It's frightening to think I've been out of school for more than a decade, but all this stuff must be really new. I remember learning math the traditional way and being assigned pages of problems for practice. We used to do timed drills where every student would get a page full of basic problems and 2 minutes to complete as many as possible.

I think the emphasis on "making learning fun" has driven common sense from educational curricula.

To be fair, though, some of the methods they're teaching in these books just mirror how you might go about solving a problem in your head. That's fine, if you want to teach kids to think about problems when they can't get out pencil and paper, but there's no need to use these methods when you have writing instruments available.

Students get plenty of practice making diagrams and breaking down problems once they get into advanced math classes where those are valid methods. When problem solving switches from applying the one method you've learned to picking the most appropriate approach from a set, these teaching methods have merit. But, that's Calculus, not fifth grade math.