Axiom Tutoring

Advanced Math, Stats, Logic, Physics, CompSci, and test-prep tutoring

Professional tutoring service offering individualized, private instruction for high school and college students.  Well qualified and experienced professional with an advanced degree from Columbia University.  Advanced/college mathematics, logic, philosophy, test prep, microeconomics, computer science and more.

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What Determines Who's Good at Math?

As a Math tutor I’ve met a lot of people struggling through Math, all from lots of different backgrounds. Young, old, men, women, racial groups, nationalities, rich, poor. Some teachers can boast the same, although usually they have a pretty homogeneous age and income group—but I think one thing I see which even teachers don’t is a lot of one-on-one interaction, obviously. I get to know my students, even spend a lot of time in their homes if that’s where we hold meetings.

I wonder if that’s why I have a particular opinion about which people are good at Math. Nearly everyone thinks it’s about the brain you’re born with and I very much disbelieve that. Sure, there are correlational studies about parents and children, twin studies. We obviously don’t know enough about the brain to be able to say what the brain physically does to solve Math problems. But the statistics—or rather, the statisticians—or rather, the psychologists who pretend to be part-time statisticians—seem to tell us that intelligence is measurable and heritable. Maybe everyone’s belief in innate intelligence is right?

There are a couple points, the first of which is the surprising nature of what biologists mean by “heritable”. For instance, the number of fingers on your hand turns out not to be heritable! Heritability is measured as the ratio of variation due to lineage against the variation in the whole population. The number of fingers on your hand has no variation within families, so the numerator of the fraction is zero—so the fraction is zero!

The definition is the best quantitative measure of what we intuitively think of as heritable: If people tend not to vary a lot in height within a family even though they vary a lot throughout the human global population, that seems to indicate that height is heritable. Makes sense, although it is fundamentally correlational. This measure does not demonstrate causation, and if families all tend to eat alike and diet is a stronger determinant of height than genes … well, you’ve got a lot of bias in your data.

Establishing causation usually requires being able to manipulate a variable while holding other variables constant. Since we don’t know enough about genetics, we can’t do that, and so the best we can do to study heritability right now is fundamentally correlational. And this isn’t just abstract nit-picking. I have serious reservations about the extent to which environmental effects have been adequately factored out of intelligence studies. If intelligent people are more common in some families, but those families have expensive prenatal care, lots of time with parents, living in a culture that values education, I think by the time a person is able to read, write, and take an intelligence test, they’ve already had a lot of biases in their data.

I also just don’t think that “intelligence” has been adequately defined in a measurable way. A reasonable definition is “The ability to solve problems in order to acheive goals.” However, that requires a measure both of the difficulty of the problem and the “capacity” to solve it. Factoring out laziness and valuable alternate goals particularly makes the second hard to measure.

So I don’t buy the genetics answer, not entirely. It can’t be nothing in the equation, but I don’t believe it’s everything either. I also don’t think it’s sheer effort. I’ve seen lots of students work hard and come out the other end not grasping the concepts well. I fully, deeply, whole-heartedly, even aggressively reject the idea that some people have Math brains and others don’t. Knowledge and the universe are not so neatly compartmentalized, and the reasoning you exercise while doing Math is fundamentally the same skill that you use while reasoning about language, strategy, organization, projecting the future, understanding the past, studying law. If you navigate the world at all you make use of the same geometric, arithmetic, and logical intuitions that mathematicians use—mathematicians just use them with an extremely large and continuous chain of iterations.

The one common factor that I’ve seen almost without exception among people who do well at Math is: Interest. If you think Math is meaningful, interesting, beautiful, worthy of study intrinsically and not for the sake of anything else—absent any physical, psychological, emotional, or economic impediments to your study, I think you have a near certain probability of succeeding in studying Mathematics. Every student I’ve seen make wild progress in their studies believed in the amazing ability of Mathematics to say something deep about reality. Every student I’ve seen disappointed with the ineffectiveness of their own studies just could not manage to give a sincere shit about about the subject. Of course most people fall in-between, both on the accomplishment axis and the interest axis.

Most people think ability causes interest. I doubt that is more than a rarity. I think interest causes ability.