Clip 6/13: Lesson - Part 6
Four students continue their discussion, checking their thinking using graphing calculators.
This is a fairly representative discussion, in terms of how focused the group is on the mathematics. I think the only thing that's exceptional is how long they sustained. You can see toward the end some of that breaking down, with the students in the background doing something else. At that point in the school year, March, most of us had been together for quite a while, so they know what strong group work looks and sounds like and how it benefits them. They know that I don't like it when the class is breaking down.
In some ways it's too bad that the cameras weren't there at the beginning of the year when we were working on all those norms because there would've been many more teacher moves to see. Regarding this group's use of the calculators to test their thinking around positive and negative numbers, I think that's a common trap that teachers are told to fall into, especially beginning teachers, that the kids need to be able to do "______" so that they can be successful at algebra. But for the most part, I think students can get by without any of those, as long as they have something and as long as they continue to attend to those things. So I'm used to kids coming in not knowing very much, although something, about working with positive or negative numbers.
With their use of the calculator, they had to realize that, "Oh okay, we don't know this offhand, so we're going to figure it out this way." I think that's, in general, the appropriate use for a calculator, unless it's an essential part of the problem.
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