Fai—Thinking Math with Scratch

One way computational literacy can support mathematics learning is that students can use computational power to offload some of the mechanics that, without computer, students have to go through in order to engage with mathematical ideas. For example, it takes a lot to construct with paper and pencil some geometrical figures before students can investigate their properties. Construction may help understanding, but some aspects of paper-and-pencil construction can be cumbersome. Students can use Scratch to construct those figures. That is very important; however, it is unclear how programming helps with the understanding.

Recently, I have been asked to think about how to support students to develop institution about derivatives and antiderivatives in ways that connect to algebraic manipulations. I find it hard to do so, because most activities I think about develop institution of the underlying mechanisms that use numerical approaches that I am still not sure how to connect to typical polynomial objects. 

Anyway, to start, I thought about line integral. We can ask students to use the Scratch Cat to measure the length of any line. Before starting with Scratch, we can talk about how to measure any lines/curves. One way to do that is to break a line into little line segments and add them up. Students can program the Cat to do that. Then we can talk about how to get the length to a closer approximation of the length. This should help students think about what a line integral means. 

I think one way to assess the line integral program is to look at how each iteration of the program moves toward systematicity.