Mathematics in Physics Education

Book Preface

In recent years, the interest in the role of mathematics in physics education has risen steadily. This can be seen in connection with the efforts of showing students the nature of physics which has gained increasing importance in physics education. Whereas the conceptual understanding of physics is an important goal of physics education, it is equally undoubted that mathematics is inevitably inherent in physics and its methods. As the physical method lives on the mathematical description of the reality, the mathematical aspects have to be taken into account from the perspective of teaching and learning physics itself as well as learning about physics. This book is devoted to the struggle to make the interplay of physics and mathematics insightful to students. Besides these fundamental considerations, there are practical aspects: the lecturers of first year university science courses all over the world complain increasingly about the difficulties of students in applying mathematical instruments to physical problems. Therefore, the questions arise: what are the deeper reasons of this deficiency, and what can be done about it during secondary school? The research about this topic has become more intense during the last 15 years and has reached a certain state that makes it desirable to gather the most important results from people working in the field in a book. We collected results of research on teaching and learning about the role of mathematics in physics gained so far and cover the whole spectrum of research, the theoretical foundation, as well as empirical results. The book should also raise the awareness of the role of mathematics in physics education and induce further research projects.

The research areas addressed in this book cover a broad range. Therefore, the book is divided into four parts, each concentrating on a specific aspect. In the first part, “Perspectives on Mathematics in Physics Education,” theoretical viewpoints are treated, enlightening the interplay of physics and mathematics and also including historical developments. In the second part, “Learning Mathematization,” with the most contributions, we delve into the learners’ perspective. In this part, not only aspects of the learning by secondary school students but also by students just entering university or teacher students are considered as far as they could shed light onto learning in secondary school. The third part “Teaching Mathematization” includes a broad range of subjects from teachers’ views and knowledge, the analysis of classroom discourse, and an evaluated teaching proposal. In the last part, “Facilitating Mathematization by Visual Means,” approaches are described that take up mathematization in a broader interpretation. These contributions show that formal thinking might start before the use of mathematical elements in a narrower sense and thus prepare mathematization. We hope this book will be a valuable source for researchers in the field, teacher educators, advanced students, as well as interested teachers. We have to thank all the contributors of the book for their patience and, especially, Marisa Michelini for her constant support.

Dresden, Germany Gesche Pospiech
July 2018