In "Mathematical Thinking and Problem Solving
," Judah Schwartz (somewhat) jokingly makes the suggestion that we should never ask students to engage in a problem/task that has only one right answer (if even a right answer at all). The idea really caught my attention. Schwartz knows that the suggestion may be unrealistic, but striving for that would have profound impacts on many aspects of math education.
This idea resurfaced for me this week. I was finishing up a lesson sequence
designed to get students thinking about exponential growth and percent change. We were working on this last problem (video) in that sequence:
I was really dissatisfied with how it was went. I heard students saying "I don't know what to do" more often than usual, which was frustrating. I could be wrong here, but after reflecting on the lesson I couldn't help but think that the elusive "right answer" might have been the problem here. It is almost as if I was taunting students by covering up something that they were supposed to somehow (magically) discover. All of the students had the original dollar and they all had the final copy. It's not a stretch here to at least experiment with different percentages and see how close you can get…but nobody did that without me suggesting it. I'm still not sure exactly what went wrong here, but I would love thoughts and suggestions.
Helping students to trust their own thinking and feel comfortable experimenting is frickin' hard. That doesn't mean we should resort to easier, more mundane forms of math education that make us, as teachers, feel better about ourselves.
I just came across this video
(look for the one by Annie Fetter). It seems to be exactly in line with what I am thinking with this post.