Here is an example of what math reasoning sounds like. The first time he was explaining it to me, he was far clearer and didn't get confused. The students were trying to figure out whether 33 groups of 3 penguins worked. The initial problem was trying to figure out how many ways 100 penguins could be organized into equal groups.
He knew you could reverse 33 groups of 3 penguins into 3 groups if 33. From there he added the 33's together to make 99. He has one penguin left over so this combination can't work.
Math reasoning is a huge component of our math curriculum. My goal in grade two is to get them to reason why a strategy or answer will or will not work. When this happens it's truly amazing to hear them thinking and being logical as to why it does or doesn't work. This boy clearly has mathematical reasoning for this particular problem. He understood that by switching or reversing the combinations, you could find other combinations.
We want them to be thinking about the reasons why it should work because of what the numbers can and can not do. This particular student isn't doing gobs and gobs of math worksheets, instead they are working in a problem based math classroom where it challenges him to think and reasoning. I love it when this happens, now I just need them all to do this :-).
As a class we had to find out how many different ways 60 penguins could be organized. When we first got started we were stuck on 2 or 3 ways. Ms. Brown told us to go and get Unifix cubes (blocks), this sure helped a lot. It worked much better for us. We then worked as a class to find 12 ways to organize the 60 penguins. We were surprised at all of the different ways.