Richard Skemp Response

I found the description of relational and instrumental understandings a helpful lens for thinking about both teaching and learning. I agree with the author that teachers and students would possess or aspire to a deep relational understanding of the material and concepts in the ideal world. However, I wonder how practical this is in the public school system, where classrooms are crowded and resources are scarce. I also think Skemp may overvalue relational understanding relative to its counterpart. Students who rely on instrumental understanding to achieve immediate success may parlay this success into a deeper understanding. Gradually, building their relational understanding over time as they become more familiar and engaged with the material.  In fairness, Skemp mentions this as an advantage of instrumental understanding but seems to strongly favour relational as the ideal pursuit. As a counterexample, I have a deep relational understanding of how bike parts influence the ride quality of a given mountain bike. However, the depth of this understanding was only possible through the slow accumulation of knowledge. Over time, I moved from a cursory understanding, which kept the bike running, to a deeper understanding, such that I could engage with all kinds of bikes.

I also reacted strongly to Skemp’s perspective on the misalignment between student and teacher with respect to how each is setting an expectation about what understanding they are seeking. I like the idea of thinking about things in terms of what the student is seeking and how that might mismatch with the teacher's expectations and vice versa. However, even in Mathematics, I don’t think it’s black and white (relational or instrumental). I’m more inclined to see this interactional match along a spectrum of overlapping expectations, where the student is seeking some level of understanding, and the teacher can offer a level of instruction that meets the student’s expectations and encourages them to engage. In general, I like the idea that we can encourage deep understanding and achievement by simply sparking an interest in the subject matter. Whether this happens using an instrumental, relational, or mixed approach seems less important.