Monday, November 19, 2012

Some notes about mathematical thinking

It's been interesting to watch Carter's concept of place value begin to form. It's one of the most important foundational concepts for elementary mathematics, and so I've been really interested to see how it falls in place for Carter.

Everything still centers around counting for him at this point. He can count to well over 100 and can correctly read numbers with up to 3 digits without assistance, but needs help when there are thousands (or more) involved. That is, he can look at 371 and correctly read it as, "three hundred and seventy-one," but if that number is, say, 49,371, he needs help.

He can add and subtract on his fingers and has committed many of the within-10 addition and subtraction facts to memory. (Note that I don't believe in flash-carding kids; this has all happened organically and in a child-led way, as has all his learning.) He can use his fingers to add and subtract within-20, and I've been trying to guide him towards the counting-up strategy rather than the count-them-all strategy he uses now, but he is still a bit reluctant to try that without help, which tells me he's not quite ready. When the numbers get bigger than 20, we get out the place value blocks and use those to add and subtract -- and that's when I have to contain my excitement, because place value is so cool and so important!

It's very clear what his ZPD is right now, and when I have a chance (and when he's in the mood) I will pose problems that push that cognitive ceiling up a bit. But he's so focused on writing these days that math has taken a back seat. We played with place value ideas this morning a bit, but what he really wanted to do was write numerals. So he wrote and I made representations with place value blocks, something that reinforces those concepts well.

He does know how to represent numbers as sets of 100s, 10s, and 1s with the blocks, and he can decompose higher units into smaller ones - though not in the context of a computation just yet. Still, it's good to see that progress in his thinking. My goal is to help him have a very solid conceptual foundation for mathematics. And it's also fun to use his development as an example in the courses I teach, heh.

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