The Learning and Teaching of Number

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 the relationships 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