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Development of Teachers' Knowledge and Expertise in Practice
This volume explores how and when teachers' knowledge develops through teaching. The book presents international views on teachers' learning from their practice; the chapters are written by mathematicians or mathematics educators from Brazil, Canada, Israel, Mexico, UK, and USA. They address diverse content – numerical literacy, geometry, algebra, and real analysis – and a variety of levels – elementary school, secondary school, undergraduate mathematics, and teacher education courses. The authors employ different methodological tools and different theoretical perspectives as they consider teaching in different learning environments: lecturing, small group work on problems and tasks, mathematical explorations with the support of technological software, or e-learning. Despite these differences, the authors exemplify and analyze teachers’ learning that occurred and address the question: "What kinds of knowledge are developed as a result of teaching mathematics and what are the factors that support or impede such development?" Further, the chapters explore interactions and interrelationships between the enhancement of mathematical and pedagogical knowledge. The important and original contribution of this book is that it ties together the notions of teachers’ knowledge and complexity of teacher’s work, while presenting them from a relatively unexplored perspective – learning through teaching mathematics.
Theoretical and Methodological Perspectives on Teachers’ Learning through Teaching -- Teachers’ Opportunities to Learn Mathematics Through Teaching -- Attention and Intention in Learning About Teaching Through Teaching -- How and What Might Teachers Learn Through Teaching Mathematics: Contributions to Closing an Unspoken Gap -- Learning Through Teaching Through the Lens of Multiple Solution Tasks -- Examples of Learning through teaching: Pedagogical mathematics -- What Have I Learned: Mathematical Insights and Pedagogical Implications -- Dialogical Education and Learning Mathematics Online from Teachers -- Role of Task and Technology in Provoking Teacher Change: A Case of Proofs and Proving in High School Algebra -- Learning Through Teaching, When Teaching Machines: Discursive Interaction Design in Sketchpad -- What Experienced Teachers Have Learned from Helping Students Think About Solving Equations in the One-Variable-First Algebra Curriculum -- Examples of Learning through teaching: Mathematical pedagogy -- Exploring Reform Ideas for Teaching Algebra: Analysis of Videotaped Episodes and of Conversations About Them -- On Rapid Professional Growth: Cases of Learning Through Teaching -- Interactions Between Teaching and Research: Developing Pedagogical Content Knowledge for Real Analysis -- Teachers Learning from Their Teaching: The Case of Communicative Practices -- Feedback: Expanding a Repertoire and Making Choices.