> In short, we need to stop conflating logical foundation with pedagogical foundation.
YES. I want to put this on a T-shirt and strut around wherever they write high school math curricula.
YES. I want to put this on a T-shirt and strut around wherever they write high school math curricula.
Adoption throughout the primary and secondary system is a different story. There's been some progress, of course, but if you've ever seen people speak about "common core" with contempt, you are seeing some of the primary forms of resistance. There's an entire social psychology and politics around this that has to do with temperaments who fit comfortably into rote execution for the most broadly useful skills and will be allergic to reframing that requires indirect exploration for conceptual foundations -- it messes with sense of status and security on some deep levels. Parents with this profile hate it; then their kids are a bit more likely to hate it too for reasons of nature or nurture. Some teachers will fit this profile too (though probably more rarely). People who influence curriculum are likely to have the politics influence their choices.
Better math pedagogy is certainly not a solved problem even at the cutting edge, but it's more solved than you'd think looking at the overall state and a lot of the reasons are social.