Duolingo for math
An idea I roll around in my head from time to time, not as an idea to be taken literally (i.e. not as something to implement literally), but as a tool to generate new ideas, is trying to imagine what a Duolingo for math would look like. Specifically, the thing that's great about Duolingo for learning is that each task is very bite-sized (can be completed in under a minute). Can a series of such small tasks be deployed for math, in a way that leads to deep understanding?
Tinkering in math requires loading the situation into working memory
ok so what if you made a bunch of evaluation problems for a language like haskell, in the style of Duolingo? you'd have levels like "map", where the prompts are expressions like map (+9) [1..10] or whatever, and you'd have to select the correct response. The idea is to unconsciously figure out the rules of the language, just like you do in the actual duolingo. Can you do this for more complicated things in programming? e.g. instead of solving a programming problem, can you just do it through multiple choice? I'm thinking about Hamish Todd's "vow of silence" for video game development. Is that even possible when teaching things like math and programming? My reductions anki cards kind of have this flavor, though in that case i already have learned the formal definitions, and i'm just now trying to make them intuitive. Maybe Execute Program already sort of does this?
one thought is that language learning is special because the human brain has specialized hardware/software to learn language. that's why duolingo can get away with those 5-second tasks. you cannot do such a thing with math, or physics, or econ. but is this really true?
