Skemp Article

I used to believe that we learn Math by repetition. After I read this article, I still believe we learn Math by repetition but with some degree of understanding. What I did not realize was that Math learning is a life-long process. By teaching instrumentally, it is true that “the rewards are more immediate, and more apparent” and students “can get the right answer more quickly and reliably by instrumental thinking.” But without further understanding the concepts, instrumental teaching may require a lot of “new rules” as the conditions change. One may argue that “the relational understanding would take too long to achieve” but if the concepts are learnt, then it will be easier remember and possibly dig deeper into the topic. It is also mentioned in the article that “learning relational mathematics consists of building up a conceptual structure” and the author uses the analogy of a person with a mental map of a town can correct his own mistake if taking the wrong turn. It is very much the same in studying Math, if we comprehend the concepts. With “the importance of examinations for future employment” it is unfortunate that the direction of Math learning for the majority of students is to achieve good grades instead of developing a full grasp of Mathematical concepts. Therefore, I believe that relational understanding is important, nevertheless, there are still a lot of challenges faced by both students and teachers.