My grandfather counted in threes for his entire life because working in the stock yards of Omaha the cows came down the schute in threes. The application of such math fed him until he died at the age of 85. I'm sure he never heard of an algebraic space, Clifford's or anyome else's.
Teach people the kind of math that feeds them. The kind they can hack their way out of a box with. Teach them math which like a good screwdriver can be a lever and a hammer too when necessary.
But teaching every kid as if the best thing school can do for them is to guide them to the door of calculus through which they will pass unto untold collegiate adventures has been a disaster and should stop.
You will still have your math majors. The school system should make an effort to conduct those kids towards that end but that should cease to be the emphasis. The school of wizarding has a way of finding its own and we should be focused on more people getting more use out of the math they do learn.
