One thing that struck me was that I have felt the exact same reservations towards "instrumental math" that Skemp lists in this article. This was a sadness I felt to how (I thought) math was often taught, as if some of the beauty within was completely overlooked and ignored. In grad school I read "The Mathematician's Lament" by Paul Lockhart, an article that plays with the idea "what if we taught music like we teach math". I was struck to read the very similar analogy given by Skemp in this article, some 30 years prior to Lockhart. Back in grad school I felt validated in my feeling that "instrumental" is somehow missing the point, and I was annoyingly sanctimonious about it (despite never taking the "devil's advocate path").
Since that time, my perspective has gained some nuance. When I read Skemp's football analogy on page 3 I wondered to myself: are there not skills used by both sports that would transfer from one to the other? I finished the article disagreeing with Skemp that instrumental and relational math are so distinct, and my long-standing skepticism of instrumental math has softened. I see these different approaches as two sides of the same coin. Though the sides are certainly different, they are not necessarily opposing. And each offers a different way to teach, both of which carry their own merit and both of which I will try to use appropriately in my teaching. After all, the title of the article is "Relational Understanding AND Instrumental Understanding" not "Relational Understanding OR Instrumental Understanding".
Lovely, Tara! I really appreciate your nuanced, ‘both/and’ approach— and I find it’s really much more helpful than extremes of ‘either/or’ in human situations like teaching.
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