These issues of math ability are a source of head shaking for me when I read about them as here. I had strong linguistic skills but was bored by math and dropped it my senior year in high school. Doing classics in college encountered the realm of pop science/math books and I was intrigued by a heuristic text on calculus and Newton (by a ‘Kline’, his book was once popular, Booyer, A History of Calculus, but the recent Calculus Wars may be the best here?) and one on the calculus wars of Newton and Leibnitz (not the later book by that name). The enigma of differentials seemed amazing. This so intrigued me that I signed up for a course in calculus. To do that I had to review high school math and trigonometry. I was amazed to see how easy that was and that took about a week. From there I taught myself a lot of math by myself and the physics that went with it up through vector analysis for electromag-, tensor analysis for relativity, as I then began to phase out slightly. String theory I never reached. In the peace corps I ended up teaching physics to A level students. with no course in physics. I had learned how to learn, and that in my case came with a degree of maturity that was post-adolescent.
The point was obvious that judgements of teenagers on math are worse than misleading, they lobotomize students, one reason being the crushing blow of doing poorly in a subject. It was clear to me that for some reason self-teaching was a thousand times better than passive learning. No way around it. So the moral is to never prejudge students. The way to reform teaching is elusive, but the subject of high school math is so ‘easy’ objectively that failure to learn is largely the result of the school situation. In a future culture learning should be taken for granted and not produce the casualties now so unfairly judged over idiot questions like high school algebra.
The book must have from a Morris Kline, 1959, Mathematics and the Physical World.