[FakeComments]

When you try to understand math education, remember that it’s basically what would happen if foreign language classes were designed and taught by people who only spoke English and had no training in formal language theory.

Of course it’s largely a disaster: it’s taught by people who brag about hating the subject!

Algebra education can (and does) safely begin in first grade, with the introduction of workbooks: “4 + [ ] = 7” is a common exercise, and involves the implicit solving of a basic linear equation, where you solve for the value which goes in the box.

That you can teach algebra to first graders, but math education is so abysmal, only speaks to the complete disregard mathematics is given in education.

But what else would you expect when you leave it up to people who hate math?

[tpurves]

Can confirm! Have a first grader and she actually found learning basic adding/subtraction, and now multiplication more fun by learning it through games played with implicit basic algebra. “I am thinking of a mysetry number, can you guess it? X marks the soot where the number goes... I’ll give you a clue 2 plus x equals 4. Or 9 times x equals 18.” Etc. She’ll laugh and play this game all day, and make up algebra puzzles for us too. Great way to learn her basic math and implicitly algebra too through play rather than by rote, or the plodding pace of the grade school system.

[philwelch]

Heh, this reminds me of a fond story. My eighth grade algebra teacher (who did seem to genuinely love math) once said that mathematics was a game invented by man. I didn’t appreciate this at the time but I wish this was the mentality.

IMO the US math curriculum now is designed to train kids to become pre-PC-era clerks (who only need basic, manual arithmetic) rather than engineers.

[ams6110]

I remember that, and hated it. Why? Because I had real trouble memorizing sums and products. I still have to stop and think to do simple sums in my head. I sometimes still count on my fingers when I add two numbers. And these types of problems were taught as memorization. Four plus what equals seven? You either knew it or you didn't.

If they had taught us how to solve these problems, I think I would have enjoyed it more. "You can take away the four from both sides, and there's the answer" somehow that would have been easier for me to work with.

[mntmoss]

I was frustrated in this way during my math education, but lately my opinion about memorization has softened a bit.

The trick is that it has to be approached in the same way as in sports: Demonstrate a technique, explain the principles, attempt in live play, then return to drill muscle memory(now that the student has discovered how bad they are at it). Music is very similar - you can play a song badly, then drill scales and arpeggios a while, come back and suddenly you play the song better.

The point of memorizing is, in the end, to make the knowledge closer and more available to you. But there are several ways in which this cycle drops the ball during education and succumbs to rote learning as the sole factor:

* The teacher themselves doesn't understand the principle, and thus is poor both at explaining concepts and grading results. "You get a zero," they will shrug, when the student has misunderstood something and turns in a problem set with wrong answers.

* The principle isn't connected to "live play", making the technique unrelated to existing knowledge. It's the way in which education systemically fails most frequently, and it starts with having classes specialized per subject and limiting the crossover between them. All too often, all that happens is that you do some problem sets, get tested a little later, and that's it - and so all your focus as a student is on passing, not on learning.

* The drill focuses overly much on tricks and "gotchas" and not on developing confidence and long-term retention, making the student uncertain about how to generalize the technique to the tricks. In comparison, when I took judo, we drilled all techniques on one side only, for the entire semester. Is it useful to be able to mirror the techniques? Yes, but that doesn't mean that any study time needs to be allocated to it.

[heavenlyblue]

Yeah, the sum issue seems like a concoction of taking the difference of sets and then taking their lengths.

Explaining sets (buckets of fruit) and then explaining their difference could work better.

[lenticular]

This was true for me. I absolutely hated math in middle and high school. I never studied for it and got mediocre grades. I had a few teachers who really had no enthusiasm or drive to make it interesting. Fortunately, I started taking some community college classes my last couple of years, where I really fell in love with linear algebra. I wound up being a math major in undergrad and a geophysics PhD.