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It seems like it had some false starts, but it had a lot of good ideas, and modern math education is much better off for having tried it. The article says that it went out of fashion, but math classes through all levels of elementary and secondary school are still designed such that you can't pass without understanding what you're doing (unless you are forced to pass by NCLB).
>produced students who had "heard of the commutative law, but did not know the multiplication table."
This is still true today if you look at young students, since the commutative property of addition is taught with addition, which is all taught before multiplication. I don't know why this is stated as a bad thing, though. If you don't even know that addition is commutative, then you don't know what addition is, which could make it hard to understand what multiplication is.
