Skemp (1976)

I'm impressed that this piece was published 44 years ago. After three weeks of readings throughout my classes in my first month in teacher's college at UBC, it immediately stands out as one of the articles I will continue to think about. "Relational understanding and instrumental understanding" is still remarkably relevant in 2020, in math education and throughout STEM education. 

Skemp compares and contrasts the two meanings of understanding: relational, knowing both what to do and why, and instrumental, using rules without grasping the reasons. He goes as far as stating that math taught in each of these ways ought to be thought of as its own class. I agree with the supporting points for each type of understanding; such as the immediate rewards the students feel through instrumental understanding and the adaptability to new tasks in relational understanding. However, I am optimistic that the best of each approaches can be applied to our classrooms.

I think there is material that must be taught in an instrumental manner, such as the memorization of multiplication rules and times tables. However, over the course of a student's education, I think it is our responsibility as teachers to build the schemas of what we teach so that students can engage in relational understanding. My teaching philosophy is centered on an interdisciplinary approach to problems in STEM. Though subjects are neatly packed into their own discretely labeled entities, I think it is important to show our students how concepts from one lesson apply to other units and to other subjects. The fire may need to be sparked by some instrumental kindling but it needs relational logs to flourish.