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n my opinion, someone whose mathematical thinking is weak enough that they don't understand pre-algebra, algebra, and basic geometry ( 7th grade or 8th grade math) well enough to teach it when they have a textbook available to refer to, has no business professionally directing the mathematical development of children, period.

I guess I haven't given this a great deal of in-depth thought. I agree that teachers even of early primary grades should have a strong foundation in basic math proficiency, such as pre-algebra, algebra, and basic geometry; that is actually going to come up. Graphing functions, not usually, unless we're talking about our kids. I can see the argument, and yet I guess I think I would rather teachers got really strong pedagogical instruction in good teaching, or perhaps stronger mentoring, than intensive testing and tutoring in higher-order math.

This is again with the caveat that I actually do not know what basic high school level math is. I don't think algebra and geometry are tpyically taught in junior high to nonhonors track kids, are they?