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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.
Section 1: Mathematical, Epistemological, and Curricular Perspectives.- Thinking About The Teaching of Geometry Through the Lens of Geometrical Work and Geometrical Paradigms.- Epistemological Features of a Constructional Approach To Regular 4-Polytopes.- Geometry Opportunites For Reasoning and Proof in Secondary School Textbooks in Trinidad and Tobago.- Enacting Functions from Geometry To Algebra.- Section 2: Studies of Geometry Instruction and Teacher Knowledge.- Examining The Work of Teaching Geometry as a Subject-Specific Phenomenon.- Creating Profiles of Geometry Teachers' Pedagogical Content Knowledge.- Symbiosis Between Subject Matter and Pedagogical Knowledge in Geometry.- Designing Instruction Towards Mathematical Literacy in Geometry: a Case Study.- Minding the Gap: a Comparison Between Pre-Service and Practicing High School Geometry Teachers' Geometry Teaching Knowledge.- Some Notes on Teaching Geometry in Secondary School: a Teacher Training Experience.- Section 3: Studies of Geometry Thinking and Learning.- Exploring Models of Secondary Geometry Achievement.- Connectedness of Problems and Blockage Resolution in the Solving Process: a Major Educational Challenge.- The Use of Writing as a Metacognitive Tool in Geometry Learning.- Development of Spatial Ability Results from the Research Project Geodikon.- Middle School Students' Use of Property Knowledge and Spatial Visualization in Reasoning About 2D Rotations.- Aspects of Spatial Thinking in Problem Solving: Focusing on Viewpoints in Constructing Internal Representation.- Engaging Students with Non-Routine Geometry Proof Tasks.- Playing With Geometry: An Educational Inquiry Game Activity.- Differences in Self-Reported Instructional Strategies Using a Dynamic Geometry Approach that Impact Students' Conjecturing.- Conclusion.- The Editors.
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