A small anecdote in relation to a recent coffee conversation I had with @TaliaRinger (which they relate over at https://twitter.com/TaliaRinger/status/1681410191278080000 ): Yesterday I spoke with a children's book author who was interviewing me as part of a series she was writing on contemporary scientists. She freely admitted that she did not have great experiences with her math education at an under-resourced school and chose very early on to focus on writing instead. Nevertheless we had an excellent conversation about many mathematical topics that she was not previously familiar with, such as proof by contradiction, Cartesian coordinates, Mobius strips, or compressed sensing, all of which she found fascinating (and said she would read up on more of these topics herself after our interview). I posed to her the isoperimetric problem (using the classic story of Queen Dido from the Aeneid as the intro) and she correctly guessed the correct shape to maximize area enclosed by a loop (a circle), and instantly grasped the analogy between this problem and the familiar fact that inflated balloons are roughly spherical in shape. I am certain that had her path turned out differently, she could have attained far greater levels of mathematical education than she ended up receiving.

This is not to say that all humans have an identical capability for understanding mathematics, but I do strongly believe that that capability is often far higher than is actually manifested through one's education and development. Sometimes the key thing that is missing is a suitable cognitive framework that a given person needs to align mathematical concepts to their own particular mental strengths.

Talia Ringer on Twitter

β€œTerry Tao and I spoke over coffee for like two hours yesterday, in part about diversity in how people think about math. We both agreed that people who hit these walls early mostly don't learn the way of thinking about math that works for them. It's an educational failure”

Twitter

@tao @TaliaRinger Professor Tao, as a longtime admirer of your writings and as a mathematics teacher to young pupils who seek advanced mathematics lessons outside school hours, I strongly agree with what you write here. Many American pupils have received such bad mathematics instruction in elementary school that they end up with correct understanding of mathematics being replaced with nonsense they hear in class, so that the first task for many outside teachers is to correct misunderstandings. That's regrettable.

I suppose you are familiar with the work of Liping Ma on how primary mathematics education is done in United States schools and how it could be better done, but I'll link to the latest edition of her book Knowing and Teaching Elementary Mathematics here for interested onlookers. Her book was life-changing for me and for many other readers.

https://www.taylorfrancis.com/books/mono/10.4324/9781003009443/knowing-teaching-elementary-mathematics-liping-ma

Knowing and Teaching Elementary Mathematics | Teachers' Understanding

The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of

Taylor & Francis