Skemp's article on relational and instrumental understanding elaborates on a basic idea which many of us are familiar with in mathematics: simply being able to 'do' the problems, and properly understanding what they mean. Skemp's analogy with 'faux amis' introduces the idea in a very natural way.
The first thing that made me pause to reflect was when the initial analogy was drawn between the term 'faux amis' and relational and instrumental understandings. I reflected on the fact that perhaps in assessment, relational and instrumental understandings show up in similar ways, but are very different in nature. The second place I paused was ni the devils advocate section. I had assumed that instrumental understanding may only convenience the student in being an 'easier' way to get through a math class, but I had not considered that there was a case to be made for teachers to teach instrumental understanding. Finally, the idea that practicing different pathways between points in a students schema does not necearilly develop that schema. Not only does a student need to always develop their schema, or relational understanding, but they need to be able to navigate with proficiency and efficiency. Going back to map analogy, a student should know the map of the city relatively well, but also be capable of taking transit or walking or biking to navigate throughout.
I believe that in education we should always be striving for relational understanding over instrumental understanding in mathematics. I believe relational understanding not only lends itself to better learning math in the future, but opens the doors for relational approaches to learning throughout life.
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