Exit slip Sept 9

Our group had a interesting discussion on Skemp’s (1976) concepts of "instrumental" and "relational" understanding:

1. We reached a consensus that instrumental and relational understanding exist on a continuum rather than as separate categories. They are interdependent, with one supporting the other. For instance, we debated whether a student’s ability to graph polynomials of degree 2 or 3, and then apply that knowledge to graph polynomials of degree 5, was an example of instrumental or relational understanding. We concluded that this example falls somewhere in between, illustrating the continuum.

2. We agreed that there is no single "best" order to teach these understandings. The approach is often topic-dependent, with some concepts benefiting from a big-picture (relational) introduction and others from procedural (instrumental) grounding. Additionally, it can be tailored to students’ learning preferences—some may thrive with instrumental understanding first, while others benefit from relational understanding as an initial motivator.

3. (We didn’t have time to discuss this point.)

4. While assessments for instrumental understanding are common and varied, evaluating relational understanding could extend beyond traditional methods. This might include conversational assessments or group challenges where students apply their knowledge in novel contexts, encouraging them to think critically and creatively.