One thing that I agree with is the statement that mathematics education today is fostering instrumental understanding. I experienced this in high school because my teacher taught instrumental mathematics. I was solving a variety of questions and ended up memorizing the procedures and formulas. Hence, I had a hard time understanding some of the concepts relationally. We can observe that this point aligns with Skemp's article. However, one point that I disagree with is his idea of what mathematics should look like in today's education. I believe that everything is grade-dependent. If teachers concentrate on the art of explanation with a higher-level mathematics topic, then it may get too abstract and be difficult for students to understand. Hence, I believe that instrumental teaching can be helpful for students to a certain extent.
Tuesday, September 19, 2023
Lockhart's Lament
One thing that I agree with is the statement that mathematics education today is fostering instrumental understanding. I experienced this in high school because my teacher taught instrumental mathematics. I was solving a variety of questions and ended up memorizing the procedures and formulas. Hence, I had a hard time understanding some of the concepts relationally. We can observe that this point aligns with Skemp's article. However, one point that I disagree with is his idea of what mathematics should look like in today's education. I believe that everything is grade-dependent. If teachers concentrate on the art of explanation with a higher-level mathematics topic, then it may get too abstract and be difficult for students to understand. Hence, I believe that instrumental teaching can be helpful for students to a certain extent.
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Interesting commentary! It can be challenging to teach in ways different from those that our own teachers used. I think there is a role for instrumental learning at some points in a person's mathematics education -- but even for very young children, there are lots of important 'why?' questions that need to be addressed, and these are not necessarily satisfied by formal proofs! Check out Eugenia Cheng's new book, Is Math Real? ...
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