The Learning and Teaching of Geometry in Secondary Schools ─ A Modeling Perspective

What role might geometry play in the mathematical education of adolescents during the next century, and how might teachers and researchers contribute to explore those opportunities and challenges?

The Teaching and Learning of Geometry provides an initial consideration of these questions and a primer for teachers and young scholars to get involved in addressing them. Geometry has long been a mainstay of the secondary school curriculum internationally, charged with the responsibility of introducing students to the practices of theoretical mathematics. This book provides a pedagogical framework for the teaching and learning of geometry grounded in theory and research. It can support teacher preparation and professional development, and orient classroom research by teachers and development efforts directed to teachers.

Areas covered include:-

• Curricular perspectives in teaching and learning geometry
• Cognition in geometry
• Teacher knowledge, thinking and beliefs
• Instructional exchanges and classroom interventions
• Ideas for classroom research

Curriculum developers can use this book as a resource for textbook writing, and teacher developers can use this book as a resource for inservice and preservice teacher education course development. Graduate students and teacher-researchers will find in this book both a framework to orient them to the research literature and a guide for short-term classroom research projects.

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of advanced textbooks for teacher education which aims to advance the teaching of maths by integrating mathematics content teaching with the broader research and theoretical base of mathematics education.

Pat Herbst is an Associate Professor of Education and Mathematics at the University of Michigan in the United States of America. A former high school mathematics teacher in Argentina, Pat’s research focuses on the nature of the mathematical work that students do in secondary classrooms and on the work teachers do to manage knowledge development. He has studied mathematical work, student thinking, and teacher decision-making in geometry classrooms with particular attention to the use of reasoning and proof to solve problems and develop new ideas. Pat’s research aims at describing and explaining the work that teachers do to create and sustain mathematical activity and knowing in classrooms; his research also includes identifying and measuring the sources of justification for teachers’ decisions, including knowledge, situational norms, and professional obligations. Pat has pioneered the use of animated depictions of classroom stories to prompt conversations about instruction among teachers, and using these conversations to understand teachers’ reasoning and decision making. He teaches courses on mathematics instruction, curriculum, and research in the doctoral specialization in mathematics education, and a course on secondary mathematics instruction for the teacher education program. He received his doctorate from the University of Georgia in 1998. Pat is on the Editorial Boards of Educational Studies in Mathematics, Journal of Mathematics Teacher Education, and Recherches en Didactique des Mathematiques.

Taro Fujita is an Associate Professor of Mathematics Education at the University of Plymouth, UK, working in the initial teacher training of primary teachers. Originally trained as a mathematics teacher in Japan, he teaches the teaching and learning of mathematics in primary schools and higher mathematics to specialist (elementary geometry, number sequences, group theory, and so on). He also supervises research projects undertaken by both under- and post-graduate students. His main research interests include the history of mathematics education in the early twentieth century, the teaching and study of geometry and proof, the use of technology in the teaching and learning of proof in geometry, and mathematics education as design science. In particular, he is interested in how learners engage productive reasoning processes in geometry. He received his doctorate from the University of Southampton, UK in 2003. He is an editorial assistant of the International Journal for Technology in Mathematics Education.

Stefan Halverscheid is professor of Mathematics Education at the Georg- August University Gottingen since 2009. His research interests are the study of epistemic dispositions and actions for and during the learning of mathematics. For this, he works with quantitative empirical studies for the cognitive dispositions and qualitative studies for learning situations in the contexts of mathematical modelling and problem solving in geometric as well as interdisciplinary settings. He studied mathematics, physics and teacher education at Hamburg, Warwick and Bochum, where he obtained his doctorate in differential and complex geometry in 2001. He taught four years at a high school and lectured in teacher education at Munster, Oldenburg and Bremen, where he became, in 2006, assistant and later associate professor. He was member of the board of the Center of Teacher Education at Bremen University and of the Center of Educational Research at Gottingen University, where he is dean of studies for mathematics (2010-2013).

Michael Weiss has been (until 2012) an Assistant Professor in Mathematics and Education at Oakland University and is now an Assistant Professor of Mathematics Education at Michigan State University in the United States of America. With a background in both pure mathematics and education research, and experience as a high school mathematics t