The Learning and Teaching of Number Paths Less Travelled Through Well-Trodden Terrain

Numbers are the backbones of mathematics. From 1 to infinity, numbers accompany and underlie the learning of mathematics and research. While perceived as familiar and understood, numbers present fascinating and often mysterious patterns, relationships and pedagogical issues. The Learning and Teaching of Number explores how mathematics education research has addressed issues related to the structure of numbers and number operations and provides a classroom context. It invites readers to explore less-travelled paths through a well-trodden terrain of number. This fascinating book combines mathematical content with pedagogical ideas and research results. Focusing on number, the book illustrates central ideas related to numbers via a variety of tasks at different levels of complexity. The Learning and Teaching of Number will allow the reader to examine and develop personal understanding of number sets and therelationships among them; enhance personal understanding of familiar topics associated with number operations; engage in a variety of tasks and strengthen personal problem-solving skills; enrich their repertoire of mathematical tasks and pedagogical actions; and consider research ideas and results related to teaching numbers, number operations and number relationships. This is a valuable resource for teacher education courses, graduate programs in mathematics education and professional development programs. Teacher trainers and maths teachers will find their personal understanding of numbers and relationships enriched and will draw connections between research and classroom pedagogy which will extend and enhance their teaching.

Preface Entering the Terrain Getting Ready to Act Snapshot 1 – Capturing Numbers Snapshot 2 – Departing Base Ten Snapshot 3 – Measuring with Numbers Snapshot 4 – Exploring Variations in Algorithms for Arithmetic Operations Snapshot 5 – Cycling Through Numbers Snapshot 6 – Representing Numbers Multiplicatively Snapshot 7 – Revisiting Fractions Snapshot 8 – Transitioning Between Numerical Domains Snapshot 9 – Playing with Numbers Final Word

Rina Zazkis is Professor of Mathematics Education at the Faculty of Education and an associate member in the Department of Mathematics at the Simon Fraser University, Canada. She holds an appointment of Tier 1 Canada Research Chair, a prestigious recognition of excellence in research and research training. John Mason spent 40 years at the Open University constructing distance-taught courses in mathematics and mathematics education. He is perhaps best known for Thinking Mathematically and Researching Your Own Practice Using the Discipline of Noticing. His main interests arein the nature and role of attention, the use of mental imagery and the fostering of mathematical thinking. Igor’ Kontorovich is Senior Lecturer in Mathematics Department at the University of Auckland, New Zealand. He is interested in understanding the processes that people go through when learning and teaching mathematics in secondary school and university.