Commentary on Richard Skemp's "Relational Understanding and Instrumental Understanding"

As a former mathematics student who plans to teach mathematics in the days ahead, I found Richard Skemp’s essay, “Relational Understanding and Instrumental Understanding” very interesting. Skemp introduces the idea of a difference between these two types of understanding, by relating the idea of “Faux Amis” or false friends – words in two different languages that look very similar but have different meanings. Skemp claims, “I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’”. It is interesting to realize this statement is something I had thought about in the past, but only as it related to different learning styles. I am sure anyone who has studied math at any serious level has identified themselves as someone who understands relationally, although most, if not all, have used many instrumental ‘tricks’ along the way.
Skemp goes on in the article to take the “Devil’s Advocate” position in an attempt to understand the benefits of Instrumental Understanding (It is clear early on that Skemp favours Relational). Under this position he states, “instrumental mathematics is usually easier to understand”, “the rewards are more immediate”, and “one can often get the right answer more quickly and reliably by instrumental thinking”. He counters his own opposing stance by claiming relational mathematics “is more adaptable to new tasks”, is easier to remember”, “it can be a goal in itself”, and its “schemas are organic in quality”.
Skemp continues with good reasons for why the two types of understanding should be understood by math teachers and the benefits of both in different situations. Skemp’s article highlights a very interesting theory behind why the teaching of mathematics may cause its dislike for so many people, and not the mathematics itself.