This is kind of a rant, but I think we heap a whole bunch of expectations on math progress in school, that are unrelated to math and create a burnout atmosphere. There's a culture of fear surrounding math. Most adults, even people who are in supposedly technical occupations, outwardly hate math. Most can proclaim that they set their math aside after it got them through school.
Yet it's also chosen as an arbitrary measure for ranking children and gating their academic and career choices. Kids are "ahead" or "behind" in math. They're tutored during the summer and sent to cram schools. They're tested at every grade level. Math determines access to many fields of study in college. School districts are ranked by math scores.
We have some vague sense that math is important for something. Maybe it fosters intelligence or diligence, both of which are valuable I suppose. But never math for its own sake.
I loved math in school and was even on the state math team. Sadly much of the math I learned in high school and even college I had to unlearn (the worst example being assuming everything is a normal distribution and reporting mean and standard deviation instead of looking at a histogram).
I'm convinced that the best way to teach stats is to start people with data and graphing. The formal mathematics of statistics is certainly a fascinating discipline (my grandfather was a professor of statistics) but for the rest of us, the formulas are a work-around to the problem of dealing directly with the data and doing repetitive calculations by hand.
The formulas and proofs are certainly valuable, but could come later. And the graphs remain useful (at least for a hack like me) for confirming our understanding of the formulas.
Also, data and graphing would be a way to ease students into programming.
I agree, but have to caution that the abstract and dry stuff is still part of math. It was what turned me on to math. I'd favor a blending of math and science curricula, and use more data analysis when teaching science.
It's a dilemma because math is so broad, and has both pure and applied sides. And a challenge for changing curricula is that the public defines "math" as the precise sequence of topics that they studied in school (and hated).
Yet it's also chosen as an arbitrary measure for ranking children and gating their academic and career choices. Kids are "ahead" or "behind" in math. They're tutored during the summer and sent to cram schools. They're tested at every grade level. Math determines access to many fields of study in college. School districts are ranked by math scores.
We have some vague sense that math is important for something. Maybe it fosters intelligence or diligence, both of which are valuable I suppose. But never math for its own sake.
Disclosure: College math major.