probably using the C rods less than half the time. Lots of games too.<br /><br />I think they would be a brilliant addition to K-2 classes, but it's crucial for teachers to have a good feel and liking for a pedagogy with them. Way back when they were first introduced, they went into classes, but not necessarily with the professional development to use them appropriately. So they went into cupboards...Mr Gregghttps://www.blogger.com/profile/15114830266540886842noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-65142978651170354902017-01-22T14:22:38.899-08:002017-01-22T14:22:38.899-08:00I am laughing because I am so impressed that you a...I am laughing because I am so impressed that you actually understood what I was talking about. It felt so clunky when I was trying to explain it, but you definitely got the gist of what I was I wondering. In our district our K-2 teachers hardly use Cuisinaire rods at all. I have been thinking a lot this year about how I can change that because they seem like such an important model of the relationships that you describe above. We use a lot of place value blocks, five frames, ten frames, counters, number tracks, number lines, etc. The K students do a lot of counting activities, but I am starting to wonder if the Cuisinaire rods can deepen understanding. Do you use Cuisinaire rods exclusively?Sarah Cabanhttps://www.blogger.com/profile/04396651374828741208noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-90685057802309360302017-01-22T13:49:18.424-08:002017-01-22T13:49:18.424-08:00Yes, making the hundred faces is atypical with Cui...Yes, making the hundred faces is atypical with Cuisenaire rods, in that it's a lot about counting. What they really do distinctively is different, and not about counting. End to end and side by side they show arithmetic relationships geometrically. And young children seem to grasp this easily. They don't all always remember what the relationship is called (eg "difference") or what symbol to use (though most do) but they do all see these relationships. And they're all happy to explore them physically, all going off in different directions.<br /><br />The nesting thing is interesting. In a sense that's what's removed. The nesting is part of cardinality. Each set of numbers contains all the smaller sets of numbers. Seeing numbers as lengths is very different to seeing them as nested sets. So, with the yellow-pink-white example up above, if we count the white as one, we look and we see the five as being equivalent to the four plus the one. Maybe, in a kind of duck-rabbit way, we also see that five minus four is one, or that five minus one is four. But we're not looking at the ones inside the five particularly, unless we deliberately set out to imagine that. At least that's how I see it, and how it seems to be for older students I've taught. What do you think?Simon Gregghttps://www.blogger.com/profile/07751362728185120933noreply@blogger.comtag:blogger.com,1999:blog-3071719252136968205.post-78265990042063440122017-01-22T10:59:52.251-08:002017-01-22T10:59:52.251-08:00Simon this is such an interesting progression, par...Simon this is such an interesting progression, particularly because it seems "backwards" from how I think as an adult and I think backwards from how we often teach cardinality and ordinality. Teachers often introduce the abstract numbers first. It is so fascinating that you kind of flipped the progression. You focussed on the relationships first. When doing the Hundreds face challenge with older students, I move pretty quickly to the numeric representations of each rod. The way you describe the progression, the students really own the "relationships" first. Then, they bring the numbers. So interesting. I can't wait to hear how this evolves. Do your students "see" that the white "nests inside the read like the number one "nests" inside the number 2? I feel like I want to ask your students a question that gets at this concept, but I don't know what the question is. It sounds like your students stay really grounded in the "color" of the rod. Do you think they intuitively know that the red rod is equal to "2" or have they not made that connection that. I loved reading this. It really made me think. I am still thinking. Sarah Cabanhttps://www.blogger.com/profile/04396651374828741208noreply@blogger.com