At my current institution, “Mathematics for Elementary Teachers” is a one-semester course that meets for 6 hours per week, ostensibly divided into three hours of lecture and three of laboratory weekly. I have been teaching that course for many years — indeed, no one else currently in my department has taught it — and in that time, I have looked at many textbooks for that audience and that course. As is the case with many standard service courses, there seems to be considerable agreement on most of the topics to be covered, so I have developed my own core list of criteria for evaluating these books.

First, I hope that a math-for-elementary-teachers textbook will be a resource for future teachers — something they can keep with them as they move out of my class and into their first teaching position. On that score, Stein and Wallace have written a fine text. The emphasis is on the mathematics, and while the students’ goal to teach is not far from the surface, the content manages to dominate. Indeed, there is no laundry list of NCTM Standards to detract from the primacy of the mathematics. (I accept that others may regard this as a flaw.)

I also hope that students will find the mathematics they will use as professionals in their textbook, and so I look carefully for a full section explaining the normal distribution and the mathematics behind percentiles, which teachers will need when trying to interpret their students’ standardized test results. Unfortunately, no such section is present here, though there is a very brief mention of percentiles. While that is a flaw in my opinion, it’s one that can be easily filled in by those who feel it’s important.

That, however, is the only concern I have about this book. The standard topics are all here and covered in an unusual level of detail — which is to be expected when the book includes more than a year’s worth of material. A student armed with this book and with the experience of learning from it will be well-prepared, mathematically, for a career as an elementary school teacher.

Mark Bollman (mbollman@albion.edu) is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.

## Comments

## Christine von Renesse

This book provides a wonderful range of topics across all grades. In addition to the content typically covered in an elementary and middle school mathematics class you can find star polygons, Fermat's last theorem, semi-regular tessellations, perspective drawings, line designs, box puzzles and many more. Many chapters also contain interesting historical connections or explorations.

I like the balance between short descriptions and examples and the wealth of interesting explorations. In working with school teachers I often find it challenging to convey to them what I consider a "good problem" and how to find one. In my opinion a good problem motivates students to explore a mathematical question for which they want to know the solution without having to be told how to do it. Well, this book really provides a school teacher with many good problems to run or enrich a mathematics classroom. The material is challenging enough to cover part of high school mathematics as well.

Having taught classes for future teachers and offered professional development for many years now, I strongly believe that it is necessary to focus on inquiry-based learning and teaching instead of a mostly lecture-centered classroom. It is very difficult for College students and school teachers to shift their beliefs towards teaching mathematics in an inquiry-based way - mostly because their own experiences in lecture based mathematics classrooms have left them to expect that a problem cannot be solved unless an expert first explains how to do it. For that reason I find it essential to use books like Robert Stein's that support the inquiry of mathematics.

The focus of the book is clearly the mathematics (and not the methods of teaching it) but the book does provide much more: It covers in detail the different models for the operations, it repeatedly emphasizes the need to understand rather than memorize, and gives many helpful suggestions and connections for the use of the problems in a classroom.

I highly recommend Robert Stein's book as a resource for content and methods classes for future teachers as well as a support for in service school teachers.