Some obscure opinions about school math:
Conversation
We should be teaching far fewer integration techniques in calculus and spending more time on differential equations.
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Speaking of calculus, teach differential equations before implicit differentiation so that kids understand what dy/dx = -y/x means.
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Logistic equations are cool. Logs are cool, but we should bring back log tables and teach students to make computations with them. Also log/log graphs are great. Log rules aren't very important.
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There are a lot of great logic puzzles and I'd like to see more math curricula incorporate them more thoughtfully, because that's a source of fun for a lot of kids.
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Even though I like a lot of what we teach in Grades 2-5, I think a lot of kids thrive on novelty and I think it would be better if there was at least one obviously unfamiliar topic that kids learned every year --- not just "fraction addition but NOW with unlike denominators."
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I've heard arguments both ways but I'm now feeling convinced that there's no reason to maintain use of➗when there's the perfectly good / symbol for division. Thanks to for prompting this change.
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Function notation is great but we should just agree to use square brackets to emphasize that it's not multiplication. f[x] not f(x). In general people should put me in charge of notation and I'll promise to clean things up.
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If we're changing function notation, I want something more radical than just changing the bracketing. x>f>g or something similar is better, in my view, than g[f[x]].
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In programming languages like F# and Elm there are ‘piping’ and ‘composition’ operators, which look like:
- x |> f |> g = g(f(x))
- g <| f <| x = g(f(x))
- f >> g = g ∘ f
- g << f = g ∘ f
