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Children's Mathematics
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Children's Mathematics
Making Marks, Making Meaning

Second Edition
  • Elizabeth Carruthers - Early Years Researcher, Head of Children's Centre and formerly NNS Consultant
  • Maulfry Worthington - Doctoral Research: Free University, Amsterdam and former NNS Consultant


August 2006 | 280 pages | SAGE Publications Ltd

Based on the authors' many years' experience in teaching children ages three to eight years and on their extensive research with children in the home, nursery and school, this resource discusses the development and range of young children's mathematical marks and visual representations. It illustrates 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 reflect deep levels of thinking, and identifies this as the key to success in school mathematics and 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.

 
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 Mathematics

 
 
Making 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 Exploration

 
 
Early Writing, Early Mathematics
The Significance of Emergent Writing

 
Young Children Explore Symbols

 
Early Writing and Early Mathematical Marks

 
Early (Emergent) Literacy Is Often Misunderstood

 
Conclusion

 
 
Bridging the Gap between Home and School Mathematics
Disconnections

 
Understanding Symbols

 
Mathematics as a Foreign Language

 
Becoming Binumerate

 
Teachers' Difficulties

 
Conclusion

 
 
Making 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 Counting

 
 
Understanding 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

 
Conclusion

 
 
Environments 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

 
Conclusion

 
 
Case 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

 
Conclusion

 
 
Developing 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 Mathematics

 
 
Involving 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

 
Conclusion

 
 
Children, Teachers and Possibilities
Inclusion

 
Children's Questions

 
Teachers' Questions

 
It's All Very Well - But What About Test Scores?

 
Reflections

 

' 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


This was already an adopted book, in its previous edition. The new edition build upon this, and appears to be the only reliable text on the ground once occupied by Hughes' excellent "Children and Number".

Mr Ralph Manning
Sch of Education & Lifelong Learning, University of East Anglia
October 12, 2010

Preview this book

Sample Materials & Chapters

Foreword and preface (143kb)


Elizabeth Carruthers

Maulfry Worthington

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ISBN: 9781412922838
£32.99 

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