Learning Through Teaching Mathematics

This volume explores how and when teachers' knowledge develops through teaching. It presents international views on teachers' learning from their practice; the chapters are written by mathematicians from Brazil, Canada, Israel, Mexico, UK, and USA.

The idea of teachers Learning through Teaching (LTT) when presented to a naïve bystander appears as an oxymoron. Are we not supposed to learn before we teach? After all, under the usual circumstances, learning is the task for those who are being taught, not of those who teach. However, this book is about the learning of teachers, not the learning of students. It is an ancient wisdom that the best way to truly learn something is to teach it to others. Nevertheless, once a teacher has taught a particular topic or concept and, consequently, truly learned it, what is left for this teacher to learn? As evident in this book, the experience of teaching presents teachers with an exciting opp- tunity for learning throughout their entire career. This means acquiring a better understanding of what is being taught, and, moreover, learning a variety of new things. What these new things may be and how they are learned is addressed in the collection of chapters in this volume. LTT is acknowledged by multiple researchers and mathematics educators. In the rst chapter, Leikin and Zazkis review literature that recognizes this phenomenon and stress that only a small number of studies attend systematically to LTT p- cesses. The authors in this volume purposefully analyze the teaching of mathematics as a source for teachers' own learning.

Is innovative in its systematic view on teaching of mathematics as a source for teachers' own learning Contains interesting and challenging mathematical examples that teachers learned when they taught mathematics Contains a variety of research methodologies and frameworks for the analysis of the developments of mathematics teachers' knowledge

Klappentext

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.

Inhalt
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.