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"mathematics education of elementary pupils in the United States is lousy largely because the mathematical education of elementary teachers (at all levels) is lousy"

This is something I've noticed in the time I spent working with teachers. It amazes me how many 4th-6th grade teachers don't understand fractions, but are trying to teach them to kids!

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What do you mean when you say they don't understand fractions?

I mean, I have watched groups of elementary school teachers work on the same sort of problems they assign (fractions being one example) and struggle mightily. They understand the basic concept of what a fraction is, but many of them get bogged down in the algorithms because they don't really understand what the algorithms represent.

What is a "common denominator" beyond "the thing you put fractions over to be able to add them"? Many of the teachers I've worked with would struggle to explain this to students.

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