Singapore's math program in elementary is actually much less recitation and rote based than we are used to in Western mathematics education.

Indeed, it's very much pictorial and intuition-building in ways that fans of DI tend to look down on. It's concept and problem solving before rote.

I don't know so much about these countries in primary education, but I do have a few Japanese textbooks from secondary school translated into English and published by the AMS. This material also seems less rote-heavy than I am used to.

E.g. I'm looking at an on-level grade 7 mathematics textbook, and it's spending a lot of pages justifying the idea of negative numbers in addition and subtraction and with pictorial representation and has comparably few problems to do.

In a US math textbook, this material would have been done before grade 7, but in less depth. There would be a whole lot of rules, algorithms, and rote practice.