Conceptual Maths

Written by Peter Mattock, Conceptual Maths: Teaching 'about' (rather than just 'how to do') mathematics in schoolsaims 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 Mathsis 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 Mathsalso includes a glossary covering the key mathematical terms.

Suitable for teachers of maths in primary, secondary and post-16 settings

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Empowers teachers to support students on a comprehensive and coherent journey through school mathematics, showcasing the best models, metaphors and representations and providing excellent examples, explanations and exercises that can be used across the curriculum.

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The approach that Conceptual Maths takes encourages teachers to develop their own conceptual understanding in order to promote teaching for understanding in the classroom. Congruence of shapes is considered alongside algebraic equations and equivalent fractions, for instance, highlighting the concept of the equivalence relation and showing that three 'topics' that are taught separately are actually closely linked. This focus on concepts over processes makes Conceptual Maths a valuable read for anyone teaching mathematics.

Jemma Sherwood

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Mattock's Conceptual Maths provides a real focus on the understanding of concepts and the need for teaching for understanding. Key to this are the connections made between different concepts, subconcepts and procedures. Representations repeat to support connecting ideas and these are repeated across numerous concepts. For example, repeated representations show clear connections between multiplication of integers and multiplication of surds and how these ideas link to those of factors, multiples and equality. As a primary practitioner, I do not understand surds. However, I can clearly see how the ideas connect and how what I teach at a primary level supports and is developed by maths teaching at secondary level.I also particularly like Mattock's focus beyond number and calculation. While Conceptual Maths naturally begins with these building blocks, chapters on measures, shape and data allow explicit opportunities for teachers both new and experience