Skemp’s Discussion (Exit Slip)

Are the two kinds of understanding distinct/separable?

The two approaches target different parts of the brain, as they are essentially computational vs conceptual. And depending on the grade level, those different types of understanding will affect the understanding of the students differently.

Is there a “best” order?

Like many answers, it will depend on the students. Some students will rely on formula before learning the origins of the questions, while some want to visualize it in their heads before learning the math of topics. It also depends on grade levels, since it’ll be better to relationally understand some topics before instrumentally understanding them (graphing, for example).

What kinds of activities promote each one?

Instrumental will involve repetition and “traditional math,” such as Kumon, math drills, and timed drills. Relational will include having tutors explain the deeper connections, discussions, having the students independently teach each other, using models, and using real life examples.

How to assess understanding?

Using low stakes, so the students don’t feel pressured to perform. Throwing curveballs and trick questions, so that they need to use understanding, not just patterns memorizing. We can also add layers to the questions, such as multi-part questions. And lastly, we can also give them the correct answer and ask them to find the process to get there, forcing them to understand the question before anything else.