Skemp's Article

In the article, Relational Understanding and Instrumental Understanding, Skemp writes about the differences between Relational Understanding and Instrumental Understanding and how they affect the student learning processes in current education system. I read this article with a great interest because I remember feeling lost back in my high school mathematic classes, even though I was getting all the answers right. Reading this article made me realize that the reason for my confusions was due to the fact that I only had instrumental understanding of the concepts, not the relational understanding, which is what I searched for.

“A person who is unaware that the word he is using is a faux ami can make inconvenient mistakes.” -Starting the article with defining a new term, faux ami, seems like a very nice way of introducing the topic, since it helps the readers to think of the importance of understanding the true meaning of the word.
“This anticipates one of the arguments which I shall use against instrumental understanding, that it usually involves a multiplicity of rules rather than fewer principles of more general application.” -People often think that instrumental understanding can be achieved with less effort than relational understanding. However, this quote points out that in long term, instrumental understanding involves memorizing more rules and requires more efforts.
“The other mis-match, in which pupils are trying to understand relationally but the teaching makes this impossible, can be a more damaging one.” -I agree with this statement. When I was in my high school years, I always wanted to understand more about mathematical background than just using given formulas to solve problems. However, most high school teachers tended to enforce instrumental understanding only, which created a lot of confusions in my part.
“There is more to learn-the connections as well as the separate rules-but the result, once learnt, is more lasting. So there is less re-learning to do, and long-term the time taken may well be less together.” -This quote illustrates one of the practical advantages of the relational understanding very well; relational understanding is a more effective form of learning in a long term.
“But the most important thing about an activity is its goal.” -I think it is really important that the students and the teachers have the same goal, in order for the learning/teaching processes to become more effective.