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Skemp Article

Overall I really liked this article, and found a lot in it that resonated with my own experience learning mathematics. In high school I had an incredible math teacher that definitely subscribed the the "relational understanding" view of mathematics. However, in grade 12 AP calculus he was gone for a semester and our replacement teacher taught in a much more "instrumental understanding" way. I struggled more in that semester than ever before in math, much like the anecdote in the article about the seven-year-old who had extreme difficulty with an "instrumental understanding" approach to mathematics.

As I was reading the article, several pieces stood out to me. I really enjoyed the metaphor of faux amis and the idea that there are not just two different approaches to math, but in fact two different mathematics. While I'm not sure I agree completely with Skemp on this, I think it's a valuable way to think about the two different ways that math is taught, and how the "instrumental understanding" approach fosters a completely different attitude in students towards mathematics than the "relational understanding approach". I was also struck by the parable about teaching music as a purely written subject. I thought this metaphor perfectly captured how and why teaching math for "instrumental understanding" both makes it more difficult in the long run, and robs students of the passion they might feel for the subject. Another part of the article that stood out to me was the piece about walking through a town in order to create a mind map, or simply to get from point A to point B. I think this was possibly the strongest argument in the article for teaching mathematics with a "relational understanding approach". In my experience tutoring mathematics, I have seen students get stuck so many times because they made one mistake and could not get back on track with the steps they had memorized to solve the problem. Having a relational understanding of mathematics is much more versatile, and allows you not only to make mistakes, but to learn from those mistakes and recover.

I fully agree with Skemp on this issue. While I understand that sometimes it may be hard to find time or room in the curriculum to teach every concept for relational understanding, I think the benefits outweigh the challenges in every sense. While instrumental understanding may be faster and easier to teach in the beginning, the gaps in "relational understanding" will pile up over time and it will become difficult to teach for any kind of understanding.

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