Will We Ever Teach “Advanced” Topics in High School?

I once taught a little bit of group theory in a math for liberal arts class once. My pretense then was that I was teaching about symmetry. The class was too small to make an effective sample size. They were also largely uninterested; at one point, no one showed up to class. I was largely inexperienced, and I would like to think that if I ever had the chance to do something similar I would do a better job. But the point does remain that there was nothing dramatically difficult about the basics of the topic.

In fact, there are many mathematical ideas that seem to go unexplored in earlier mathematical education. My post-secondary mathematical education was basically a path to learning calculus. I learned a little more about conics while preparing for a competitive math test. I learned about vectors in physics (which seems standard). And I learned about Mobius strips in an English class! (In relation to Eliot’s Four Quartets.)

Back in high school, I had a very linear view of mathematics. One idea progresses to the next and so on. Even then, this view was false once you looked deeper. But I think that there would be a benefit to being exposed to some more variety in mathematical topics. Topology was never mentioned as far as I could tell, despite some of its ideas being novel and much more visually striking. I’ve already talked about how little analysis is in calculus.


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