Education References

Here are some references that I have found interesting and/or useful regarding math education.

Books:

Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, by Liping Ma, 1999. This book is the result of a comparative study of elementary school mathematics teaching in China and the U.S. Since it came out it has become a standard reference for people involved in math education. Even though it deals with fundamental (i.e. elementary school) mathematics, it makes for extremely interesting reading and applies to mathematics education at all levels. (A review in the AMS Notices ran in September 1999.)
What the Best College Teachers Do, by Ken Bain, 2004. Ken Bain is the director of the Center for Teaching Excellence at NYU. He ran a study over the course of a decade on over 100 of the best college teachers in the country, throughout multiple disciplines, looking at their methods and approaches to teaching. This book contains the results of that study and is aimed at people who are involved in college teaching at any level and in any discipline.
Teaching First: A Guide for New Mathematicians, Thomas Rishel, 2000. This is an excellent book with great insights for beginning teachers.
How to Teach Mathematics, 2nd edition, Steve Krantz, 1999. This is a primer on how to teach mathematics with particular emphasis on the college level. The second edition also contains a large appendix with essays by other mathematicians and mathematics educators in response to the first edition of this book.
California Dreaming, by Suzanne Wilson, 2003. This is a history of K-12 mathematics education in the US with a particular focus on the "Math Wars" in California during the 1990's. There is a review by Anthony Ralston in the AMS Notices (www.ams.org) in the November 2003 issue.
The Great Curriculum Debate: How Should We Teach Reading and Math?, Tom Loveless, Editor, 2001. This is a book of essays regarding the "Math Wars" and the "Reading Wars" which took place during the 1990's.
Mathematical Cognition, James M. Royer, ed, 2003. This is a collection of essays regarding various aspects of cognitive psychology with respect to mathematical cognition. It has a variety of different viewpoints, as well as an essay on the history of K-12 math education in the U.S. (There is an online preprint of this particular essay as well.)
The Teaching Gap, James Stigler and James Hiebert, 1999. This book is a comparison of the mathematics teaching practices of the U.S., Japan, and Germany based on data collected via the Third International Mathematics and Science Study (TIMSS).

Other References:

"Research Mathematicians and Mathematics Education: A Critique," by Anthony Ralston, AMS Notices, April 2004.
"Purposes and Methods of Research in Mathematics Education," by Alan H. Schoenfeld, AMS Notices, June/July 2000.
NCTM Standards: This is the website for the National Council of Teachers in Mathematics Principles and Standards for School Mathematics, i.e. "NCTM Standards." These are a set of recommended standards for what students should learn in K-12 schools, and the latest revision of them took place in 2000. They have been very influential (and divisive) over the past 20 years.
Mathematical Education of Teachers This is a website for the book "The Mathematical Education of Teachers," i.e. MET, produced by the AMS/MAA/CBMS. You can download most of it from this website for free. This is a set of recommendations for how future mathematics teachers should be educated, and it came out in 2001. You can read two reviews of MET in the October 2001 issue of the AMS notices (free online as always at www.ams.org). One of these reviews is by Steve Krantz, and it is an extremely interesting read.
Website of Hung-Hsi Wu, a professor of mathematics at Univ. of California, Berkeley. He has written extensively regarding mathematics education, and has posted a large number of insightful articles and essays on his page.

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