The first thing that make me stop while reading this article is that words all have different meanings under different culture. Same for using mathematics and using everyday spoken language. This reminds me how important it is to get a professional way of using language while teaching. Next content stops me is about the different effective ways of teaching math which are instrumental and relational ways. I can understand the reason behind his argument and I totally agree with the benefits of both methods he mentioned. Last thing I really like is that he used the example of music teaching method. The difference between understanding something in theory and really grasping its essence and application can make the learning different. This is an interesting idea.
Skemp points out that instrumental learning is different from relational learning, and that it is important to understand the ideas behind math problems rather than memorize the procedures for solving them. And I agree. It is important to have a deep understanding of the ideas in order to have a long-term understanding of the mathematical subject.
Hi Sally, I like the point about understanding the idea behind math problem rather than memorizing it, could you share a specific example from your own experience where understanding the underlying ideas of a math problem led to a deeper and more lasting understanding?
ReplyDeleteHi Joy, Yes. While learning the Pythagorean Theorem, I visualized the theorem using geometric proofs. I drew squares on each side of the right triangle. The area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides. This visual representation gives me a deeper understanding of the theorem. Someone might memorize this formula and use it to solve problems without really understanding why it works. This will limit their understanding and prevent them from applying this theorem to different types of questions.
Delete