This article has summarized in words ideas that I have had for years. Through my time tutoring students who were failing math, I experienced the two types of understanding. These families wanted a passing grade, and the students wanted instrumental understanding. I would often teach two lessons in parallel, teaching instrumentally first, relationally second. I prefaced the in-depth (what I now know as relational) lesson with “I have taught you the raw ideas of how to do this, now this is how/why the math works.” I provided relational knowledge as a bonus, for them to learn from or tune out if they choose.
My favourite part of the article was the
analogy to the music lessons. This encapsulated what I have been trying to tell
my non-math friends for years. It was such an elegant analogy that my jaw
dropped. I cannot wait to share these ideas with my adult friends. It will be
the key to make them finally understand why I love a subject that they learned
to hate.
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