Mathematics in Physics Education

Description

This book is about mathematics in physics education, the difficulties students have in learning physics, and the way in which mathematization can help to improve physics teaching and learning. The book brings together different teaching and learning perspectives, and addresses both fundamental considerations and practical aspects. Divided into four parts, the book starts out with theoretical viewpoints that enlighten the interplay of physics and mathematics also including historical developments. The second part delves into the learners’ perspective. It addresses aspects of the learning by secondary school students as well as by students just entering university, or teacher students. Topics discussed range from problem solving over the role of graphs to integrated mathematics and physics learning. The third part includes a broad range of subjects from teachers’ views and knowledge, the analysis of classroom discourse and an evaluated teaching proposal. The last part describes approaches that take up mathematization in a broader interpretation, and includes the presentation of a model for physics teachers’ pedagogical content knowledge (PCK) specific to the role of mathematics in physics. Front Matter ....Pages i-x Framework of Mathematization in Physics from a Teaching Perspective (Gesche Pospiech)....Pages 1-33 Front Matter ....Pages 35-35 The “Math as Prerequisite” Illusion: Historical Considerations and Implications for Physics Teaching (Ricardo Karam, Olaf Uhden, Dietmar Höttecke)....Pages 37-52 Students’ Understanding of Algebraic Concepts (André Heck, Onne van Buuren)....Pages 53-74 Mathematical Representations in Physics Lessons (Marie-Annette Geyer, Wiebke Kuske-Janßen)....Pages 75-102 What Is Learned About the Roles of Mathematics in Physics While Learning Physics Concepts? A Mathematics Sensitive Look at Physics Teaching and Learning (Olaf Krey)....Pages 103-123 Front Matter ....Pages 125-125 Blending Physical Knowledge with Mathematical Form in Physics Problem Solving (Mark Eichenlaub, Edward F. Redish)....Pages 127-151 Theorems-in-Action for Problem-Solving and Epistemic Views on the Relationship Between Physics and Mathematics Among Preservice Physics Teachers (Ileana M. Greca, Ana Raquel Pereira de Ataíde)....Pages 153-173 Learning to Use Formulas and Variables for Constructing Computer Models in Lower Secondary Physics Education (Onne van Buuren, André Heck)....Pages 175-194 Graph in Physics Education: From Representation to Conceptual Understanding (Alberto Stefanel)....Pages 195-231 Comparing Student Understanding of Graphs in Physics and Mathematics (Maja Planinic, Ana Susac, Lana Ivanjek, Željka Milin Šipuš)....Pages 233-246 Combining Physics and Mathematics Learning: Discovering the Latitude in Pre-service Subject Teacher Education (Terhi Mäntylä, Jaska Poranen)....Pages 247-266 Front Matter ....Pages 267-267 Role of Teachers as Facilitators of the Interplay Physics and Mathematics (Gesche Pospiech, Bat-Sheva Eylon, Esther Bagno, Yaron Lehavi)....Pages 269-291 A Case Study of the Role of Mathematics in Physics Textbooks and in Associated Lessons (Lena Hansson, Örjan Hansson, Kristina Juter, Andreas Redfors)....Pages 293-316 Starting with Physics: A Problem-Solving Activity for High-School Students Connecting Physics and Mathematics (E. Bagno, H. Berger, E. Magen, C. Polingher, Y. Lehavi, B. Eylon)....Pages 317-331 Front Matter ....Pages 333-333 Taking the Phys-Math Interplay from Research into Practice (Yaron Lehavi, Roni Mualem, Esther Bagno, Bat-Sheva Eylon, Gesche Pospiech)....Pages 335-353 Algodoo as a Microworld: Informally Linking Mathematics and Physics (Elias Euler, Bor Gregorcic)....Pages 355-385