[Gimpei]

I had a similar experience where math went from being easy and fun to an intimidating and painful slog. My problem was just how focused most courses are on learning techniques for solving problems. I found all those endless substitutions that you learn in calculus to be infinitely dull and so it was difficult to do a good job. Ditto for the solution techniques for differential equations. Don’t get me started on matrix inverting. I think I had to do a 5x5 matrix once for a homework assignment. What a colossal waste of time.

Proof-based math classes came like a revelation to me. When I took Real Analysis, for the first time in over a decade, math was fun. You weren’t just memorizing and reapplying recipes. You were seriously thinking about unique problems and devising solutions. And all the while, you were learning where all these techniques actually came from and how everything connected together.

I don’t understand why we can’t have more proof heavy math in high school. Who cares whether you remember the arctan substitution or whatever in an integral; I’d always just use a solver for that anyway. I’d rather be learning about what an integral is in the first place.

[nicf]

I'm a private tutor who works with adults on proof-based math. I've often had a similar thought to the one you're expressing here --- I also found proofs pretty revelatory when I first exposed to them and wondered where this magical tool had been all my life --- but I wonder how well this experience would scale to the mass of students in high school math classes.

After teaching proof-writing to my students for several years now, I've seen a lot of variation in how quickly students take to the skill. Some of them have the same experience that it sounds like you and I had, where it "clicks" right away, some of them struggle for a while to figure out what the whole enterprise is even about, and everything in between. Basically everyone gets better at it over time, but for some that can mean spending a decent amount of time feeling kind of lost and frustrated.

And this is a very self-selected group of students: they're all grown-ups who decided to spend their money and spare time learning this stuff in addition to their jobs! For the kind of high school student who just doesn't really think of themselves as a "math person", who isn't already intrinsically motivated by the joy of discovering what makes integrals tick, I think it would be an even harder sell. High school math teachers have a hard job: they have to try to reach students at a pretty wide range of interest and ability levels, and sadly that often leads to a sort of lowest-common-denominator curriculum that doesn't involve a lot of risk-taking.

[ninetyninenine]

A wonder no one uses this for programming.

[nicf]

Uses what?

[ninetyninenine]

Proofs

[AntoniusBlock]

A more rigourous approach was tried after WW2, when Americans feared the Soviets were edging ahead mathematically/scientifically. It was called "New Math" [0]. For an example of the type of textbook high school students were taught from, check out Dolciani's Modern Introductory Analysis (the 1960s and 1970s editions only; the later editions were dumbed down, especially when Dolciani died) [1], which starts with set theory, logic, field axioms, and proof writing techniques.

[0] - https://en.wikipedia.org/wiki/New_Math

[1] - https://archive.org/details/modernintroducto00dolc

[cultofmetatron]

> I don’t understand why we can’t have more proof heavy math in high school.

proof based math requires critical thinking and its a lot harder to scale the teaching of critical thinking. We dont' pay enough for teachers of quality to be able to do this at the public school level. Its also much harder to test for in standardized tests.

[zozbot234]

> Its also much harder to test for in standardized tests.

You could test it using interactive proof verifiers. This would also make it a lot easier to teach, since proof verifiers can handle even very complex mathematical proof via the repeated application of a mere handful of rules. (The rules are also surprisingly similar to the familiar "plug and chug" workflow of school-level math, only with different underlying objects - lemmas and theorems as opposed to variables and expressions.)

[Evil_Saint]

I completely disagree. Proofs are very abstract. Learning to read them is a skill you have develop before you can learn anything from them.