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Visible Maths: Using representations and structure to enhance mathematics teaching in schools Paperback – 22 Feb. 2019

4.3 out of 5 stars 17 ratings

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What a great read this is! ’Visible Maths’ will quickly become essential reading for teachers of maths interested in teaching for secure and deep understanding rather than chasing quick wins or thinking they have to follow the latest educational fads.

An ideal guide for those educators who want to help their pupils ‘see’ and ‘feel’ the mathematics.

- Steve Lomax, mathematics adviser and national teaching for mastery lead

’Visible Maths is a thoughtful, careful and thorough exploration of some of the most useful visual models we can use to teach mathematics. Considering and critiquing the representations in this book will no doubt help teachers of maths at any stage of their career and will encourage them to engage with not only some of the deepest ideas, but also the deepest connections that make our maths classrooms so powerful. We ‘see’ mathematics in many different ways at different times in our teaching of the subject, and Peter has captured much of that interesting and shifting variety here.

- Lucy Rycroft-Smith, Research and Framework Design, Cambridge Mathematics

’Visible Maths’ is an essential read for any teacher of maths looking to improve their use of manipulatives and visual representations in order to help develop their pupils’ conceptual understanding. Throughout the book Peter demonstrates his superb pedagogical and subject knowledge to show how, through the use of representations, typically ‘difficult’ topics can be made more accessible for all pupils.

An invaluable resource to refer to again and again, this book deserves a place on the shelf in every school’s maths department.

- Jonathan Hall, Lead Maths Practitioner, Leeds City Academy and creator of mathsbot.com

In ’Visible Maths’, Peter Mattock provides a very thorough overview of how a variety of different representations can be developed to explore working with number and algebra in primary and secondary school mathematics education. I am sure that the book will become a must-have resource for all teachers of maths, and equally should be central to the discussions of any maths department as they plan their approach to the use of representations and models.

Peter presents a carefully argued approach to the use of the different representations, clearly setting out how and when different approaches might be most beneficial and when they are less helpful. The copious supply of examples provided illustrate, in colour, the different approaches – offering clear insights into mathematical structure and how this might best be revealed in the classroom. Although some readers may have met some of the approaches before, I feel sure that all will find things here that will challenge their thinking – for example, the suggested use of vectors at much earlier stages in the development of working with number.

I recommend Visible Maths to all those who constantly consider different ways of supporting their teaching and their pupils’ learning.

- Geoff Wake, Professor of Mathematics Education and Convenor of the Centre for Research in Mathematics Education, University of Nottingham

Covering various areas in the subject of mathematics, from counting to simultaneous equations, ’Visible Maths’ provides a practical guide to using representations and manipulatives in the classroom. Counters, bars (including Cuisenaire rods and algebra tiles), vectors and number lines feature throughout, demonstrating how we can offer pupils coherence in the representations we choose to use, irrespective of the complexity of the topic we are studying.

Overall, the book is a great resource for professional development and is a must-read for all teachers of maths.

- Emma McCrea, teacher trainer and author of ’Making Every Maths Lesson Count’

’Visible Maths’ is a beautifully presented, comprehensive manual containing detailed guidance on how a wide variety of visual representations can be creatively used in the classroom to support pupils’ deep understanding of mathematics. There is no other book like this, as it contains so much wisdom and practical advice on how to get the very best out of visual representations.

- Dr Colin Foster, Reader in Mathematics Education, Mathematics Education Centre, Loughborough University

From the Inside Flap

Peter Mattock's Visible Maths: Using representations and structure to enhance mathematics teaching in schools supports teachers in their use of concrete and pictorial representations to illustrate key mathematical ideas and operations.

Viewing the math lesson as an opportunity for pupils to develop a deep understanding of mathematical concepts and relationships, rather than simply to follow fixed processes that lead to 'the answer', is increasingly recognized as the pinnacle of best practice in math education.

In this book, Peter Mattock builds on this approach and explores "€" in colorful detail "€" a variety of visual tools and techniques that can be used in the classroom to deepen pupils' understanding of mathematical operations. Covering vectors, number lines, algebra tiles, ordered-pair graphs and many other representations, Visible Maths equips teachers with the confidence and practical know-how to take their pupils' learning to the next level.

The book looks at the strengths, and flaws, of each representation so that both primary and secondary school math teachers can make informed judgements about which representations will benefit their pupils. The exploration begins at the very basics of number and operation, and extends all the way through to how the representations apply to algebraic expressions and manipulations. As well as sharing his expert knowledge on the subject, Peter draws on relevant research and his own experience of using the representations in order to support teachers in understanding how these representations can be implemented effectively.

Visible Maths also includes a glossary covering the key mathematical terms, as well as a chapter dedicated to answering some of the questions that may arise from the reading of the book. Furthermore, the accompanying diagrams and models are displayed in full color to illustrate the conceptual takeaways and teaching techniques discussed.

Suitable for math teachers in primary and secondary schools.

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