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.

Gesche Pospiech, TU Dresden, GermanyMarisa Michelini, University of Udine, Italy
Bat-Sheva Eylon, Weizmann Institute of Science, Israel

Framework of Mathematization in Physics from a Teaching Perspective, Gesche Pospiech.- Part I:  Perspectives on Mathematics in Physics Education.- The "math as prerequisite illusion: Historical considerations and implications for physics teaching, Ricardo Karam , Olaf Uhden, Dietmar Höttecke.- Students understanding of algebraic concepts, Andre Heck, Onne van Buuren.- Mathematical representations in physics lessons, Marie-Annette Geyer, Wiebke Kuske-Janßen.- What is learned about the role of mathematics in physics while learning physics concepts? A mathematics sensitive look at physics teaching and learning, Olaf Krey.- Part II: Learning Mathematization.- Blending physical knowledge with mathematical form in physics problem solving, Mark Eichenlaub, Edward F. Redish.- Theorems-in-action for problem solving and epistemic views on the relationship between physics and mathematics among pre-service physics teachers, Ileana M. Greca, Ana Raquel Pereira de Ataíde.- Learning to use formulas and variables for constructing computer models in lower secondary physics education, Onne van Buuren, Andre Heck.- Graph in physics education: from representation to conceptual understanding, Alberto Stefanel.- Comparing student understanding of graphs in physics and mathematics, Maja Planini, Ana Su¨ac, Lana Ivanjek, ´eljka Milin-¦ipu¨.- Combining physics and mathematics learning: Figuring out the latitude in pre- service subject teacher education, Terhi Mäntylä, Jaska Poranen.- Part III: Teaching Mathematization.- Role of teachers as facilitators of the interplay physics and mathematics, Gesche Pospiech, Bat-Sheva Eylon, Esther Bagno, Yaron Lehavi.- A case study of the role of mathematics in physics textbooks and in associated lessons, Lena Hansson, Örjan Hansson, Kristina Juter and Andreas Redfors.- Starting with physics -  A problem-solving activity for high-school students connecting physics and mathematics, Esther Bagno, Hannah Berger, Magen, E. , Polingher, C. , Yaron Lehavi, BatSheva Eylon.- Part IV:  Facilitating Mathematization by Visual Means.- Taking the Phys-Math interplay from research into practice, Yaron Lehavi, Roni Mualem, Esther Bagno, Bat-Sheva Eylon.- Algodoo as a Microworld: Informally Linking Mathematics and Physics, Elias Euler, Bor Gregorcic.