At 08:16 PM 9/1/00, Wayne Bishop wrote: >A bit mathematically arrogant perhaps, but it does bring up a serious >concern. Too many of our education students take history of mathematics >as a way to *avoid* mathematics and history of mathematics "education" >tends to be even less mathematically oriented. Its a bit like a student >blind from birth taking art history or deaf from birth in music history.
Of course, Wayne commenting on math history is a bit like an agronomist (or shall we call him a "horticulturist") taking over a biology department and preaching on the evils of genetics. But this may be too personal a comment.
An anecdote, of sorts: last semester I was in a History of Mathematics course with two dozen students. Exactly one was an "education" student, but 6 were history students. The course was both mathematically rigorous and intensive, but the subject matter was historical development of mathematics, not group theory.
The course that Wayne described would be more appropriate for a math department SEMINAR (as a course in automorphic functions may be an interesting seminar in number theory and a course in decidability may be a seminar in logic), not a course in history of mathematics. Too many arrogant mathematicians think they are experts in math history when they don't even know how mathematics has changed over the years (nor do they even accept the fact that it HAS changed).
At 11:37 AM 9/1/00, David Slavit wrote: >Tena, > >One *suggestion* I would make would be to accompany your history of math >discussion in tandem with a history of mathematics education, particularly >during the last century.
Although I find the topic fascinating and would add Dewey's Psychology of Number and much written by David Eugene Smith in the first quarter of the XXth century, this is not an appropriate focus for history of mathematics. Furthermore, even if this IS the main focus, one cannot help but to go at least a century further back, to the time when Euclid as the mainstay of mathematics began its decline. Unfortunately, without sufficient background, the changes in *philosophy* of mathematics that took place at this time may be beyond the reach of most math ed and undergraduate math students. They may benefit much more from the actual history of a few mathematical concepts between, say, 400 BCE and 1750 CE (for instance, one can take one thread to be "equations" and another "quantity").
As for textbooks, even the revision of Boyer is a bit to jumpy, so Katz probably has the best currently published book, complete with exercises. The only drawback is the price--Katz weighs in at nearly $100.