Relational and Instrumental Understanding

After reading Richard R. Skemp’s paper on “Relational Understanding and Instrumental Understanding” (1976) I find myself assessing what type of mathematics teacher I intend to be. His arguments fostering the easy-to-teach instrumental understanding in students pose valid concerns. The teaching with mnemonic devices without sufficient explanation to answer why allows “rewards [that are] more immediate [and] more apparent” for students. Students respond well to positive outcomes and are motivated to continue. From a professional perspective, not giving detailed reasoning can be detrimental. Without explanation, the memorization of directions to get the answer becomes like “a multiplicity of rules rather than fewer principles of more general application.” Students sacrifice understanding concepts for the sake of passing important examinations, “answer[ing] correctly a sufficient number of questions.” One clashing of intentions rises when “pupils whose goal is to understand instrumentally [encounter] a teacher who wants them to understand relationally.” I like Skemp’s map analogy, comparing getting lost in using the right equations to making a wrong turn in a series of directions. As a teacher candidate, I want to stress understanding of concepts so that they can be applied to the corresponding problems seamlessly, helping their intellectual growth in the long run, while at the same time not forgetting to balance both relational and instrumental understanding.