I agree with Skemp’s argument that relational understanding is important in math. I've thought about this a lot after taking some courses in teaching and about how people learn. When tutoring my students, I regularly ask concept check questions to confirm the student's relational understanding. It is easy to breeze past a section of homework or topic without checking the students ability to show that they really understand. Possibly, this is a result of the teacher’s assumptions on students’ ability. I have done similar reflection on topics I studied in school. I computed without thinking about what I was really doing and followed a set of rules laid out by the teacher. Without really knowing what I was doing, there was no room for challenging the process or finding new ways to solve the problem. It limited my thinking.
Skemp states that aiming for student relational understanding is a long process compared to instrumental understanding. However, the former has long term benefits. He relates instrumental understanding to learning a set of routes with instructions at each choice point determined “by the local situation”. Instead, relational understanding builds conceptual structures (schemas) that “produce an unlimited number of plans''. Students who learn through relational understanding become independent of external guidance for a route map. There are long term benefits that help students get further while taking less time in total because they do less relearning. This promotes life-long, self-sustained learning where students are aware of a range of possibilities, intrinsically motivated, and more satisfied with their learning.
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