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I don't think that's true for everyone. Your math PhDs and enthusiasts appreciate math as beautiful in and of itself. The disconnect might be that they forget many others do want skin in the game, and that makes the teachers not understand what the students need.


Oh, of course, they exist. But my guess is that's the extreme minority, and I was making suggestions in the realm of "We seem to be doing math badly in general population education, what to do about it?"


Part of the problem with math is that it's often taught using examples that are so trivial that they don't require the techniques being taught. If harder examples aren't introduced pretty early, students are left with the idea that they don't need to learn the techniques. You don't really need know any real techniques to figure out that 2x+4=8, you can kinda just figure out that 4+4=8, so x is 2, and if you can't figure that out intuitively, you can just guess and check a few numbers until you have the correct answer. If the entirety of algebra 1 or pre-algebra is taught with similar examples, students will pass the standardized test but not have any of foundations necessary for further math classes and actually won't even have the ability the solve even slightly more complicated versions of the same sorts of problems.


It's decently rare, but the people who actually like mathematics tend to become mathematicians. Hence they become the spokespeople for mathematics, as well as the experts who are consulted about how to teach and structure curicula. They also become maths teachers.




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