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Mathematics in Physics Education

Gesche Pospiech, Marisa Michelini, and Bat-Sheva Eylon, editors
Publication Date: 
Number of Pages: 
[Reviewed by
Andrzej Sokolowski
, on
While the tools of mathematics support the discoveries of natural phenomena and their concise symbolic notation, the scope of mathematics used to support physics education is described as unsatisfactory by contemporary research. The book Mathematics in Physics Education, containing studies of 33 researchers, mainly from Germany (6), Israel (6), and Sweden (6), strives to respond to this deficiency and provide didactical solutions to induce more algebraic reasoning to physics teaching at the high school level. The authors identify barriers preventing students from activating their more in-depth mathematical knowledge in learning physics and provide suggestions for pathways to help overcome these barriers. 
The research papers are targeting the math-physics interplay from various perspectives, grouped in four chapters. Historical perspectives on the supporting role of mathematics in physics education initiate the book (chapter 1). In chapter 2, the authors bring students’ perceptions and views of how to mathematize physics concepts. Teacher’s perspectives on mathematizing physics concepts are presented in chapter 3. The final chapter presents two research papers on how students learn physics by real or simulated experimentation.
The book provides a wealth of research findings on how mathematical structures are currently used in physics. Populated by diagrams represented, for example, modeling in physics (Fig. 1.1, p.7) or the relation between schemes and mental models (Fig. 7.2, p. 159) the book offers ready- to- use pathways to enhance the teaching of physics not only in the area of the epistemology of physics. Certain areas could get more attention to enhance and support the theme of the book. 
Limiting Case Analysis. The idea of applying functional analysis and considering limiting cases is an emerging compelling mathematical reasoning with a high potential in physics. Limiting case analysis surfaced in several research papers in this book; for example, on p.120, p.129, and p.146. Yet, focusing on particular phenomena does not display the full potential of this strategy. The readers would perhaps welcome suggestions of generalization of this sophisticated calculus concept across physics curricula. Research papers investigating how this strategy helped students learn physics and succeed in problem-solving would be a great asset. 
Graph Analysis in Physics. A substantial amount of research presents findings on how physics students perceive graphs in physics versus how they perceive graphs in mathematics. The perceptions are obviously different due to focusing on different aspects of graphs; in physics on extracting phenomena behaviors, in math on learning the craft of graph analysis. The different perceptions can also account for the fact that in physics, graphs are not explicitly described as function representations. Perhaps instead of discussing the differences, including more studies that attempt to merge these views could open an area for designing a new physics curriculum. For example, (p. 215) students are to predict shapes of graphs for the motion of Toy-cars. Possible graphs are described as triangular or trapezoidal graphs. Students might not find such graphs descriptions in their mathematics classes. Perhaps using the language of mathematics, thus describing the graphs as piecewise with different slopes and attempting to write using a piecewise notation would better support the math-physics interplay that the book emphasizes?
Problem Solving and Function Attributes. While there is a visible notion that the interplay between physics and math can be supported by functional analysis, there are not many studies in this book that would investigate how students solve physics problems using attributes of algebraic functions.  For example, the interpretation of the vertex of a parabola as means of learning the time and the maximum height a projected object attains, or solution of a system of two-position functions as a point when one object passes the other. It seems that such examples could enrich the interplay and provide opportunities for students to find more logic and usefulness of algebraic structures in physics.  


 Andrzej Sokolowski is a researcher interested in applying mathematical modeling to develop scientific inquiry.