While there is a great deal of common ground between mathematics and mathematics education, academia being what it is the interaction between the two often degenerates into a turf war. There is the ongoing tussle regarding what courses should future teachers of mathematics take, whether there should be an emphasis on education classes or on learning more mathematics. As is mentioned in one article in this collection, this dispute can be summed up with a simple Venn diagram where the two circles represent education and math content.
The purpose of this book is to try to calm this academic kerfuffle and try to get both sides, which need each other and often face the same powerful opponents, to work together. On the other side is the continuing decline in the mathematical skills of the next generation of students, a trend that alarms every person in the mathematical/scientific community. The book contains a series of papers written by people in both the math and mathematics education communities regarding their differences as well as their common purpose.
Some very valid and important points are made in these papers. One of the most important is that there is reason to believe that the increased mathematical background of an instructor does not necessarily correlate with an increase in the quality of the instruction. The great Martin Gardner often said that the reason he was so good at explaining math was because he did not know very much of it. This forced him to thoroughly think through a subject before he wrote about it. Of course, the only person that could justifiably make such a statement about the great one was Gardner himself.
Some of the other topics of the papers include the role of the history of mathematics in the preparation of educators, the role of visualization, the philosophy of mathematics, various problem solving tactics, the current and future role of technology in instruction and what the expectations are between the two camps of mathematics and mathematics education. Veterans of math departments will have already experienced much of what is described.
The rise of the Common Core Standards in Mathematics (CCSM) in the United States has opened yet one more front in the struggle to teach mathematics. There is opposition to the guidelines, although when I read through the list of math topics by grade it comes across as a very reasonable list of things students should be able to understand. The CCSM is one area where the mathematics and mathematics education communities should be occupying the same space, for the obvious and unfortunate alternative is additional erosion in the level of math instruction. This is one of many areas of agreement described in this book where it is in the best interests of both groups to present a united front.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.