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Mathematical Modelling for Teachers

Jürgen Maaß, Niamh O'Meara, Patrick Johnson, and John O'Donoghue
Publication Date: 
Number of Pages: 
Springer Texts in Education
[Reviewed by
Katherine Safford-Ramus
, on
During the Thirteenth International Congress on Mathematical Education (ICME-13) held in Hamburg, Germany in 2016 a thematic afternoon session was devoted to mathematical modeling, a long tradition in the German-speaking countries. As a member of the NSF-supported American delegation to the conference, I was designated to focus on the various modeling sessions at the conference which included that thematic afternoon. While not explicitly stated within this volume, the influence of that tradition flavors the work presented by these authors.
This book, however, is not a theoretical work. It is, as the title states, a practical guide for those who intend to augment their current classroom instruction with opportunities for students to engage in modeling. Each chapter is organized as a dialogue with the reader and at various points, you are invited to ponder and respond to questions that spur reflection on your current classroom practice as well as your knowledge of modeling and mathematics. Where appropriate, the philosophical and theoretical underpinnings of the book are presented but they appear as supporting actors, not the principal players. The reader is invited to be a person of action and to indorse modeling as a prominent activity in the mathematics classroom.
The first two chapters introduce the basic tenets of modeling and argue for it to be central to classroom teaching.  The next three chapters invite the reader to delve ever deeper into ways that modeling can be included in instruction. First, the authors discuss alterations to standard textbook problems that render them to be modeling activities.  Next, they offer a chapter rich in examples drawn from everyday situations.  A third, lengthy chapter gives a detailed description of a project that can be used over an extended period of time to actively engage students in modeling.  The example project given focuses on gambling and by a strange coincidence was read by me over Superbowl weekend.  I was able to envision its incorporation through the myriad ways people were reported to be betting on that game. 
A fourth chapter presents real-world examples of modeling performed by experts. This is followed by one containing advice for teachers concerning ways to implement modeling in their classrooms. The final two chapters offer findings from empirical research and a theoretical framework to support the authors’ case. This book was written by authors who work within the European Union and the examples presented utilize metric measures and the Euro currency.  The American reader will find, however, that several of the resources suggested for additional problems are US-based and the problems presented with EU values can be easily translated to United States measures.
The primary audience for this volume is secondary school teachers. It could be read independently, incorporated into pre-service preparation courses, or used as the focus of a departmental study circle.  A broader audience would include instructors in developmental programs at the college level. The student body there has already visited the mathematical content of secondary school and could benefit from instruction that centered on the application of that content in domestic and industrial situations. In truth, the methodology promoted by the authors extends well into the college-level courses particularly elementary calculus.

Katherine Safford-Ramus recently retired as a Professor of Mathematics at Saint Peter’s University, Jersey City, New Jersey.  Her research focuses on adults learning mathematics.  She is the author of Unlatching the Gate: Helping Adult Students Learn Mathematics and most recently edited Contemporary Research in Adult and Lifelong Learning of Mathematics: International Perspectives, a volume based on papers from the Topic Study Group 6 of the Thirteenth International Congress on Mathematical Education.

See the table of contents in the publisher's webpage.