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

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.

Thinking About The Teaching Of Geometry Through The  Lens Of Geometrical  Work And Geometrical Paradigms

Alain Kuzniak

Epistemological Features Of A Constructional Approach To Regular 4-Polytopes

Stephan Berendonk and Marc Sauerwein

Geometry Opportunites For Reasoning And Proof In  Secondary School Textbooks In Trinidad And Tobago

Andrew A. Hunte

Enacting Functions  From Geometry To Algebra

Scott Steketee and Daniel Scher

Section 2: Studies of Geometry Instruction and Teacher Knowledge

Examining The Work Of Teaching Geometry As A Subject-Specific Phenomenon

Patricio Herbst, Nicolas Boileau, and Umut Gürsel

Creating Profiles Of Geometry Teachers’ Pedagogical Content Knowledge

Agida G. Manizade and Dragana Martinovic

Symbiosis Between Subject Matter And  Pedagogical Knowledge In Geometry

Mohan Chinnappan,  Bruce White, and Sven Trenholm

Designing Instruction Towards Mathematical Literacy In Geometry: A Case Study

Ui Hock Cheah

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

Shawnda Smith

Some Notes On Teaching Geometry In Secondary School: A Teacher Training Experience

Alejandra Almirón, Susana Ammann, Fernando Bifano, Rosa Ferragina, Gema Fioriti, Leonardo Lupinacci, and José Villella.

Section 3: Studies of Geometry Thinking and Learning

Exploring Models Of Secondary Geometry Achievement

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

Connectedness Of Problems And Blockage Resolution In The Solving Process: A Major Educational Challenge

Josep Fortuny, Michel Gagnon, and Philippe Richard

The Use Of Writing As A Metacognitive Tool In Geometry Learning

Luz Graciela Orozco Vaca

Development Of Spatial Ability Results From The Research Project Geodikon

Guenter Maresch

Middle School Students' Use Of Property Knowledge And Spatial Visualization In Reasoning About 2D Rotations

Michael T. Battista and Leah M. Frazee

Mitsue Arai

Engaging Students with Non-Routine Geometry Proof  Tasks

Michelle Cirillo

Playing With Geometry: An Educational Inquiry Game  Activity

Yael Luz and Carlotta Soldano

Differences In Self-Reported Instructional Strategies Using A Dynamic Geometry Approach That Impact Students’ Conjecturing

Brittany Webre, Shawnda Smith, and Gilbert Cuevas

Conclusion

The Editors