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.

This volume, which is the output of a DAAD-funded collaboration between the University of Siegen and the Hanoi National University of Education, discusses and summarizes theoretical foundations of common grounds of mathematics and physics education. This interdisciplinary perspective enables especially teachers who have only been trained in one of these subjects to enrich their pedagogical content knowledge. The starting point is a description of characteristics of the disciplines and their historical genesis, followed by comparative studies. This edited volume brings together thirteen stimulating contributions on educational aspects of both disciplines written jointly by experienced researchers from Germany and Vietnam.

Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding.

This book discusses novel research on and practices in the field of physics teaching and learning. It gathers selected high-quality studies that were presented at the GIREP-ICPE-EPEC 2017 conference, which was jointly organised by the International Research Group on Physics Teaching (GIREP); European Physical Society – Physics Education Division, and the Physics Education Commission of the International Union of Pure and Applied Physics (IUPAP). The respective chapters address a wide variety of topics and approaches, pursued in various contexts and settings, all of which represent valuable contributions to the field of physics education research. Examples include the design of curricula and strategies to develop student competencies—including knowledge, skills, attitudes and values; workshop approaches to teacher education; and pedagogical strategies used to engage and motivate students. This book shares essential insights into current research on physics education and will be of interest to physics teachers, teacher educators and physics education researchers around the world who are working to combine research and practice in physics teaching and learning.

This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementation of representations should consider design principles for using multiple representations. Investigations regarding their effect on classroom communication as well as on the learning results in all levels of schooling and for different topics of physics are reported. The book is intended for physics educators and their students at universities and for physics teachers in schools to apply multiple representations in physics in a productive way.

This book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students’ skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such training The book draws on current research in developing students’ mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton’s laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.

This open access report explores the nature and extent of students’ misconceptions and misunderstandings related to core concepts in physics and mathematics and physics across grades four, eight and 12. Twenty years of data from the IEA’s Trends in International Mathematics and Science Study (TIMSS) and TIMSS Advanced assessments are analyzed, specifically for five countries (Italy, Norway, Russian Federation, Slovenia, and the United States) who participated in all or almost all TIMSS and TIMSS Advanced assessments between 1995 and 2015. The report focuses on students’ understandings related to gravitational force in physics and linear equations in mathematics. It identifies some specific misconceptions, errors, and misunderstandings demonstrated by the TIMSS Advanced grade 12 students for these core concepts, and shows how these can be traced back to poor foundational development of these concepts in earlier grades. Patterns in misconceptions and misunderstandings are reported by grade, country, and gender. In addition, specific misconceptions and misunderstandings are tracked over time, using trend items administered in multiple assessment cycles. The study and associated methodology may enable education systems to help identify specific needs in the curriculum, improve inform instruction across grades and also raise possibilities for future TIMSS assessment design and reporting that may provide more diagnostic outcomes.