Response to "Relational Understanding and Instrumental Understanding" by Richard R. Skemp

Before entering the education program, I already have a general idea about how am I going to teach math. When the author said that it may be hard to realize how widespread the instrumental approach is (page 3), I paused and reflected on myself. And the answer is, yes, I didn’t realize that my intended way of teaching is very instrumental. I never question myself why multiplication of two negative number becomes a positive number because it was also taught to me as a rule. And I proceeded to ask myself: do I regret about not being taught in a relational away? The answer is no, and it can be explained by the author’s view on the over-burdened syllabi (page 11) — with the number of topics covered on exams, I simply didn’t have time to learn everything and truly understand it. 

The author also discusses the two types of confidence students get: one is the self-satisfaction from getting problems right in a speedy manner (instrumental understanding), and the other is the confidence from a complete schema (relational understanding). As a student who has studied math for 18 years since kindergarten, I have experienced both. I agree with the author in the sense that relational understanding is important in order to engage students. In fact, I only fell in love with math after I entered university where I gained a more systematic understanding of mathematics. But, my confidence from instrumental understanding in the early years is the reason why I can enjoy mathematics at the university level. In my opinion, a teaching style that uses the combination of instrumental and relational understanding is ideal for the current curriculum, and teachers should not fear to explore the methods for relational understanding.