## Saturday, April 16, 2011

### Inverse Problems:

I feel that we give students too many problems in which they have reduce the complexity of the world down to a single number. We describe some complex situation involving an object moving, and students should find the average velocity–a single number to describe some important feature. Or, perhaps, we give students some combination of resistors in a circuit, and students should find the equivalent resistance–a single number that describes something important. Here are some forces acting on an object, find the acceleration.

How often do we ask students to come up with 4 different situations in which the average velocity of a trip would work out to 55 mph?

How often do we ask students to come up with 4 different ways to get an equivalent resistance of 10 Ohms?

How often do we ask students to describe three different situations in which an object would roll down a ramp with an acceleration of 3 m/s per second?

I think there is a lot of value to these inverse questions, including, but not limited to the fact that

- They require and value creativity
- There are many, many ways for students to be right.
- They seem to require that students engage with the concept (not the equation)
- Procedural aspects are used to check their solutions (not arrive at them)
- Attempts that don't work out can be revealing to students, but on their own terms
- A comparison of solutions across students can highlight important features of the concept

I'm wondering if this should only be used as a learning tool, or if such questions are also viable candidates for assessment.