David Boyce

Written by Peter Mattock, Conceptual Maths: Teaching ‘about’ (rather than just ‘how to do’) mathematics in schools aims to empower teachers to support students on a comprehensive and coherent journey through school mathematics. Showcasing the best models, metaphors and representations, it provides excellent examples, explanations and exercises that can be used across the curriculum. Concepts are at the heart of the study of mathematics. They are the ideas that remain constant whenever they are encountered, but which combine and build upon each other to create the mathematical universe. It is the structure of each concept that gives rise to the procedures that are used in calculation and problem-solving – and, by learning about these structures, a learner can make sense of how different processes work and use them flexibly as need demands. In his first book, Visible Maths, Peter Mattock focused on the use of representations and manipulatives as images and tools and how this can provide a window into some of these mathematical structures. His aim in Conceptual Maths is to go deeper, beyond the procedures, and to shed greater light on the structures of the subject’s different concepts. The book explores how a variety of visual tools and techniques can be used in the classroom to deepen pupils’ understanding of mathematical structures, concepts and operations, including: number; addition and subtraction; multiplication and multiples; division and factors; proportionality; functionality; measures; accuracy; probability; shape and transformation; and vectors, among many others. In so doing, Peter equips teachers with the confidence and practical know-how to help learners assimilate knowledge of mathematical concepts into their schema and take their learning to the next level. Containing numerous full-colour diagrams and models to illustrate the conceptual takeaways and teaching techniques discussed, Conceptual Maths also includes a glossary covering the key mathematical terms. Suitable for teachers of maths in primary, secondary and post-16 settings Contents include: Introduction Chapter 1: Number Chapter 2: Addition and subtraction Chapter 3: Multiplication and multiples Chapter 4: Division and factors Chapter 5: Equality/equivalence/congruence Chapter 6: Proportionality Chapter 7: Functionality Chapter 8: Measures Chapter 9: Accuracy Chapter 10: Shape Chapter 11: Transformation and vectors Chapter 12: Chance Chapter 13: Charting and graphing Chapter 14: Data handling Glossary Bibliography