Mathematical Encounters and Pedagogical Detours Stories of Disturbance and Learning Opportunities in Teacher Education

This book explores the idea that mathematics educators and teachers are also problem solvers and learners, and as such they constantly experience mathematical and pedagogical disturbances. Accordingly, many original tasks and learning activities are results of personal mathematical and pedagogical disturbances of their designers, who then transpose these disturbances into learning opportunities for their students. This learning-transposition process is a cornerstone of mathematics teacher education as a lived, developing enterprise. Mathematical Encounters and Pedagogical Detours unfold the process and illustrate it by various examples. The book engages readers in original tasks, shares the results of task implementation and describes how these results inform the development of new tasks, which often intertwine mathematics and pedagogy. Most importantly, the book includes a dialogue between the authors based on the stories of their own learning, which triggers continuous exploration of learning opportunities for their students.

Chapter 1. Disturbance as a driving force.- Chapter 2. A fictional dialogue on infinitude of primes.- Chapter 3. Encounters with Euclidean propositions.- Chapter 4. Stories on problem-solving instruction.- Chapter 5. Encounters with Cardano’s method.- Chapter 6. Synthesizing exception-barring and what-if-not: If not, what yes?.- Chapter 7. From “obviously wrong” methods to surprisingly correct answers.

Boris Koichu is an Associate Professor at the Department of Science Teaching of the Weizmann Institute of Science. His research interests are in the area of mathematical problem solving and problem posing, from middle school to university. Part of his research focuses on exploring mechanisms of collaborative problem solving in choice-affluent learning environments, such as a dialogical classroom or an online forum. Another part of his research is devoted to implementability of mathematics education research on problem solving and problem posing, by means of creating long-term co-learning partnerships between mathematics teachers and mathematics education researchers.

Rina Zazkis Rina Zazkis is a Professor at Simon Fraser University in the Faculty of Education and an Associate Member in the Department of Mathematics. Her research interests are in mathematics education at the undergraduate level and teacher education, focusing on the uses of mathematical knowledge in teaching. She conducted extensive research on teaching and learning of elementary Number Theory.  She is interested in storytelling and dialogic approaches in teaching and research. In 2016 Zazkis was appointed as Tier 1 Canada Research Chair, a prestigious recognition for excellence in research and research training.