My ideal curriculum would have number sense and developing intuition as core tenants, as I feel like these are the most pragmatic skills regardless of how far one goes into mathematics. Every rule and theorem should be exposed and explored as a consequence of the intuitions we’ve already developed; no one should learn the standard arithmetic algorithms without deeply understanding where they came from and why they work. No one should have to memorize which operations have which properties; commutativity, associativity, and distribution are obvious properties of multiplication if you think of multiplication as repeating groups.

I would emphasize the multitude approaches to solving any problem and stress how these approaches are related, how they‘re different manifestations of the same concepts. I would treat logic and critical thinking as equal partners with creativity when it comes to problem solving.

And I would want to see deep and abiding connections made between the topics, never teaching topics in isolation, but building deeper and more complete intuition by seeing how prime numbers relate to geometry and fractals and groups, how groups relate to matrices and permutation, and how permutations relate to probability and cryptography.

It would be visual, it would be expressive, and it would be hands on.