The Learning and Teaching of Geometry in Secondary Schools
A Modeling Perspective
1st Edition
Published on 20. March 2017
Book
Paperback/Softback
250 pages
978-0-415-85691-1 (ISBN)
Description
IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education.
The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction.
Areas covered include:
teaching and learning secondary geometry through history;
the representations of geometric figures;
students' cognition in geometry;
teacher knowledge, practice and, beliefs;
teaching strategies, instructional improvement, and classroom interventions;
research designs and problems for secondary geometry.
Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students' study of geometry in secondary schools.
The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction.
Areas covered include:
teaching and learning secondary geometry through history;
the representations of geometric figures;
students' cognition in geometry;
teacher knowledge, practice and, beliefs;
teaching strategies, instructional improvement, and classroom interventions;
research designs and problems for secondary geometry.
Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students' study of geometry in secondary schools.
More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Illustrations
13 s/w Photographien bzw. Rasterbilder, 19 s/w Zeichnungen, 4 s/w Tabellen
4 Tables, black and white; 19 Line drawings, black and white; 13 Halftones, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 14 mm
Weight
389 gr
ISBN-13
978-0-415-85691-1 (9780415856911)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Pat Herbst | Taro Fujita | Stefan Halverscheid
The Learning and Teaching of Geometry in Secondary Schools
A Modeling Perspective
Book
03/2017
1st Edition
Routledge
€215.77
Shipment within 15-20 days
Pat Herbst | Taro Fujita | Stefan Halverscheid
The Learning and Teaching of Geometry in Secondary Schools
A Modeling Perspective
E-Book
03/2017
Routledge
€59.49
Available for download
Pat Herbst | Taro Fujita | Stefan Halverscheid
The Learning and Teaching of Geometry in Secondary Schools
A Modeling Perspective
E-Book
03/2017
Routledge
€59.49
Available for download
Persons
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 Goettingen, 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 Muenster, Oldenburg and Bremen Universities, and was Dean of Studies and Dean of the Faculty of Mathematics and Computer Science at Goettingen.
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.
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 Goettingen, 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 Muenster, Oldenburg and Bremen Universities, and was Dean of Studies and Dean of the Faculty of Mathematics and Computer Science at Goettingen.
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.
Content
IMPACT-Series Foreword
Acknowledgments
Introduction
Chapter 1: The Discourse of Teaching and Learning Secondary Geometry through History
1.1. Introduction
1.2. Overview of This Chapter
1.3. The Development of Geometry up to the So-Called Foundational Crisis
1.4. The Shaping of Geometry Curricula in the Nineteenth and Twentieth Centuries
1.5. Recent Developments
1.6. Conclusion
Chapter 2: Geometric Figures and Their Representations
2.1. Introduction
2.2. Conceptions of Figure: What Ee Mean by Conception
2.3. Initial Conceptions of Geometric Figures
2.4. The Geometric Diagram in the Literature
2.5. A Modeling Perspective in the Study of Figures
2.6. Conclusion
Chapter 3: Students' Thinking and Learning in Geometry
3.1. Introduction
3.2. Conceptions of Figure and Students' Cognition
3.3. Geometric Figures and Students' Learning as Progressive Change in Cognition
3.4. Enriching Semiotic Registers, Operations, and Control Structures with DGS
3.5. Theoretical Underpinnings for Learning Trajectories of Geometric Figures
3.6. Conclusion
Chapter 4: Teaching Practice and Teacher Knowledge in Geometry Instruction
4.1. Introduction
4.2. Teaching Practice in Geometry
4.3. Teacher Knowledge of Geometry
4.4. Studies of Preservice Teachers' Knowledge of Geometry
4.5. Another Look at Elementary and Middle Grades Teachers
4.6. Beliefs of Secondary Geometry Teachers
4.7. Conclusion
Chapter 5: Improving the Teaching and Learning of Geometry in Secondary School Classrooms
5.1. Introduction
5.2. Communication Tasks: A Contribution of the Theory of Didactical Situations to the Design of Interventions
5.3. Secondary Geometry in the Service of Modeling the Experience with Shape and Space
5.4. Communication Tasks in the Teaching and Learning of Geometry
5.5. Concluding this Chapter
Chapter 6: A Conclusion and a Beginning: Doing Research on The Teaching and Learning of Secondary Geometry
6.1. Introduction
6.2. Research questions
6.3. Conclusion
References
Acknowledgments
Introduction
Chapter 1: The Discourse of Teaching and Learning Secondary Geometry through History
1.1. Introduction
1.2. Overview of This Chapter
1.3. The Development of Geometry up to the So-Called Foundational Crisis
1.4. The Shaping of Geometry Curricula in the Nineteenth and Twentieth Centuries
1.5. Recent Developments
1.6. Conclusion
Chapter 2: Geometric Figures and Their Representations
2.1. Introduction
2.2. Conceptions of Figure: What Ee Mean by Conception
2.3. Initial Conceptions of Geometric Figures
2.4. The Geometric Diagram in the Literature
2.5. A Modeling Perspective in the Study of Figures
2.6. Conclusion
Chapter 3: Students' Thinking and Learning in Geometry
3.1. Introduction
3.2. Conceptions of Figure and Students' Cognition
3.3. Geometric Figures and Students' Learning as Progressive Change in Cognition
3.4. Enriching Semiotic Registers, Operations, and Control Structures with DGS
3.5. Theoretical Underpinnings for Learning Trajectories of Geometric Figures
3.6. Conclusion
Chapter 4: Teaching Practice and Teacher Knowledge in Geometry Instruction
4.1. Introduction
4.2. Teaching Practice in Geometry
4.3. Teacher Knowledge of Geometry
4.4. Studies of Preservice Teachers' Knowledge of Geometry
4.5. Another Look at Elementary and Middle Grades Teachers
4.6. Beliefs of Secondary Geometry Teachers
4.7. Conclusion
Chapter 5: Improving the Teaching and Learning of Geometry in Secondary School Classrooms
5.1. Introduction
5.2. Communication Tasks: A Contribution of the Theory of Didactical Situations to the Design of Interventions
5.3. Secondary Geometry in the Service of Modeling the Experience with Shape and Space
5.4. Communication Tasks in the Teaching and Learning of Geometry
5.5. Concluding this Chapter
Chapter 6: A Conclusion and a Beginning: Doing Research on The Teaching and Learning of Secondary Geometry
6.1. Introduction
6.2. Research questions
6.3. Conclusion
References