which describes improved university courses for students who plan to become elementary teachers. That is a big emphasis in the United States now--international comparisons have shown that mathematics education of elementary pupils in the United States is lousy largely because the mathematical education of elementary teachers (at all levels) is lousy,
so United States mathematicians are trying to do something about that that is more effective than the 1960s attempt at "new math."
Yes, Stillwell's book, mostly aimed at mathematics students who will go on to be mathematicians rather than schoolteachers, is also an outcome of thinking about curriculum reform. He describes his motivation for writing his excellent book as attempting to understanding concepts of mathematics he still didn't understand after he earned his Ph.D. at MIT.
"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!
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.
I am reading just now a very interesting book The Mathematics Pre-Service Teachers Need to Know
ftp://math.stanford.edu/pub/papers/milgram/FIE-book.pdf
(posted on
http://hub.mspnet.org/index.cfm/13083
which warns that it may be a slow download)
which describes improved university courses for students who plan to become elementary teachers. That is a big emphasis in the United States now--international comparisons have shown that mathematics education of elementary pupils in the United States is lousy largely because the mathematical education of elementary teachers (at all levels) is lousy,
http://www.ams.org/notices/200502/fea-kenschaft.pdf
so United States mathematicians are trying to do something about that that is more effective than the 1960s attempt at "new math."
Yes, Stillwell's book, mostly aimed at mathematics students who will go on to be mathematicians rather than schoolteachers, is also an outcome of thinking about curriculum reform. He describes his motivation for writing his excellent book as attempting to understanding concepts of mathematics he still didn't understand after he earned his Ph.D. at MIT.