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Comparison of Mathematics and Physics Education I

Simon Friedrich Kraus and Eduard Krause, eds.
Publication Date: 
Number of Pages: 
[Reviewed by
Andrzej Sokolowski
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The book Comparison of Mathematics and Physics Education 1 is the first book of the series edited by Simon Friedrich Kraus and Eduard Krause and published by Springer Spektrum. The volume is a product of a joint effort of cooperation between the Hanoi National University of Education, Vietnam, and the University of Siegen, Germany. Aiming at improving teachers' pedagogical content knowledge, the book summarizes theoretical foundations of mathematics and physics education, reaching out to their historical development.
The inductively organized book content is composed of three parts. Part 1 discusses a general idea of interdisciplinarity at high school and university levels, pinpointing a need for intertwining the didactics of mathematics and physics to develop students' holistic perspectives on learning the laws of nature. Part 2 zooms into the contents of both disciplines, also referring to an abstract nature of modern mathematics.  An unquestionable asset of this book is citing students' perspectives on mathematics and physics that the readers will find in this chapter. Part 3 is designated to extracting topics of a special significance in both the didactics of mathematics and physics that could be used in school practice. This part can be considered a departing point for volume 2 of the series.
The book is heavily populated by references to historical developments of scientific and mathematical laws, making it an excellent resource for teachers seeking to enhance their lessons’ contents. For example, the readers can find a detailed derivation of Galilei's law of uniformly accelerated objects, learn about the genesis of implementation calculus to physics or details of Euclid's geometry and its effects on the development of modern geometry. Alongside finding roots of complex numbers using the Moivre theorem, the reader can also find a review of the Van der Waals gas law or applications of linear differential equations. 
To link the historical development of mathematics and physics content, the authors reviewed contemporary theories of education and applications of terms such as preconceptions or misconceptions that are frequently used in mathematics and physics. Departing for this stage, they brought to life the cognitive processes of constructing new knowledge in mathematics and physics. They identified similarities and pointed out the differences. Modeling as an effective way of merging observations, data, and abstract mathematical representations to enhance understanding is also discussed.
Problem-solving in mathematics and physics are primary types of assessments. The book concludes by providing definitions and descriptions of problem-solving in both subjects. While Pólya’s cycle is designated as a primary theoretical scheme to support problem-solving in mathematics, Friege's model that requires a deep understanding of the scientific concepts before an attempt to embrace these entities in problem-solving can be made appears as the main framework to support problem-solving in physics. 
The design of the book's structure that intertwines mathematics and physics considering various layers of their mutual entanglement is promising enough to look forward to reading the other volumes of this book series. 


Andrzej Sokolowski, Ph.D., is a researcher interested in using mathematical reasoning as a method of supporting physics understanding. He is also a mathematics and physics adjunct professor at Lone Star College, TX.