Math is abstraction. But there is more than one kind of abstraction. There is the abstraction that engages with concrete reality, and there is abstraction that divorces itself from reality. The first type of abstraction is what intelligence is all about. The second… I don’t trust it, and I would never teach it to a child.

I have an almost superstitious distrust of pure math. I’ve known people who get good at solving a particular type of puzzle but are no use at all when it comes to real life. I used to like puzzles when I was a kid, but then I sensed that I was wasting my brain. I looked around and it dawned on me that I was getting good at the wrong thing.

Mostly true I guess, but if you don’t have some basic-level statistical thinking and data analysis, like how the average and the median are two different things, boy are you ever going to get screwed over by smooth-tongued sharpies.

Along those lines, Mrs. Mike in Boston, who is the homeschooling czarina around here, prefers the Challenge Math series by Ed Zaccaro (there are three levels, Primary Grade Challenge Math, Upper Elementary Challenge Math, and Challenge Math) to Humble Math.

Zaccaro has a real-world motivation for each lesson and example. For percentages, it’s sale prices and comparing raises in salary. For simple trig, it’s needing to buy a ladder that will reach the top of a 100-foot building when set at such-and-such an angle. And for the statistical thinking I mentioned earlier, there’s the case of a classroom of kids all of whose families make under $30k a year, except for one whose dad makes $20 million on Wall Street– so someone calculates the average family income to claim that this is the rich classroom, which using the median would disprove.

She was surprised to prefer Zaccaro’s books to Glenn Ellison’s Hard Math books, which have a good reputation and an MIT pedigree. Those books are certainly well done and not bad, but Ed Zaccaro’s material somehow just manages to engage the kids better.

A child hating math is a warning sign. It may be that he is being taught badly, or it may be that he is not mathematically inclined. Try teaching him a different way. If that works, you can blame his former teachers. If it doesn’t, sign him up for shop.

This is why I never un-ironically tell anyone to learn to code. The world doesn’t need any more bad coders.

All math beyond arithmetic is a specialized job skill. For the next level, double entry bookkeeping is far more broadly useful than algebra. And algebra is of little use unless you go on to calculus.

The people who know calculus will end up working for the people who know double entry bookkeeping, and wondering why.

My claim: He overemphasizes the value proposition of academic learning. He overemphasizes it a lot.

I’ve never met an unschooler who said: ooh, engineering is interesting, and was put off by having to learn the math, or programming.

All the homeschooled kids of any flavor do very well at reading / writing. And they learn the math better than anyone else.

I know of at least 3 distinct experiments where folks decided to teach math to a crowd of kids who actually wanted to learn. Not “my parents want me to,” but kids saying: “no, really, I want to learn math.”

In all 3 cases, it took less than 50 contact hours over the course of a 6-9 months for every kid in the class to learn all of k-8 math, at a level most 9th graders aren’t ready for.

I taught one of those experiments personally.

His worry about prep is completely unfounded, in my (larger-than-his) experience.