[ef4]

> The thing is, I can't think of another way to teach the curriculum.

But there's already a rich literature of real-world results for better ways to teach mathematics. See for example Seymour Papert's "Mindstorms" as a starting point (and much has been done since it was written ~30 years ago).

All children already learn quite a lot of fairly deep mathematical intuitions. We just take them for granted because everybody learns them.

For example: conservation of volume, the concept of "integer", order independence of cardinality, projecting orientation onto other reference frames, the equivalence between ordinal and cardinal numbers.

Everybody learns these things because they're embedded in our environments, and we can learn them playfully as children. When we create environments that embed even richer concepts, children learn those concepts just as easily. This is the explicit design goal of LOGO, and the whole family of descendants it has inspired.

Teaching in this way requires a degree of freedom and play that normal schools generally don't tolerate, which is why these proven, powerful tools still haven't taken over the world.