In September, while taking that Jo Boaler class I’ve mentioned, I finished a section about asking open questions that allow students to use different approaches and learn from each other. That’s a valuable idea, I thought. Unfortunately it’s just not compatible with my upcoming unit. Simplifying expressions is all about getting a single answer and there’s really just one way to do it.
The idea of asking open questions kept turning in my mind, though, until an application was suddenly obvious. I would keep the goal of having students write expressions in simplest form intact, but would add a dimension by having students also write expressions in non-simplest equivalent forms. This would allow students to follow their own thought processes and provide individualized responses, while also developing the concept of equivalence.
I wrote an expression in simplest form on the board, then asked students to write it in equivalent ways using
- Subtraction (the requirement of like terms for addition and subtraction was a worthwhile challenge)
- Negative Exponents*
We used this activity during the simplifying unit, and returned to it during reviews of previous material. Some students understood the meaning of the activity quickly, while at least one didn’t perceive it until just before the spring final: “Oh! We’re just writing things that will give us that first thing.” Bingo. Sometimes comprehension takes time. That’s why I’m in favor of continual review and intelligently designed cumulative finals rather than the take-a-test-and-forget-about-it model.
*I didn’t think to include negative exponents in the list until late in the year.