"solve 20*10 by moving blocks into sets of ten"
this is what I'm worried about - we teach kids this one, extremely simple way to do things, and once they hit algebra they're screwed
This is actually a good method to
initially teach kids arithmetic. It's hard to fathom not being able to understand why the fastest algorithms and techniques for doing arithmetic work, but that's the reality for lots of people who had bad math teachers in the early grades. If you teach kids a method that is easy to understand conceptually, they won't feel as uncertain when you teach them the 'normal' way of doing math.
I'd compare this to how most high school calculus classes are run. Students get taught the limit definition of a derivative first, and then after they've learned it they get taught all the various rules and shortcuts for differentiation. Without the conceptual background of knowing how a derivative works, none of those rules make any sense and most students would forget them almost immediately.
the multiple methods thing leaves people confused and provides very unnecessary uses. I wish the American education system would realize that you can't make everyone a genius unless you manipulate genes, (which I'm totally okay with.) which leaves schools scrambling to find good results for the 3 standardized tests kids have to take every trimester
I don't think we should structure our educational system with failure in mind. In almost any other discipline of academia, the goal everyone works towards is improving the system at hand. If you're a medical researcher working on a cancer treatment, you work to make treatments that help everyone with cancer with the assumption in mind that it's possible. There's no evidence that (healthy) people are born with inherently lower/higher intelligences because of certain genes. In fact, the apparent heritability of intelligence probably has much more to do with environment (wealth, access to good schools, family structure, etc) than anything in your genome.