[hakfoo]

That sounds like a nice idea, but the problem is that there are many different ways to reason about most math problems.

If a curriculum is badly designed, it's going to dump one model on the students, and that's going to come to the detriment of some of them. Maybe you already learned your multiplication tables, and sitting around and drawing a 5x6 grid and counting the squares is going to frustrate and annoy. It's almost certainly going to drive parents wild, because they won't be raised with the jargon and rules, leaving them unable to help.

There's also the risk that any new material is poorly debugged or documented. When it's just about "a single right answer", we probably can get consensus that 5x6=30. But if we try to grade the reasoning tools used to get there, those are often not as universally standardized. One kid draws his 5x6 grid horizontally, and one draws it vertically. The teachers and grading rubrics have to have enough understanding and flexibility to recognize they're equivalent. In the worst case, you end up distracting students from the actual concepts by weighing them down with a bunch of unrelated rules unique to the teaching system.

I recall taking a maths class once which basically covered the same problems several times over, each time using a different model to solve them. I could see a case for a course like that. But that was a 400-level elective college course, so there's probably different constraints and expectations than when you're trying to teach 4th grade students multiplication.

The other worry I have is that we're doing a lot of window-dressing in the name of reducing "math anxiety". Every few years they try to dress up math concepts in a new way in the hopes students will find them less intimidating. Why does this seem to be unique to math? There seems to be no rush to replace Shakespeare in the schools with something students can more easily reason about.