International Perspectives on the Teaching and Learning of Geometry in Secondary Schools

1. Front Matter

   Pages i-vi

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2. International Perspectives on Secondary Geometry Education: An Introduction

   • Patricio Herbst, Ui Hock Cheah, Keith Jones, Philippe R. Richard

   Pages 1-4

3. Thinking About the Teaching of Geometry Through the Lens of the Theory of Geometric Working Spaces

   • Alain Kuzniak

   Pages 5-21

4. Epistemological Features of a Constructional Approach to Regular 4-Polytopes

   • Stephan Berendonk, Marc Sauerwein

   Pages 23-38

5. Opportunities for Reasoning and Proving in Geometry in Secondary School Textbooks from Trinidad and Tobago

   • Andrew A. Hunte

   Pages 39-58

6. Enacting Functions from Geometry to Algebra

   • Scott Steketee, Daniel Scher

   Pages 59-86

7. Examining the Work of Teaching Geometry as a Subject-Specific Phenomenon

   • Patricio Herbst, Nicolas Boileau, Umut Gürsel

   Pages 87-110

8. Differences in Self-reported Instructional Strategies Using a Dynamic Geometry Approach that Impact Students’ Conjecturing

   • Brittany Webre, Shawnda Smith, Gilbert Cuevas

   Pages 111-126

9. Creating Profiles of Geometry Teachers’ Pedagogical Content Knowledge

   • Agida G. Manizade, Dragana Martinovic

   Pages 127-144

10. Symbiosis Between Subject Matter and Pedagogical Knowledge in Geometry

    • Mohan Chinnappan, Bruce White, Sven Trenholm

    Pages 145-161

11. Minding the Gap: A Comparison Between Pre-service and Practicing High School Teachers’ Geometry Teaching Knowledge

    • Shawnda Smith

    Pages 163-180

12. Designing Instruction in Geometry: Using Lesson Study to Improve Classroom Teaching

    • Ui Hock Cheah

    Pages 181-195

13. A Professional Development Experience in Geometry for High School Teachers: Introducing Teachers to Geometry Workspaces

    • José Villella, Gema Fioriti, Rosa Ferragina, Leonardo Lupinacci, Fernando Bifano, Susana Amman et al.

    Pages 197-213

14. Development of Spatial Ability: Results from the Research Project GeodiKon

    • Guenter Maresch

    Pages 215-230

15. Middle School Students’ Use of Property Knowledge and Spatial Visualization in Reasoning About 2D Rotations

    • Michael T. Battista, Leah M. Frazee

    Pages 231-263

16. Exploring Models of Secondary Geometry Achievement

    • Sharon L. Senk, Denisse R. Thompson, Yi-Hsin Chen, Kevin J. Voogt

    Pages 265-282

17. Engaging Students with Non-routine Geometry Proof Tasks

    • Michelle Cirillo

    Pages 283-300

18. Aspects of Spatial Thinking in Problem Solving: Focusing on Viewpoints in Constructing Internal Representations

    • Mitsue Arai

    Pages 301-317

19. Playing with Geometry: An Educational Inquiry Game Activity

    • Yael Luz, Carlotta Soldano

    Pages 319-337

20. The Use of Writing as a Metacognitive Tool in Geometry Learning

    • Luz Graciela Orozco Vaca

    Pages 339-355

This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters  examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. 

Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.

• geometry learning
• geometry instruction
• teacher knowledge of geometry
• technology use in geometry
• geometry curriculum
• geometry in secondary schools
• teaching and learning geometry
• geometrical paradigms
• Regular 4-Polytopes
• Geometry To Algebra
• Geometry teachers
• mathematical literacy
• pre-service geometry
• geometry learning
• Geodikon
• spatial thinking in problem solving
• spatial visualization
• non-routine geometry
• playing with geometry
• dynamic geometry approach

“Research interests concerning and approaches to the teaching and learning of secondary geometry are wide and diverse. … The variety of interests and approaches is reflected in the collection of papers presented in the monograph. … What is clear from each offering is the recognition of the importance and power of geometry, the need for those concerned to comprehend concepts, and the influence of teachers on the outcomes of their wards.” (Rachael Horsman, Research in Mathematics Education, November 19, 2018)

• School of Education, University of Michigan, Ann Arbor, USA

  Patricio Herbst

• Institute of Teacher Education, Penang, Malaysia

  Ui Hock Cheah

• Département de didactique, Université de Montréal, Montreal, Canada

  Philippe R. Richard

• School of Education, University of Southampton, Southampton, United Kingdom

  Keith Jones

Policies and ethics