An Anecdote in Old-School Pedagogy?
After 430 days without calculus IA (which I loved, as my GPA reflected), I went to apply for IB today. I openly admit that I’ve done very little save for this week in using calculus in my life. It simply hasn’t appeared in the realms of algorithmic design, theory of computer science, and discrete math, and of course not in gamelan. I remembered the chain rule for the most part, most common derivatives [*] brushed up on optimization and related rates, sketching graphs from derivatives, anti-derivatives, indeterminate forms, implicit differentiation, and so on. I’d been told to expect related rates, derivatives of varying types, and graphs of various functions.
The actual test was one problem, finding f’ when f(x)=x(sin(root(x)). Which was great, except it took me a second to remember root(x)=x^.5, and I made a careless error- accidentally writing an “x” in lieu of writing a “root (x)” in my final answer. Yet, after I had simplified it all, my prospective teacher appeared a little bothered. Having given d/dx(root(x)) to be (1/2(rootx)), it was awkward to be lectured on how to find that d/dx(root(x)) to be (1/2(rootx)) and how everything I had explained actually worked. Regardless, I was pleased, and eager to show anything else or dive further into the material. The teacher’s diagnosis, however, was different: I would be allowed to take the course, but they heavily expected me to need a tutor as of day one in order to pass. I’ve dealt with integration a little on my own, and I know that if I need a great deal of help with them, then the class will be in the same situation.
This didn’t bother me a ton, but made me reflect on how long it’s been since I’ve had a teacher emphasize Knowledge and Comprehension over Analysis and Synthesis. I was attracted to Computer Science because it returned me to an upper tier of Bloom’s Taxonomy:
Knowledge —> Comprehension —> Application —|
|—> Analysis —> Synthesis —> Evaluation
lower level learning ——>|
|—–> upper-level learning
I don’t disagree that memorization and recitation is, on a basic level, integral to the understanding of concepts. However, I am opposed to the opinion that if analysis, synthesis, and evaluation take place regularly, but knowledge temporarily suffers as a result, that the overall level of understanding suffers a great deal. Beginning memorization through application allows for the entryway into a field, but it is ultimately when the student sees the first three categories as tools used in the upper three that true, visceral learning takes place. And to me, evaluation is the learning style that takes place most outside of the classroom. It’s not just defending or rejecting an idea- it’s the muddy, intangible way that we as scholars attempt to connect everything around us. Forgive the bad example, but it’s John Nash in A Beautiful Mind, seeing the overlapping structures of the light’s reflection in a punch bowl and an ugly tie. It’s my quiet fascination with the overlap of approaches in conceptualizing contemporary music and contemporary art. Ultimately, that’s what the allure in teaching is to me- opening up this experience to others while continuing it yourself.
[*]
(e^(csc^2(tan(1/x^.5)))? No thanks. x^2*(sin(tan(3x^3-2x^2+x)))? Surprisingly enough, sure.
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