As fate would have it, I was invited to review this book at the same time that I was reviewing Mathematical Methods in Science by George Pólya. Although separated by fifty years, the message of both texts is the same, namely, that good secondary school mathematics education must locate the rationale for studying the subject in real-world applications. Maasz and O’Donoghue reason that the process of studying real-world problems prepares the students to be better citizens, individuals who learn to work with others, consider multiple solution strategies, and examine other factors that might influence one solution choice over another.
As the title states, the book is a collection of case studies centered on the process of developing mathematical models for real-world situations. The studies span a variety of topics from science, technology, probability, statistics, and everyday life. All of the authors work in the European Union and the discourse reflects that fact. An American reader would have to adjust the concepts of some chapters to fit the eyes and ears of students in the United States. For example, the chapter on teaching geometry using rugby and snooker would have to be “translated” into the language of pool and soccer or football. On the other hand, the chapter on political polls and surveys has universal implications, particularly this year as Americans are barraged daily with the results of the latest election poll.
This is not a “how-to” book with sixteen lessons that an instructor can slot into their lesson plans for the week. It is, rather, a thought-provoking text that invites teachers to consider the occasional inclusion of real-world topics into their curriculum and demonstrates examples of ways in which that goal can be achieved. It is a collection of works largely written by authors for whom English is a second language, so there is a slight variation in the writing styles. A minor irritant for me was the occasional illustration in German or Dutch that lacked a translation. That was, however, far outweighed by the breadth of examples that triggered the questions “How can I use this in my classroom?” and “What situations from the lives of my students could I model mathematically?” in my role as a mathematics teacher in service courses at my college. None of the authors are George Pólya, yet his spirit lives on in their reports about teaching application-centered mathematics.
Katherine Safford-Ramus is Professor of Mathematics at Saint Peter’s College, the Jesuit College of New Jersey. She has been teaching mathematics at the tertiary level for 28 years. From October 2005 to October 2006, she served as the co-director of the Adult Numeracy Initiative, a project of the United States Office of Vocational and Adult Education, a division of the Department of Education. Safford is the author of Unlatching the Gate: Helping Adult Students Learn Mathematics. Her current research continues to focus on adults learning mathematics and, in particular, professional development of teachers as adult learners.
1. Modelling in Probability and Statistics: Key Ideas and Innovative Examples
Manfred Borovcnik and Ramesh Kapadia
2. Problems for the Secondary Mathematics Classrooms on the Topic of Future Energy Issues
Astrid Brinkmann and Klaus Brinkmann
3. Coding Theory
4. Travelling to Mars: A Very Long Journey: Mathematical Modelling in Space Travelling
5. Modelling the Storage Capacity of 2D Pixel Mosaics
Simone Göttlich and Thorsten Sickenberger
6. Mathematics for Problems in the Everyday World
7. Political Polls and Surveys: The Statistics Behind the Headlines
8. Correlations between Reality and Modelling: “Dirk Nowitzki Playing for Dallas in the NBA (U.S.A.)”
Herbert Henning and Benjamin John
9. Exploring the Final Frontier: Using Space Related Problems to Assist in the Teaching of Mathematics
10. What are the Odds?
Patrick Johnson and John O’Donoghue
11. Models for Logistic Growth Processes (e.g. Fish Population in a Pond, Number of Mobile Phones within a Given Population)
12. Teaching Aspects of School Geometry Using the Popular Games Rugby and Snooker
13. Increasing Turnover? Streamlining Working Conditions? A Possible Way to Optimize Production Processes as a Topic in Mathematics Lessons
14. Mathematics and Eggs: Does this Topic Make Sense in Education?
Juergen Maasz and Hans-Stefan Siller
15. Digital Images: Filters and Edge Detection
16. Modelling and Technology: Modelling in Mathematics Education Meets New Challenges
List of Contributors