Comment by throwway120385 | Hacker News Reader

Comment by throwway120385 | Hacker News Reader

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No, it goes beyond that. There's "arithmetic," the applied usage of addition, multiplication, subtraction, and division to permute numbers, and then there's Arithmetic, the set of theorems and axioms that give rise to that system of applied arithmetic. Memorization only works for the applied part, and children aren't usually taught that there is a system of reasoning behind those rules. Without that, no amount of mathematical dexterity in pushing symbols across a page will help them understand anything past the 100 level, and sometimes not even that.

I also think there's a huge undercurrent of resistance from adults to having children learn that system of reasoning because adults don't understand why it's useful, and in my experience when people don't understand something they dismiss it.

Edit: A nice example of another axiomatic system that might be more approachable is Euclid's Elements, in which five postulates are used to develop a system of geometry using an unmarked straightedge and a collapsible compass that you could, if you were careful, use to build bridges and other large buildings.

Once I got to calc2 and 3. I was so mad. I realized I had spent nearly a decade memorizing things. When I could use calculus to have a factory that made formulas and the rules were on a whole simpler to remember and apply.

Similar here: There were all sorts of volume and area equations I could never remember, then one slow day at work I decided to try and derive the volume of a spehere using what I'd just learned in calculus. After doing so each part of the equation made sense instead of appearing random, and two decades later I still remember it without having to derive it again.

Did you not get to doing lots of integrals? A whole new field of patterns to memorise, which I hated.

Good point, but there are probably plenty of formulas that can be derived with simple integrals, as a backup for if those formulas are forgotten.

Unfortunately, integration, as opposed to derivation, is made of pattern recognition. It's simply that way, like differential equations.

I had a lucky experience taking HS calculus the semester before as physics. I saw other students torturing themselves memorizing the formulae from the physics text and even then struggling to apply it to novel problems.

For the most part, knowing basic calc, it was possible to just draw a free body diagram and either integrate or take a derivative to get the answer. Didn't memorize much beyond f=ma and v=IR, for better or worse.

I still firmly believe that physics and calculus should be introduced together to provide a tangible and practical base to understand the mathematical theory.

It's common in European universities to not have "service courses" that the math departments provide to other departments. The other departments teach the math that is part of their field!

Non-calculus based physics is violence.

The study was limited to cities in India. We shouldn't put much weight into this applying globally.

I mean I remember seeing this first-hand student teaching Mathematics 13 years ago in the US. They got to me having never seen any of that stuff, and the curriculum attempted to provide a good education in mathematics. But the staff and the way the whole system is structured is to skip all of that and memorize the single rule you need to know to get through the test. So it's all done by rote and the only time you find out how you've been cheated is when you try to go through Calculus.

And I remember that was how we learned everything when I was a kid, and the teachers chose not to do anything else. I also remember from my math ed curriculum one of the professors joking about the elementary education students complaining about having to learn middle school math from the college perspective. So I think portions of this apply here.

I've also seen carpenters apply trigonometry very effectively to do things like cuts for roofs and stair jacks, so there's certainly a lot of truth to people learning maths by occupation and not in a formal setting, and I think part of it is the formal setting.

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