This book challenges traditional beliefs and practices of teaching 'written' mathematics in early childhood. It gives theoretical underpinnings and offers exciting insights and context to children's early mathematical thinking and in particular into children's mathematical graphics, showing how this supports their understanding of the abstract symbolic language of mathematics. Drawing on a wide range of examples, it illustrates and explains how children explore and communicate their mathematical thinking through their mathematical graphics, and how this begins in play. The book looks at the power of children's own marks, symbols and other graphical representations to convey meanings, exploring how they support complex thinking. The authors explore the relationship between children's play and meaning making. Rather than viewing mathematics as a separate subject or as a set of basic 'skills' to be transmitted, they demonstrate that in supportive learning cultures children develop their own mathematical thinking to solve problems. Key features include: Numerous new examples and case studies of children from birth to 8 years,highlighting the complexity and richness of children's thinking Explanation of pedagogical issues - showing how they can support rich play and mathematics Draws on the authors' latest research This book is valuable reading for students, teachers, primary mathematics coordinators' and all early years' professionals working in the Early Years Foundation Stage and Key Stage One.
Helps you appreciate children's scribbles as the beginning of early mathematical development Children's Mathematical Graphics offers a flexible training resource and a comprehensive framework for providing Continuing Professional Development (CPD). It will also help you support teachers and practitioners to: appreciate early mark-making and its relationship to children’s mathematical graphics recognize and begin to understand children’s mathematical graphics develop their pedagogy and practice The CPD booklet outlines some 38 sessions that can be used as training and includes prompts for discussion, learning points, and how to run the activities. The CD will include give examples to include in the CPD activities and could be useful in PowerPoint presentations.
Developing Children's Mathematical Graphics is a comprehensive resource offering a complete framework for providing flexible professional development. The pack will help those leading professional development to support early years practitioners and teachers in developing their understanding of children's mathematical graphics by: Appreciating young children's early use of graphical marks and representations, and their relationship to children's emerging understanding of the abstract symbolic language of mathematics Recognizing and beginning to understand children's mathematical graphics Developing effective pedagogy and practice Elizabeth Carruthers and Maulfry Worthington challenge the traditional beliefs and practices of teaching 'written' mathematics in early childhood. They look at the power of children's own marks, symbols and other graphical representations to convey meanings, exploring how they support complex thinking. The authors explore the relationship between children's play and meaning making. Rather than viewing mathematics as a separate subject or as a set of basic 'skills' to be transmitted, they demonstrate that in supportive learning cultures children develop their own mathematical thinking to solve problems. The pack includes: A copy of the book Children's Mathematical Graphics: Beginnings in Play giving a theoretical underpinning and context to children's mathematical thinking through their own mathematical graphics An A4 CPD booklet outlining in detail numerous sessions which can be used flexibly for professional development - including prompts for discussion and activities, learning points, photocopiable materials and guidance on how to run the sessions A CD comprising of powerpoint slides, examples and resources to include in the CPD sessions Laminated examples of children's graphics with short written explanations This resource pack is designed for early years settings and early years and primary mathematics advisors working in the Early Years Foundation Stage and Key Stage 1. It is an invaluable source of guidance on harnessing the beginnings of written mathematics and the resource pack has the capacity, in a fairly fundamental way, to help change the way we think about and approach early mathematical development.
′In Case Study 5 (a grassroots ′Children′s Mathematics Network group′) the initiative supported the participants in their professional change by giving them a space for the detailed and joint consideration of children′s mathematical thinking. Another significant feature of this initiative is its focus on careful consideration and analysis of children′s mathematics, and the ways in which professionals can support and encourage the children′s mathematical thinking and reasoning... The standard of the mathematical understanding, thinking and reasoning that the displays revealed was far higher than the specified curriculum objectives for children of this age...′ - Researching Effective CPD in Mathematics Education (RECME) project: (NCETM, 2009) ′The review also plays great score by play-based learning of a mathematical nature, and makes specific recommendations regarding early mark-making as a precursor to abstract mathematical symbolism′. Section 115 features children′s mathematical graphics and emphasises: ′The role of mark-making in children′s cognitive development is set out in the taxonomy (Carruthers and Worthington, 2006)′. The report recommends that ′local authorities, leaders, managers and head teachers should provide a culture with a significant focus on mathematical mark-making′ and ′a learning environment that encourages children to choose to use their own mathematical graphics to support their mathematical thinking and processes′ - The Williams Maths Review: (DCSF, 2008) `At the very heart of the success of the book is the authors′ ability to see mathematics through young children′s eyes by listening to and reflecting on the constant efforts made by children to make sense of their world. This is a liberating book which proposes that the teaching of mathematics could and should be a highly creative and enjoyable proceess′ - Branwen Llewelyn Jones, Early Years Consultant at PACE Ltd / TACTYC ′Ground breaking... To single out any one chapter would be unfair because there is something thought-provoking and inspirational throughout. If you want to expand your understanding upwards and outwards then get a copy soon′ - Times Educational Supplement ′I first read Children′s Mathematics, Making Marks, Making Meaning a couple of years ago and it had an immediate impact on my own thinking and teaching, and the work I do with trainee teachers. I′m sure you will find it compelling reading too. I think it has the potential to change, in a fundamental way, how we think about early mathematical development′ - Lynne McClure, Editor, Math Co-ordiator′s File, Mathematics Association ′In their exceptionally readable and informative book, Children′s Mathematics, Making Marks, Making Meaning Carruthers and Worthington (2006) draw attention to one of the main goals of early years teaching, that is, to help children make links between the mathematics they have already encountered (and continue to engage with) at home and the more abstract mathematics of the school. These authors suggest that by encouraging children to represent mathematical ideas in their own ways and, crucially, by talking to the pupils about the marks they have made, we are given a "window" onto their thinking that may otherwise be inaccessible′ - Liz Pumphrey, NRICH This book draws on the authors′ many years of teaching children aged three to eight years and also on their extensive research with children in the home, nursery and school. The authors explain the development and range of young children′s mathematical marks and visual representations, showing how children make mental connections between their own early marks and subsequent abstract mathematical symbolism, and go on to develop their own written methods. Combining theory and practice, this acclaimed book demonstrates how children′s own mathematical graphics are highly creative and show deep levels of thinking. The authors show how this is the key to success in school mathematics and to higher levels of achievement. The authors are winners of TACTYC′s (2003) Jenefer Joseph Award for the Creative Arts (3 - 8) - awarded for their innovative work with children on mathematical graphics.
Drawing on their many years' experience of teaching children 3 to 8 years, the authors explain the development and range of young children's mathematical marks and representations.
Teaching mathematics to young children in creative ways is made easy with this second edition of a wonderful book, which offers the reader clear advice and lots of exciting ideas to use in any early years setting. By showing how to introduce mathematical concepts through play-based activities, this book is in tune with current thinking about best practice in teaching, and with the requirements of the Early Years Foundation Stage and current Primary National Strategy. New material includes: - an additional chapter on creative recording - a whole new chapter on ways to involve parents - discussion of policy throughout the UK - more on using ICT - case studies covering the whole birth to eight age range Essential reading for any practitioner who wants to develop their mathematics teaching, this book is equally important for all trainee teachers and early years students. Kate Tucker is an early years teacher, trainer and writer based in Exeter; she has over 20 years of experience, and has written widely on early years mathematics and Foundation Stage practice.
Offering practical guidance to teachers and novice teachers the authors explore a number of ways of helping children make sense of mathematics and suggest alternatives to the excessive use of worksheets.
The Holistic Care and Development of Children from Birth to Three provides students and practitioners with the knowledge and understanding they need to meet the complex needs of babies and toddlers. With a focus on the fundamentally holistic nature of young children’s development, and emphasising the role of play, and the emotional and physical environment throughout, the book shows its reader how to maximise each and every opportunity for learning when caring for the under threes. The text addresses both theory and practice, foregrounding the vital link between the two as the reader learns how to integrate theoretical approaches into their own setting and ways of working. From personal, physical, social and emotional development, to cooperation with parents, SEN and enabling environments, a wealth of topics are discussed in the depth and detail required to ensure that children can be given the best possible start in their critical first three years. Throughout the book, the following features help the reader to reflect on, and develop their own practice: ‘Case Studies’ put key topics in context ‘Reflective Questions’ help the reader test and consolidate their knowledge of key topics ‘Review your Practice’ boxes invite the reader to reflect on their own practice ‘Further Reading and Research’ suggestions inspire independent study in key areas. The book is also supported by a companion website featuring links to relevant videos and articles, as well as an interactive flashcard glossary.
This book stems from the authors’ shared passion for primary mathematics teaching and offers an exploration of contemporary issues facing teachers. Drawing on research and case studies from practice, the book explores a wide range of concepts as starting points for professional reflection and personal development to improve teaching and learning in primary mathematics. Topics covered include: Using children’s mathematical misconceptions to support teaching and learning The role of talk in developing mathematical understanding Evidence-based teaching and learning Making mathematics real and purposeful beyond the classroom The role of games in teaching and learning mathematics ICT and mathematics The book illustrates the ways in which professional development that is rooted in practitioner inquiry and research enables teachers to advance their practice, resulting in improved outcomes for their pupils. Improving Primary Mathematics Teaching and Learning is appropriate for teachers undertaking professional development programmes (e.g. MaST, MA programmes), trainee teachers and staff on those programmes, both local authority and independent. Contributors: Mike Askew, Sue Bailey, Elizabeth Carruthers, Victoria Grinyer, Alice Hansen, Lynne McClure, Effie Maclellan, Suzan Nelson, Carol Rushworth-Little, Steve Sherer, Ian Thompson, Vivien Townsend, Maulfry Worthington. "In this book Mary McAteer brings together contributors with a wealth of experience in research and practice. The way in which practical and theoretical perspectives are brought to life with case studies and examples make it a highly readable text and every chapter adds new insights into children's mathematics learning." Dr Julia Anghileri, University of Cambridge (retired)
