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[quote=Anonymous][quote=Anonymous][quote=Anonymous]I like fraction wheels and cooking, but it's easy to waste a HUGE amount of time on manipulatives when you should instead be drilling on paper.

I suggest "Key to Fractions", a very inexpensive four-book workbook series. Get it either used or from Rainbow Resource.  Also  math-drills.com for printable worksheets for extra practice. (They have some with autofill for answers. Don't do that, just print them out.)

NB that fractions are the most difficult topic in elementary school math; IIRC in Liping Ma's blockbuster "Knowing and Teaching Elementary Mathematics", something like 40% of teachers failed to do a fractional division problem correctly, and only one out of twenty-five or so could come up with an example of fractional division, and the one she came up with wasn't that great.[/quote]

I like to knock on FCPS all the time, but this stat amazes me. My kids upper ES teachers could all easily do this kind of math. I have no idea about lower ES, because they aren't doing fractional division. Maybe the problem was she was interviewing mostly kindergarten and 1st grade teachers?[/quote]

23 or 24 US elementary school teachers, chosen among a group specifically interested in math. Some of them were probably teaching younger grades, some of them older. My guess is the ones in upper grades were much more likely to get the right answer, but even they were poor at explanations.

She also interviewed a group of Chinese ES math teachers, and they did much, much better. I do wonder to what extent this is still true, IIRC China is moving away from its old Normal School model, and in any case it is a lot richer and more modernized now, and the more bookish men and women may be heading into other parts of the economy.

Ma's thesis is that what you want out of math teachers for ES is something she termed "profound understanding of fundamental mathematics". It is an amazing read, one of those books that really did change my thinking.[/quote]

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