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This book is a fascinating read for both primary and secondary teachers of mathematics. It explores comprehensively the use of concrete and pictorial approaches such as tallying, counters, the number line, ordered-pair graphs, proportion diagrams, bar models, base ten blocks and vectors in one dimension to represent different types of numbers and how operations using these numbers can be explained.
To begin with, this book looks at the pros and cons of each approach to represent whole numbers, both positive and negative before moving on to fractions and decimals. Addition, subtraction, multiplication and division follows, presented in a colourful, diagrammatic way surrounded with clear, logical written reasoning, allows the reader to make their own informed choice about which representation best suits their students. Once the fundamental concepts are secure, this book moves on to look at more complex ideas such as powers and roots, irrational numbers, laws of arithmetic and order of operations before moving into the abstract world of algebra, yet still applying the same concrete and pictorial approaches as before.
Primary teachers are able to appreciate the mathematics that they will teach from a variety of angles. Secondary teachers are given a valuable insight into approaches taught in feeder primaries. Both sectors can consider how the concepts are extended and how these concrete and pictorial representations can be used to demonstrate these concepts at secondary school.
Furthermore, throughout the book and in the final ‘frequently asked and anticipated questions’ chapter, ideas and appropriate questions to consider are given to support teachers in developing their own understanding of each approach and provide the structure needed to build confidence as to how they can implement these representations in their own classrooms.
Visible Maths has given me food for thought and opened my eyes to new pictorial representations that I hadn’t considered as well as making me evaluate some of the teaching approaches I currently use. I thoroughly recommend this book, especially for those adopting a teaching for mastery approach. It is also a ‘must read’ for all KS2/KS3 mathematics teachers enabling a smooth transition in the teaching of these key concepts between primary and secondary school to be achieved for the benefit of every student. ~ Helen Thompson, Assistant Principal and Head of Maths, Corby Business Academy
In this book, Peter Mattock builds on this approach and explores – in colourful 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 teachers of maths 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 colour to illustrate the conceptual takeaways and teaching techniques discussed.
Suitable for teachers of maths in primary and secondary school settings.
In addition to our LoveReading expert opinion some of our Reader Review Panel were also lucky enough to read and review this title. You can click here to read the full reviews.
Visible Maths is an attractive volume, full of practical, useful images and tools that will invigorate teachers and inspire their pupils Full review
This book is clearly laid out, has clear pictures of each representation (you would hope!) and is easy to read. Each chapter takes a particular area of mathematics and explains the different ways these could be shown visually. Full review
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. Lucy Rycroft-Smith, Research and Framework Design, Cambridge Mathematics
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
Visible Maths provides a practical guide to using representations and manipulatives in the classroom, demonstrating how we can offer pupils coherence in the representations we choose to use, irrespective of the complexity of the topic we are studying.
Emma McCrea, teacher trainer and author of Making Every Maths Lesson Count
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
|Publication date:||22nd February 2019|
|Publisher:||Crown House Publishing Ltd|
|Year Groups:||Key Stage 2, Key Stage 3, Key Stage 4|
Peter Mattock has been teaching maths for over a decade. He is a specialist leader of education (SLE) and an accredited secondary maths professional development lead, who regularly presents at conferences across the country. Peter also develops teaching for mastery in the secondary school classroom, having been part of the the first cohert of specialists training in mastery approaches by the National Centre for Excellence in the Teaching of Mathematics (NCETM).More About Peter Mattock