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 geometryCognition in geometryTeacher knowledge, thinking and beliefsInstructional exchanges and classroom interventionsIdeas for classroom researchCurriculum 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.
| Impact---Series Foreword |
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vii | |
| Acknowledgments |
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ix | |
| Introduction |
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1 | (7) |
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1 The Discourse of Teaching and Learning Secondary Geometry through History |
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8 | (40) |
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8 | (1) |
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1.2 Overview of This
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9 | (2) |
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1.3 The Development of Geometry up to the So-Called Foundational Crisis |
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11 | (7) |
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1.4 The Shaping of Geometry Curricula in the Nineteenth and Twentieth Centuries |
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18 | (15) |
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33 | (13) |
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46 | (2) |
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2 Geometric Figures and Their Representations |
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48 | (29) |
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48 | (2) |
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2.2 Conceptions of Figure: What We Mean by Conception |
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50 | (2) |
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2.3 Initial Conceptions of Geometric Figures |
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52 | (7) |
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2.4 The Geometric Diagram in the Literature |
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59 | (9) |
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2.5 A Modeling Perspective in the Study of Figures |
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68 | (7) |
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75 | (2) |
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3 Students' Thinking and Learning in Geometry |
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77 | (37) |
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77 | (2) |
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3.2 Conceptions of Figure and Students' Cognition |
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79 | (12) |
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3.3 Geometric Figures and Students' Learning as Progressive Change in Cognition |
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91 | (8) |
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3.4 Enriching Semiotic Registers, Operations, and Control Structures with DGS |
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99 | (8) |
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3.5 Theoretical Underpinnings for Learning Trajectories of Geometric Figures |
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107 | (4) |
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111 | (3) |
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4 Teaching Practice and Teacher Knowledge in Geometry Instruction |
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114 | (42) |
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114 | (1) |
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4.2 Teaching Practice in Geometry |
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114 | (14) |
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4.3 Teacher Knowledge of Geometry |
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128 | (14) |
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4.4 Studies of Preservice Teachers' Knowledge of Geometry |
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142 | (2) |
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4.5 Another Look at Elementary and Middle Grades Teachers |
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144 | (3) |
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4.6 Beliefs of Secondary Geometry Teachers |
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147 | (7) |
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154 | (2) |
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5 Improving the Teaching and Learning of Geometry in Secondary School Classrooms |
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156 | (36) |
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156 | (1) |
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5.2 Communication Tasks: A Contribution of the Theory of Didactical Situations to the Design of Interventions |
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157 | (3) |
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5.3 Secondary Geometry in the Service of Modeling the Experience with Shape and Space |
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160 | (5) |
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5.4 Communication Tasks in the Teaching and Learning of Geometry |
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165 | (25) |
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190 | (2) |
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6 A Conclusion and a Beginning: Doing Research on the Teaching and Learning of Secondary Geometry |
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192 | (11) |
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192 | (1) |
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192 | (9) |
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201 | (2) |
| References |
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203 | (26) |
| Index |
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229 | |
Pat Herbst is Professor of Education and Mathematics at the University of Michigan, USA. Pat is a former high school mathematics teacher in Argentina and his research focuses on the nature of the mathematical work that students do in secondary classrooms and the work that teachers do to manage knowledge development.
Taro Fujita is a lecturer in mathematics education at the University of Exeter, UK. Originally a mathematics teacher in Japan, Taro currently teaches the learning and teaching of mathematics in primary schools and higher mathematics, and he is also editorial assistant for the International Journal for Technology in Mathematics Education.
Stefan Halverscheid is Professor of Mathematics Education at the University of Göttingen, Germany. His background is in complex and differential geometry in the presence of symmetries and in research on the teaching and learning of mathematics. He has experience as a high school teacher, has lectured in Teacher Education at Münster, Oldenburg and Bremen Universities, and was Dean of Studies and Dean of the Faculty of Mathematics and Computer Science at Göttingen.
Michael Weiss is currently on the faculty of the Department of Mathematics at the University of Michigan, USA. His background is in mathematics education and pure mathematics, and he was formerly a high school mathematics teacher in the United States.
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