When I was reading the first page of this article, I thought I was reading some article on language learning because it starts by talking about the French word Faux Amis. It made me pause for a little, and I went back to check whether this was the reading for one of my math-related classes. I stopped again when Skemp introduces the concepts of "relational understanding" and "instrumental understanding". I always thought "understanding" is just "understanding“ and I did not know that it separates into two different concepts. After reading Skemp's article, I now have a little more understanding on the two types of understanding, and I believe the type of understanding have is instrumental. Later when Skemp went on to talk about applying relational and instrumental in teaching mathematics. I paused to wonder which method should math teachers use? Although Skemp concluded that teachers should "make a reasoned choice" depending on the situation (p.11), I believe most teachers would choose instrumental mathematics over relational mathematics. If we are talking about students in elementary to high school, I would prefer instrumental mathematics because students would have to assessed through tests and exams in order to advance to the next level. Both students and teachers may not want to make the effort to discuss the content behind relational mathematics. I believe relational mathematics would be more applicable to students in the post-secondary level
That's an interesting evaluation -- but would you have felt that way as a high school or elementary student? When do students 'deserve' to have an understanding of what they are being taught?
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