> I’ve taught mathematics at community colleges for over 20 years and I’m absolutely convinced that not all people can learn algebra or calculus. To me it is obvious this is so since the mentally disabled can’t. There’s a level of “intelligence” that’s necessary to learn a given topic. Not everyone can learn all topics.

You know, if you were trying to teach Chinese to 18-year-old English-speakers at community colleges with three hours a week of lecture, you might come to the conclusion that only a few rare geniuses had the ability to learn Chinese at all, and none would ever learn more than a few hundred words. But of course over 98% of people born and raised in China learn to speak Chinese fluently by the age of 5, and that's not because of genetics; it includes almost 98% of white people born and raised there too. There are several factors that I think of as key to this difference:

1. Plausibly there is a critical period for language acquisition, and if so, it very likely ends before age 18. Looking at an 18-year-old you can't tell whether their deficits in Chinese-speaking ability are due to genetics or environmental effects in the previous 18 years. There probably isn't an early-childhood critical period for calculus (I think you need formal operational reasoning for that) but maybe there are other things you need to develop early on for calculus to be easy for you when the time comes. Like, fluency in reading, for example.

2. Three hours a week, 36 weeks a year, for two years, is a total of 216 hours. Native language acquisition more typically involves over 20,000 hours of language exposure by age 5. Sometimes it's surprising how much more you can achieve when you apply literally over a hundred times more effort. Or, to look at it a different way, how little you will achieve when you're applying less than 1% of the effort necessary to get good results.

3. Schooling is a really terrible way to learn things. Extrinsic motivation displaces intrinsic motivation, massed practice displaces spaced practice because it gets better exam scores (especially if you know when midterms are coming up), the feedback necessary for improving is delayed by hours or days by the nature of homework grading, and the pacing is inevitably far too fast for some students and far too slow for others. It's well established that individual tutoring produces results two standard deviations better than ordinary classes (Bloom's two sigma problem). That's 30 IQ points. And Bloom wasn't even spacing out practice over decades the way you ought to; he was working within the semester structure of traditional schooling, extrinsic motivation and all.

Is there a possible human culture where 98% of everybody routinely learns to do symbolic integration? Or does human nature render that impossible? Maybe. (Hell, when I have an integral to do in my head, I myself invariably settle for just approximating it unless it's a fucking monomial. Maybe I should spend a few semesters doing them on the blackboard in front of a class, I bet that would help.) But the meat grinder of community college doesn't give us much evidence about that one way or the other, except to know that we don't live in that culture today. It doesn't help us at all with the question of what to attribute to environmental effects and what to attribute to genetics.

(One indication that such radical changes may be possible is the gradual transformation of literacy; hieroglyphics were the province of the priesthood and the quasi-priestly scribes, and even after the invention of alphabets, Charlemagne and Genghis Khan were illiterate. Can you imagine trying to teach a classroom full of 18-year-olds hieroglyphics in three hours a week, if they had no previous experience with reading and writing? Yet today literacy rates are over 95% in most countries, though countries with non-phonetic orthographies like Chinese and English lag a bit behind.)