Last week, while tutoring a student for his precal midterm, I had an opportunity to teach him about the nature of understanding. Our discussion of some specific mathematics and chemistry and claims of understanding led us to ask “What is understanding? What is knowledge? What are differences in understanding, knowing, and memorizing/parroting?”
Understanding is not doing well on a test, or a few tests. An A in a class does not prove or certify understanding. Understanding is (1) knowing the essence of something, (2) knowing how an idea relates to the evidence of the senses, and (3) knowing how something is related to other things one knows, other *relevant* things.
Understanding, in short, requires essentializing, reducing, and integrating. It is a mind’s relationship to reality, not to an authority or to words on paper or in the air.
It’s for such moments and discussions that I tutor. To paraphrase Victor Hugo, “If I was tutoring for only the time we live in or tutoring only math, I would break my pencil and throw it away.”
Helping someone get an A on a test is like giving them a fish; teaching someone to reason is like teaching them to fish. The latter is by far more fundamentally and timelessly important.