Visible Maths

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 maths 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 recognised as the pinnacle of best practice in maths education. 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.

Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

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

Leading maths at any school is a unique challenge and comes with pressures not experienced in many other subject areas. The relatively abstract nature of the subject content, combined with the contrasting societal and parental attitudes to mathematics, can complicate communication and stifle progress. Most pupils and parents will recognise the importance of maths but many feel it's perfectly acceptable to be "no good" at it. Leading maths in schools is about managing these contradictions and getting the very best out of every teacher and pupil. Offering a fresh perspective and practical strategies for maths teachers and leaders at any level, Leading Mathsexplores how to make the most of a maths leadership role and manage the daily pressures and demands that come with it. Backed up by specific examples from fifteen years of experience leading maths, Peter Mattock goes on to examine the more long-term, strategic view of maths leadership, including how leaders can work with their teams to develop high quality mathematics teaching and learning for all pupils. The book covers day-to-day issues that arise when leading maths, in particular results and accountability, as well as difficult situations more generally. It offers useful takeaways at the end of each chapter, with a summary of key points and advice from the chapter. Leading Maths explores how to manage an inspection, developing improvement plans and the appraisal process, before touching on taking maths leadership beyond one specific school and into system leadership. In addition to Peter's insight, Leading Maths also contains contributions from other experienced maths practitioners, including Becky Lawrence, Jemma Sherwood, Rhiannon Rainbow and Dave Tushingham. Becky examines some of the specific approaches to leading primary maths, whilst Jemma does the same from her perspective as a maths lead across a large multi-academy trust. Rhiannon and Dave then go on to discuss how to manage significant change from their experience of adapting curriculum and CPD during the COVID pandemic - including the beginnings of their (now famous) book club. An essential guide for current, new, or aspiring maths leaders.

In Making Every Maths Lesson Count: Six principles to support great maths teaching, experienced maths teacher and lecturer Emma McCrea takes away the guesswork as she sums up the key components of effective maths teaching. Maths classrooms are incredibly complex places. At any given time, the factors influencing the effectiveness of your teaching are boundless and this can lead to relying on intuition as to what might work best. This book aims to signpost a route through this complexity. Writing in the practical, engaging style of the award-winning Making Every Lesson Count, Emma McCrea helps teachers to move beyond trial and error by sharing evidence-informed tips and suggestions on how they can nudge the impact of their teaching in the right direction. Making Every Maths Lesson Count is underpinned by six pedagogical principles challenge, explanation, modelling, practice, feedback and questioning and presents 52 high-impact strategies designed to streamline teacher workload and ramp up the level of challenge in the maths classroom. The book draws out the key findings from the latest research on memory, learning and motivation and each chapter features numerous worked examples to demonstrate the theory in action, together with a concluding series of questions that will help maths practitioners relate the content to their own classroom practice. Furthermore, Emma's writing offers clarity around the language of maths teaching and learning, and also delves into the finer points of how to identify and address any misconceptions that students may hold. Written for new and experienced practitioners alike, this gimmick-free guide provides sensible solutions to perennial problems and inspires a rich, challenging and evidence-based approach to the teaching of maths. Suitable for maths teachers of students aged 11 to 18 years, and for primary school maths specialists.

In Messy Maths: A Playful, Outdoor Approach for Early Years, Juliet Robertson offers a rich resource of ideas that will inspire you to tap into the endless supply of patterns, textures, colours and quantities of the outdoors and deepen children's understanding of maths through hands-on experience. Juliet believes being outside makes maths real. In the classroom environment, maths can seem disconnected from everyday reality but real maths is really messy. Lots of outdoor play and engaging activity along the way is a must, as being outside enables connections to be made between the hands, heart and head, and lays the foundations for more complex work as children grow, develop and learn. Following on from the success of Dirty Teaching (ISBN 978-178135107-9), Messy Maths reimagines the outdoor space through a mathematical lens providing a treasure trove of suggestions that will empower you to blend outdoor learning into your teaching practice. It is not a 'how to' guide, but rather an easy-to-use reference book replete with ready-to-use games and open-ended ideas designed to help children become confident and skilled in thinking about, using and exploring abstract mathematical concepts as they play outside. Many of these ideas and activities are also beautifully displayed in full-colour photographs throughout the book, making it even easier to jump straight into outstanding outdoor learning opportunities. Topics covered include: general advice; exploring numbers; number functions and fractions; money; measurement; time; pattern; shape and symmetry; position, direction and movement; data handling; routines; and the mathematical garden. Each chapter features a section on topic-specific vocabulary and expressions to help you integrate terminology into each area of study, while suggestions for embedding maths into routines are also provided to assist in the development of creative, progressive and flexible approaches to everyday situations. Messy Maths is suitable for early years educators (of ages 3 to 6) who want to shake up their usual classroom practice and make the most of any outdoor space - whether this be a nursery, playgroup, child-minder's back garden or a nature kindergarten as a context for maths. Messy Maths has been named the Gold Winner in the Mathematics category of the Nursery World Equipment & Resources Awards 2019. Messy Maths has been named the Silver Winner in the Outdoor Play category and Professional Books (and authors) category of the Nursery World Equipment & Resources Awards 2019. Messy Maths was a 2017 Foreword INDIES Finalist in the Education category. Messy Maths has been named a 'Gold Winner' in the IBPA Benjamin Franklin Awards 2018 in the Education category. Messy Maths is a finalist in the 2018 Education Resources Awards in the Educational Book Award category.

An all-encompassing guide to mastering teaching maths in secondary schools, Succeeding as a Maths Teacher is a unique manual that gives advice and guidance for maths teachers at all stages of their career. This handbook not only offers foundational advice on how to deliver the most effective maths lessons, but also delves deeper into key ideas for more experienced teachers, such as how the science of learning applies to mathematics and nuances in instructional design. Written by lead practitioners in maths at Ormiston Academies Trust, with a combined teaching experience of over 60 years, Succeeding as a Maths Teacher takes you from your first days in the classroom through to leading a department. Along the way, the authors explore the purpose of a maths education, topics such as modelling and questioning, how to develop a high-quality maths curriculum and the importance of planning learning over lessons, adapting your teaching in light of feedback, reasoning and solving problems, and enriching pupils' experiences of learning maths. The Succeeding As... series offers practical, no-nonsense guidance to help you excel in a specific role in a secondary school. Including everything you need to be successful in your teaching career, the books are ideal for those just starting out as well as more experienced practitioners looking to develop their skill sets.

100 Ways in 100 Days to Teach Your Baby Maths appeals to new parents looking for cheap, simple activities to improve their baby’s academic start in life but also raises important questions, such as why is there such large differences in maths ability between different countries?