It’s Incredible How Poor Math Instruction Can Be

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It’s incredible how poor math instruction can be, even at elite universities.

As Will Kinney described his experience: “The instructor … walked in, did theorem-proof-theorem-proof on the blackboard for an hour, then walked out. Three days a week the entire semester. The class started out with a dozen students, but by the end of the semester there were only three of us left.”

A couple years ago I tutored a family member who was getting screwed over by a similar situation:

• The instructor was terrible, HW was never graded (completion only), there was no textbook and no instructor notes. Only graded work was midterm, which was not returned until week before final.
• HW exercises were typically given at the most abstract level possible (whereas you really need to scaffold up to them with a series of concrete examples starting with the simplest case possible and gradually increasing in difficulty/generality).
• I'm told the instructor's class engagement was limited to "anyone have any questions about the theorem/proof that I wrote down? (silence) No? Alright, I'm going to write down the next theorem/proof."

How the f*ck is anyone supposed to learn from that?

The most charitable explanation is that lots of math instructors (esp. at elite universities), being of far outsized aptitude and often having far outsized mathematical upbringings, don’t have a good frame of reference for what high school math covers or how well non-genius students can identify and spin up on missing prerequisite knowledge.

But regardless of the root cause explanation, the sad reality is that 1) there’s an absence of incentives & accountability to enforce quality of instruction, 2) the quality of instruction becomes a roll of the dice, and 3) it’s a high-stakes game where bad rolls can have serious consequences: quality of instruction is a massive differentiator when learning math or any other relentlessly hierarchical skill domain.

The whole point of paying for someone or something to teach you is that it’s supposed to be vastly more efficient than learning on your own. And not just for the students with the highest aptitude and/or prior exposure. The point is to create a high-quality practice environment that meets the student where they are and guides them to convert work into learning progress as efficiently as possible.

Which, unfortunately, often does not appear to be the value proposition of the university experience.

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