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> 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 writ

> 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.

BeFlatXIII 5y ago
I’d be willing to bet $20 of reputation that teaching the high-level end results will leave more students with a strong theoretical foundation than starting by teaching the strong foundations. Show the students _why_ the foundation is important, don’t just save the fun bits for a valedictory lap after standardized test week.
wwweston 5y ago
I agree, but my experience with the kind of people who care about secondary curricula (people training me when I thought I might graduate in Math Ed, anyway) is that they very much believe that pedagogical foundations should start with something other than logical foundation -- there has been lots of focus on constructivism and manipulatives and geometric intuition and starting with application domains over the last few decades at the tertiary research/training level. 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.

> 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.

BeFlatXIII 5y ago

I’d be willing to bet $20 of reputation that teaching the high-level end results will leave more students with a strong theoretical foundation than starting by teaching the strong foundations. Show the students _why_ the foundation is important, don’t just save the fun bits for a valedictory lap after standardized test week.

wwweston 5y ago

I agree, but my experience with the kind of people who care about secondary curricula (people training me when I thought I might graduate in Math Ed, anyway) is that they very much believe that pedagogical foundations should start with something other than logical foundation -- there has been lots of focus on constructivism and manipulatives and geometric intuition and starting with application domains over the last few decades at the tertiary research/training level. 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.