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Children's mathematics: making marks, making meaning

Children's mathematics: making marks, making meaning

Carruthers, Elizabeth; Worthington, Maulfry

Visit the author's own website here! Children's Mathematics Network '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

eBook, Electronic resource, Book. English. Electronic books.
2nd ed.
Published London: Paul Chapman, 2006
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    Barcode Shelfmark Loan type Status
    1972416-1002 E-book Online Available
    1972416-1001 E-book Online Available

Details

Statement of responsibility: Elizabeth Carruthers and Maulfry Worthington
ISBN: 1847878814, 9781412922838, 9781847878816
Note: Previous ed.: 2003.
Note: Includes bibliographical references and index.
Physical Description: xix , 260 p. : ill.
Subject: Mathematics education; Primary education; Early childhood education; Mathematics Study and teaching (Elementary) Great Britain.
Reproduction: Electronic reproduction. Dawson Books. Mode of access: World Wide Web.
Other formats: Also available in printed form.

Contents

  1. Who Takes Notice of Children's Own 'Written' Mathematics? Children's Mathematical Graphics International Findings Studies That Relate To Mathematical Literacy Enquiring into Children's MathematicsMaking Marks, Making Meaning Children Making Meaning with Marks Different Literacies: Mathematical Literacy Children Represent Their Mathematical Actions and Understanding On Paper Learning Theories Reading and Using Mathematical Graphics Sociocultural Perspectives Contexts in Early Years Settings Teachers' Beliefs Creativity in Mathematics Summary Mathematical Schemas What Is a Schema? Schemas and Mathematics Schemas and Mark-Making Observing Schemas in a School Setting Mapping Patterns of Schema ExplorationEarly Writing, Early Mathematics The Significance of Emergent Writing Young Children Explore Symbols Early Writing and Early Mathematical Marks Early (Emergent) Literacy Is Often Misunderstood ConclusionBridging the Gap between Home and School Mathematics Disconnections Understanding Symbols Mathematics as a Foreign Language Becoming Binumerate Teachers' Difficulties ConclusionMaking Sense of Children's Mathematical Graphics The Evolution of Children's Early Marks Categories of Children's Mathematical Graphics Common Forms of Graphical Marks Early Development of Mathematical Meaning Early Explorations with Marks 'The Beginning Is Everything' Early Written Numerals Numerals as Labels Representations of Quantities and Counting The Development of Early Written Number, Quantities and CountingUnderstanding Children's Developing Calculations Practical Mathematics The Fifth Dimension: Written Calculations Representations of Early Operations Counting Continuously Narrative Actions Supporting Children's Own Mathematical Marks Separating Sets Exploring Symbols Standard Symbolic Calculations with Small Numbers Calculations with Larger Numbers Supported By Jottings The Development of Children's Mathematical Graphics: Becoming Binumerate ConclusionEnvironments That Support Children's Mathematical Graphics Rich Mathematical Environments for Learning The Balance between Adult-Led and Child-Initiated Learning Role-Play and Mark-Making The Physical Environment Practical Steps Graphics Areas ConclusionCase Studies from Early Childhood Settings The Birthday Cards A Number Line 'No Entry' Carl's Garage Children's Centres: The Cambridge Learning Network Project Spontaneous Dice Game Young Children Think Division A Zoo Visit Mathematics and Literacy in Role-Play: The Library Van Aaron and the Train Multiplying Larger Numbers Nectarines for a Picnic ConclusionDeveloping Children's Written Methods The Assessment of Children's Mathematical Representations On Paper The Problem with Worksheets Assessing Samples of Children's Own Mathematics Examples of Assessment of Children's Mathematics The Pedagogy of Children's Mathematical Graphics Modelling MathematicsInvolving Parents and Families Children's First and Continuing Educators The Home As a Rich Learning Environment What Mathematics Do Young Children Do At Home? What Mathematics Do Parents Notice At Home? Parents Observe a Wealth of Mathematics Helping Parents Recognise Children's Mathematical Marks Parents' Questions about Children's Mathematical Graphics ConclusionChildren, Teachers and Possibilities Inclusion Children's Questions Teachers' Questions It's All Very Well
  2. But What About Test Scores? Reflections

Reviews

' I purchased a copy of your book over the holidays-it is my bebtime reading at the moment but it is far too stimulating'- Philippa Cook, Nursery Teacher, Clifton High School, Bristol

'Children's Mathematics: Making Marks, Making Meaning is essential reading for students of Education and Early Childhood Studies, as well as for those practitioners working in the Foundation and Primary stages of education' - Anne Cooper, Mathematics Association

'Thought-provoking and inspirational throughout. If you want to expand your understanding upwards and outwards then get a copy soon' - John Dabell, Education Consultant, Former Numeracy Consultant & Ofsted Inspector

Praise for the First Edition:

'Children's Mathematics: Making Marks, Making Meaning is essential reading for students of Education and Early Childhood Studies, as well as for those practitioners working in the Foundation and Primary stages of education' - Anne Cooper, Mathematics Association

'The writers make a very convincing case for the usefulness of exploring children's marks in order to understand their mathematical cognition. The examples of children's written representations provide fascinating insights into how different children think about mathematics' - Katherine Canobi, University of Melbourne