Relational and Instrumental Understanding - Discission Post

Skemp’s elucidation of relational and instrumental understanding resonates with me deeply. As an engineering student, I often felt a ‘shallowness’ in the mathematics we were being taught – I realize now that this is because it was taught in such a way as to achieve instrumental understanding. I can understand the motivation – engineers are expected to interact with the real world and being able to get a correct answer - quickly - is essential. I could write pages on this point, but I’ll leave it at that.

Early in the article, Skemp notes that instrumental understanding is often used even by those with relational understanding. He later provides a very relatable analogy regarding the navigation of a city. One first develops routes through the city that function well, but do not provide an understanding of the city. It is only after one has some well defined routes that one is inspired to develop relational knowledge of the city. As such, I speculate two roles for instrumental understanding in the development of relational understanding:

1.       Instrumental understanding acts as a frame of reference for relational understanding. To walk blindly through a city is pleasant, but to without any routes/buildings/landmarks from which to relate these new places, they are lost in a cloud of information that only becomes clear after a long exploration. Having instrumental understanding allows you to more quickly process new relational information.

2.       Instrumental understanding inspires relational understanding. As a musician, I recall learning the guitar. At first, I was not interested in scales or theory – I just wanted to make music. As such, learning how to play chords and produce basics songs was extremely inspiring. This provided me with a glimpse of what was possible and served as essential building blocks later on in my musical life.

Lastly, although I mostly agree with Skemp, I disagree with his assessment that the general ‘negative attitude’ towards mathematics can be attributed to our failure to teach it with the goal of relational understanding. Both instrumental and relational understanding are necessary and can be taught in either a good or bad way. To consider instrumental mathematics as a ‘major cause’ for negative attitudes seems overly simplify the situation. I speculate that instrumental mathematics is the only type of mathematics that can be taught when teachers employ methods which are the true cause for math dysphoria.