Thursday, January 30, 2014

Identifying Effective Representations

At a recent PD, the Pre-Calc/Calc teachers at my site worked on the following question while we were on the topic of Identifying Effective Representations.

The verbal instruction given was: Solve the problem in as many ways as you can. The written instructions are as follows:

Solve the following problem, using alternative representations where appropriate.

A woman was 3/8 of the way across a bridge when she heard the Orient Express approaching the bridge behind her at 60 mph. Because she was a mathematics student, she quickly calculated that she could save herself by running to either end of the bridge at top speed. How fast could she run?

Go ahead. Try it out.

In the limited time given, we were able to find two representations that led to the solution. For me, it felt more like the same representation solved two different ways. The traditional way, if you could call it that, required more work as we solved a system of equations to get the solution. The other method we found required a little more thinking about the situation, but the path to the solution was much simpler and shorter. Can you find other effective representations?

The idea is that as we move to Common Core, it is not sufficient to just get an answer. Students are expected to solve a problem using multiple approaches and this was an example of that. How realistic is it that students will have the kind of insight that allows them to solve this kind of problem using multiple approaches and, more importantly, how do you go about teaching it in the limited time we have?

I would love to see your approach and your diagrams as you work on this problem. Link or comment below. I'll update this post with my work in a week or so.