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> the students just don't have the mathematical maturity for it. Doesn't this get at the root of the problem though? Some students have the mathematical matur

> the students just don't have the mathematical maturity for it. Doesn't this get at the root of the problem though? Some students have the mathematical maturity for it. Others don't. The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." But different students have different levels of mathematical maturity. the problem seems to stem from working in a paradigm where everyone at a particular age has to learn the same thing. It seems we should be moving in the direction of more personalization rather than less.

zozbot234 5y ago
> The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." Yes, I'm saying that the argument should be quite a bit broader than that. There's much that could be improved in how we expose students to more advanced math in early grades, and there's also much to learn from these well-established teaching approaches. If you do it badly, it's less likely to work.
mlyle 5y ago
> Some students have the mathematical maturity for it. I think part of the problem here is definitional. * My oldest son's a few years ahead in mathematical understanding. He understood algebraic concepts very early, as presented in Singapore math and then through enrichment and bantering about various problems with his mathematically-inclined parents. Kids can absolutely get algebra and learn the rules early. * But even if your 4th grader understands all the rules of symbolic manipulation, and the general concepts behind them... that's only part of what is taught in an algebra class aimed to 13 year olds. There's an emphasis on systematic process, checking for mistakes, carefully matching terms that is likely to be unnecessarily frustrating to younger kids. * Many programs for gifted youth go in exactly the wrong direction: emphasizing more rigor for the gifted youth, harder problem sets, etc. He took Algebra I with CTY and the number of opportunities for sign mistakes or mismatching coefficients per problem were dizzying. I believe we should be: * Throwing ideas at primary kids, with small numbers of degrees of freedom to make the problems manageable for a population that developmentally has less discipline. The complexity of the ideas involved can scale based on what the kid knows so far. * Throwing deep process and carefulness at older kids. The complexity of the ideas involved can scale based on what the kid knows so far, but the process and accuracy expectations can scale mostly with age.

zozbot234 5y ago

> The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." Yes, I'm saying that the argument should be quite a bit broader than that. There's much that could be improved in how we expose students to more advanced math in early grades, and there's also much to learn from these well-established teaching approaches. If you do it badly, it's less likely to work.

mlyle 5y ago

> Some students have the mathematical maturity for it. I think part of the problem here is definitional. * My oldest son's a few years ahead in mathematical understanding. He understood algebraic concepts very early, as presented in Singapore math and then through enrichment and bantering about various problems with his mathematically-inclined parents. Kids can absolutely get algebra and learn the rules early. * But even if your 4th grader understands all the rules of symbolic manipulation, and the general concepts behind them... that's only part of what is taught in an algebra class aimed to 13 year olds. There's an emphasis on systematic process, checking for mistakes, carefully matching terms that is likely to be unnecessarily frustrating to younger kids. * Many programs for gifted youth go in exactly the wrong direction: emphasizing more rigor for the gifted youth, harder problem sets, etc. He took Algebra I with CTY and the number of opportunities for sign mistakes or mismatching coefficients per problem were dizzying. I believe we should be: * Throwing ideas at primary kids, with small numbers of degrees of freedom to make the problems manageable for a population that developmentally has less discipline. The complexity of the ideas involved can scale based on what the kid knows so far. * Throwing deep process and carefulness at older kids. The complexity of the ideas involved can scale based on what the kid knows so far, but the process and accuracy expectations can scale mostly with age.