Late 30s here. I keep feeling like I should learn math better, but damn, I just never need it. It’s much easier to learn stuff I need. As it is, I’ve lost everything back to about 8th grade math because I’ve never used any of it, so it’s just as gone as all the French I used to know but never found an excuse to use.
[edit] and I’m dreading my kids getting past elementary school math because they’re gonna be like “why the hell am I spending months of my life on quadratic equations?” and I’m not gonna have an answer, because IDK why we did that either. At least I have answers for calculus, even if they’re not much good (“so you can do physics stuff”, “right, but will I ever need to do physics stuff?”, “uhhh… unless you really want to, no.”)
The quadratic equation is completing the square while inexplicably avoiding all the intuition of completing the square. For example, to solve x^2 + 6x + 5 = 0, you would re-write it as (x^2 + 6x + 9) - 4 = 0, which is (x + 3)^2 - 4 = 0 and hence equivalent to (x + 3)^2 = 4, so that x + 3 = ±2 and hence x = 3 ± 2 is 1 or 5. Euclid thought of things this way, though his language is, of course, very different to modern language; see, for example, Proposition 6 of Book II (http://aleph0.clarku.edu/~djoyce/elements/bookII/propII6.htm...).
That's the same answer as the quadratic formula, but makes a lot more sense to me! Of course I've cooked the numbers so that you don't wind up with surds in the answer, but those are just complications in bookkeeping, not in concept.
Quadratics are useful-- finding dimensions of things in the plane; relating area and constrained side lengths, etc. They come up a lot if you want to solve problems.
And good luck taking on calculus without being super solid in the mathematical tools you use against quadratics -- factoring, completing squares, manipulation of binomials, pairing up like terms, etc.
If this is true, there is surely a way to present material honing that specific skill as a game or series of games that would generate more intrinsic interest from more kids than math does.
I don’t think the methods of thinking per se are why we teach math, though. Might be part of it, but if that’s all, I think we could do a lot better for a lot less effort for all concerned. I think it’s because the math itself is useful. If in fact the point were to teach methods of thinking, I doubt we’d teach it as we do math—why would we, when it generates such resistance and loathing from so many students?
The author was a Soviet nuclear physicist (who participated in the creation of the H-bomb), so his main point isn't rigor. It can be a nice change of perspective from standard American texts.
Although Soviet-era books were notoriously terse & difficult to digest, they had some very aesthetic typesetting. I have owned a few (Problems in Physics by Irodov, & another by Krotov) and they all share similar design aesthetics.
