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Day 42: Midpoint (cont.)

Agenda item #1: U3 Quiz 1 on the basic properties of squares.

Agenda item #2: Recap the Midpoint discovery w/GSP from yesterday.

Agenda item #3: Start work on U3 WS2 - Midpoint

As mentioned yesterday, it was incredibly surprising at how little math sense students have. They can visually point out the middle of a segment, and they appear to understand the concept of average, but are generally unable to combine the two ideas. My theory is that they have only experienced math as a set of seemingly unrelated procedures one follows to arrived at a previously known conclusion.

I stressed the idea of the midpoint formula being a model that we've built that *always* works. It's not a procedure in the sense that "you should always take two numbers and add them, then divide by 2," because that procedure falls apart if you're solving for the other endpoint when given the midpoint. Instead, if you use the model as derived and substitute in the knowns and solve for the unknown, you can't go wrong. Judging by their quiz results, they bought into that methodology, but the algebra skills are still fairly weak.
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