Learning Through Teaching Mathematics

1. Front Matter

   Pages i-xii

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2. Theoretical and Methodological Perspectives on Teachers’ Learning Through Teaching

   1. Front Matter

      Pages 1-1

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3. Theoretical and Methodological Perspectives on Teachers’ Learning through Teaching

   1. Teachers’ Opportunities to Learn Mathematics Through Teaching

      • Roza Leikin, Rina Zazkis

      Pages 3-21

   2. Attention and Intention in Learning About Teaching Through Teaching

      • John Mason

      Pages 23-47

   3. How and What Might Teachers Learn Through Teaching Mathematics: Contributions to Closing an Unspoken Gap

      • Ron Tzur

      Pages 49-67

   4. Learning Through Teaching Through the Lens of Multiple Solution Tasks

      • Roza Leikin

      Pages 69-85

4. Examples of Learning Through Teaching: Pedagogical Mathematics

   1. Front Matter

      Pages 87-89

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5. Examples of Learning through teaching: Pedagogical mathematics

   1. What Have I Learned: Mathematical Insights and Pedagogical Implications

      • Rina Zazkis

      Pages 91-110

   2. Dialogical Education and Learning Mathematics Online from Teachers

      • Marcelo C. Borba, Rúbia B.A. Zulatto

      Pages 111-125

   3. Role of Task and Technology in Provoking Teacher Change: A Case of Proofs and Proving in High School Algebra

      • Carolyn Kieran, José Guzmán

      Pages 127-152

   4. Learning Through Teaching, When Teaching Machines: Discursive Interaction Design in Sketchpad

      • Nicholas Jackiw, Nathalie Sinclair

      Pages 153-168

   5. What Experienced Teachers Have Learned from Helping Students Think About Solving Equations in the One-Variable-First Algebra Curriculum

      • Robin Marcus, Daniel Chazan

      Pages 169-187

6. Examples of Learning Through Teaching: Mathematical Pedagogy

   1. Front Matter

      Pages 189-190

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7. Examples of Learning through teaching: Mathematical pedagogy

   1. Exploring Reform Ideas for Teaching Algebra: Analysis of Videotaped Episodes and of Conversations About Them

      • Michal Yerushalmy, Shulamit Elikan

      Pages 191-207

   2. On Rapid Professional Growth: Cases of Learning Through Teaching

      • Peter Liljedahl

      Pages 209-225

   3. Interactions Between Teaching and Research: Developing Pedagogical Content Knowledge for Real Analysis

      • Lara Alcock

      Pages 227-245

   4. Teachers Learning from Their Teaching: The Case of Communicative Practices

      • Helen M. Doerr, Stephen Lerman

      Pages 247-262

   5. Feedback: Expanding a Repertoire and Making Choices

      • Dave Hewitt

      Pages 263-285

8. Back Matter

   Pages 287-300

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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.

• Algebra
• Mathematics Education
• Teacher Knowledge
• Teacher Learning
• Teacher Practice
• attention
• geometry
• learning
• learning and instruction

• Faculty of Education, University of Haifa, Haifa, Israel

  Roza Leikin

• Fac. Education, Simon Fraser University, Burnaby, Canada

  Rina Zazkis

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