The biggest win of my public school education was a high school math teacher that used experimental textbooks that presented all problems as practical word problems.
The children’s performance in market maths problems was not explained by memorization, access to help, reduced stress with more familiar formats or high incentives for correct performance. By contrast, children with no market-selling experience (n = 471), enrolled in nearby schools, showed the opposite pattern. These children performed more accurately on simple abstract problems, but only 1% could correctly answer an applied market maths problem that more than one third of working children solved (β = 0.35, s.e.m. = 0.03; 95% confidence interval = 0.30–0.40, P < 0.001). School children used highly inefficient written calculations, could not combine different operations and arrived at answers too slowly to be useful in real-life or in higher maths.
Perhaps not directly relevant, but I recall one of my whacky math professors telling us that he was "a mathematician not an arithmetician", after making several arithmetic errors in a row.
When I had to calculate something in my head, I would often just estimate the result rather than find the exact answer, even if it was really simple. I just couldn’t be bothered to work it out fully if it didn’t matter.
Sometimes, I would even go out of my way to find a way to estimate the result instead of just doing the math normally in my head, lol
I often do that, too. He was just tripping all over himself trying to track a sign error through an entire blackboard worth of derivations.
who cares about signs, just provide two options as the answer haha
Hmm, as someone who teaches intermediate microeconomic theory, I'm super interested in this as it impacts my daily work.
Micro theory is interesting in that to do it well you actually need to be good at both... solving complex algebraic problems, while at the same time converting a verbal scenario into the relevant mathematical equations. I think that's what makes it hard for students. Being good at one (abstract math or word problems) isn't enough. You have to be good at both.
Related: it's about history of mathematical symbols #879051
How is it related? Does one symbol get used more in applied rather than in academic mathematics?
Didn't say from that point. The OP is talking about Maths here and is also about Mathematical symbols.
Very timely exploration of what it means to know / understand something, given the current state of AI. And what different kinds of knowing / understanding afford you in the world.
Reminds me a bit of some observations from my engineering courses. The math itself often would be not too difficult to solve (the academic part) but the real difficulty was how to translate the real life question posed by the examiner (the market or applied math part) into the equations. It's like they knew being able to tackle this difficulty is what makes for a good engineer. The math itself, one could just use tables, approximations and safety factors.
It was hard for me. Maybe that's why i took the more fundamental road, forfeiting the real life applications of it all~~