Points of Comparison (Content Methods Reflection)

My green-book planner was great fun in the first months of school. “Function wheels” is scribbled in along a margin in mid-September between “Functions Test” and “start Unit -III.” There was, theoretically a 30min gap to fill. Needless to say, by the time that day rolled around between make-up work and management battles and piles of paperwork “function wheels” didn’t actually happen. 

Mock-teaching this activity the following saturday for our Content Methods Class then was bittersweet. I hate it that the few times I’ve tried creative activities have become management disasters; but I am also invigorated by the reminder that there are creative ways to represent material and engage students’ abstract thinking... something to aspire to.

Basically the activity was to build a manipulative that was the math-equivalent of a function table. We cut concentric circles of colored card stock and attached them in the center with a paper clip. We wrote input values around the outside circle and cut windows in the top disc so that the window would show the corresponding output as we rotate the outer circle.

In the ‘protected’ setting management was fine. Clear directions were super important. I’m glad that I had pre-copied the circles and also that I had students do the cutting instead of spending that time myself. In a larger class I probably would have a harder time walking around to check that people were folding and cutting correctly but that might be helped if I found a way to get students helping each other or have a visual of different stages of the assembly process.

Two strengths of the activity I think were that the “wheel” draws out the distinction between dependent and independent variable, and the “output windows” helped me to clarify f(x)-notation ( during my ‘traditional’ lesson this was a major point of confusion... the idea that f(x) isn’t itself an expression but rather the ‘name’ for an expression and which simultaneously represents an output). At the same time, I wonder about the pay-off of spending a whole 20 minutes on what really amounts to a single function table’s worth of calculations. Still, I could envision extending the activity to have partners composing their functions which I think would be powerful conceptually. I look forward to modifying the activity to try when I introduce functions in Transitional Algebra.