At some level 'math' becomes an academic word, and what students need is more rigourous fundamental numeracy. I hate the phrase 'quantitative' reasoning, but many people outside of maths departments actually use math in fundamental, yet rigorous ways. Part of the issue seems the deference to authority in the schooling system, which is paralleled in other ways...deference to 'expertise'...or 'abstraction' when what should be the heart of the matter is actually rigor and fundamental soundness. The latter is at conflict with other pet ideas, though. Like everybody wins and the overpromotion of self esteem. The cool to hate ("fancy math") thing is just a channeled form of anti-authoritarianism. Whereas fundamental soundness is actually providing the tools for power and freedom for the individual. When schools (but rarely) teach proper maths notation...I wonder...how/are they going to swallow cs?
Students are taught that "math" is doing arithmetic by hand, simplifying and factoring expressions, memorization, plugging-and-chugging formulas, and in general performing rote computations with pencil and paper. These things are simply not pleasant for a lot of people. Nothing anti-authoritarian about it, they're just unpleasant and repetitive tasks that any good hacker would be aching to automate.
I had great science teachers who taught me about fundamental soundness, reasoning from first principles, developing/testing/revising quantative models, and describing the state and behavior of the universe (i.e. what calculus was created for in the first place). That was fun. But nobody was doing that thinking "so this is math" because it wasn't called that, it was called physics or chemistry.
When you are in an a middle or high school classroom called "Math" with a book called "Math" you are doing rote algebraic manipulation, full stop. So that is what math is to you. No wonder people hate it.
Fundamental soundness, proof, etc. has very little to do with numeracy in the sense of mental arithmetic, estimation skills. Those are useful too, but different things. I still can't multiply two-digit numbers in my head but that never posed a problem in calculus, computer science, chemistry, physics, or anything else.
> I still can't multiply two-digit numbers in my head but that never posed a problem in calculus, computer science, chemistry, physics, or anything else.
How about daily life? Would you rather pull out a calculator?
In my experience, (fast) mental arithmetic is very very useful for all sorts of things. Shopping, driving, eating, anything.
