Response to Richard Skemp's Article

Whether teaching and learning mathematics is related to developing abstract, logical, and critical thinking, performing operations and manipulations, or for something else, it was interesting to note the conflict between students’ short-term or teachers’ long-term goals. In particular, if a student is interested in knowing just enough to pass a test or exam, then it may be frustrating for teachers. Navigating through the tensions between students’ interests in learning (memorizing routines or finding answers quickly) and teachers’ goals in teaching is complicated. I think that Dr. Pinar refers to this complication in one of his books on curriculum theory.

I used to also think that teaching (instrumental vs. relational) mathematics didn’t differ much until I read this article. I was surprised when the author states that “there are two effectively different subjects being taught under the same name, ‘mathematics’.” But why just two? When I was learning mathematics, I was mostly taught through instrumental approaches. I liked these approaches, partly because it was extremely useful to quickly solve problems. So I can relate to why some students like to learn when instrumental approaches are used. The notion that instrumental approaches are more practical in every day life and relational approaches are less applicable is unfortunate. It is unfortunate, because mathematics taught through the instrumental approaches may mask the broader aims of developing an appreciation of mathematics as a discipline. I think that if mathematics is exclusively taught through instrumental approaches, it would be hard to expect students to build bridges between learning mathematics in the classrooms and their experiences outside schools.