That's the sort of thing "new math" was trying to teach. Those sorts of breakdowns are exactly what the kids who were good at math were always doing, and teaching methods eventually caught up and realized they should just teach the tricks.

Then a bunch of parents who were bad at math asked "new math? How can math change?" The fact that they even asked that question showed how their math education was lacking, but they seem to have won.

[–] mic_check_one_two@lemmy.dbzer0.com 61 points 2 months ago* (last edited 2 months ago) (13 children)

Exactly. Math has historically relied on rote memory for most mental math. Kids would have to fill out their times tables, addition tables, etc until they memorized them. I still remember getting pop quizzes in elementary school that looked like this:

You only had two minutes to fill out the entire thing, which meant you only had 1.2 seconds per answer. You didn’t have time to actually calculate them. The point was that you were expected to have them memorized ahead of time instead of calculating each one.

But rote memory is laughably bad at actually teaching concepts. You may know that 12x5 is 60, but you don’t have any understanding on why, or other ways to do that same calculation without rote memory. And rote memory is only decently reliable up to ~12x12. Anything past that, and it becomes too much info to track; kids simply start forgetting answers.

The kids who were good at math (and I mean actually good at math, not just good at memorizing things) quickly devised methods to do this shit in our heads easily. Keeping track of multiple numbers in your head gets confusing. So “line them all up, add straight down, and carry 1’s” sort of falls apart if you’re doing it in your head. Especially if you’re trying to keep track of more than three or four numbers at a time.

Essentially, 127+248+30 is the same as 105+250+50, but the latter is much easier to parse in your head. But yeah, the parents (who primarily relied on rote memory) didn’t understand why the new method would be more effective, because they didn’t understand the concepts surrounding the math.

[–] boonhet@sopuli.xyz 12 points 2 months ago* (last edited 2 months ago) (2 children)

I think it's good to have a good set of these tables memorized and then based off those you can bounce your tricks. Eg if you know 5x12 by heart, you get 5x24 by intuition. Or even if you know 24/2 for that matter. I use simple examples but this could scale to less memorable numbers too.

[–] blindsight@beehaw.org 3 points 2 months ago

It's really helpful for quadratic factoring, too, since knowing at a glance that –56 is ±7 × ±8 keeps your working memory free to actually focus on the mathematical skills/concepts/problem.

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