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I doubt anyone here learned math (at least up through calculus) without concrete examples. They were called word problems and lab assignments.



I'll be honest; I absolute love graph theory. If I had a million lives and financial independence, I would spend several of them solving graph theory problems. I don't really give a shit what the nodes and edges are. Computer network? Rigid structure? Conditional independence of personality traits? I don't care!


Word problems are still abstract manipulation of symbols, you just have to hunt around in the phrasing for the right operands or operations, which arguably makes it harder.


But the jury is still out on the question of whether concrete examples are usefull in maths education: http://researchnews.osu.edu/archive/mathed.htm


Weak study.

They made some students learn something using concrete examples only, and then expected them to be able to abstract. That's just dumb.

I learn the maths, and apply to various situations in my head to make sure I understand it.




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