′ 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 InspectorPraise 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

• Who Takes Notice of Children′s Own ′Written′ Mathematics?Children′s Mathematical GraphicsInternational FindingsStudies That Relate To Mathematical LiteracyEnquiring into Children′s MathematicsMaking Marks, Making MeaningChildren Making Meaning with MarksDifferent Literacies: Mathematical LiteracyChildren Represent Their Mathematical Actions and Understanding On PaperLearning TheoriesReading and Using Mathematical GraphicsSociocultural Perspectives Contexts in Early Years SettingsTeachers′ BeliefsCreativity in MathematicsSummaryMathematical SchemasWhat Is a Schema?Schemas and MathematicsSchemas and Mark-MakingObserving Schemas in a School SettingMapping Patterns of Schema ExplorationEarly Writing, Early MathematicsThe Significance of Emergent WritingYoung Children Explore SymbolsEarly Writing and Early Mathematical MarksEarly (Emergent) Literacy Is Often MisunderstoodConclusionBridging the Gap between Home and School MathematicsDisconnectionsUnderstanding SymbolsMathematics as a Foreign LanguageBecoming BinumerateTeachers′ DifficultiesConclusionMaking Sense of Children′s Mathematical GraphicsThe Evolution of Children′s Early MarksCategories of Children′s Mathematical GraphicsCommon Forms of Graphical MarksEarly Development of Mathematical MeaningEarly Explorations with Marks′The Beginning Is Everything′Early Written NumeralsNumerals as LabelsRepresentations of Quantities and CountingThe Development of Early Written Number, Quantities and CountingUnderstanding Children′s Developing CalculationsPractical MathematicsThe Fifth Dimension: Written CalculationsRepresentations of Early OperationsCounting ContinuouslyNarrative ActionsSupporting Children′s Own Mathematical MarksSeparating SetsExploring SymbolsStandard Symbolic Calculations with Small NumbersCalculations with Larger Numbers Supported By JottingsThe Development of Children′s Mathematical Graphics: Becoming BinumerateConclusionEnvironments That Support Children′s Mathematical GraphicsRich Mathematical Environments for LearningThe Balance between Adult-Led and Child-Initiated LearningRole-Play and Mark-MakingThe Physical EnvironmentPractical StepsGraphics AreasConclusionCase Studies from Early Childhood SettingsThe Birthday CardsA Number Line′No Entry′Carl′s GarageChildren′s Centres: The Cambridge Learning Network ProjectSpontaneous Dice GameYoung Children Think DivisionA Zoo VisitMathematics and Literacy in Role-Play: The Library VanAaron and the TrainMultiplying Larger NumbersNectarines for a PicnicConclusionDeveloping Children′s Written MethodsThe Assessment of Children′s Mathematical Representations On PaperThe Problem with WorksheetsAssessing Samples of Children′s Own MathematicsExamples of Assessment of Children′s MathematicsThe Pedagogy of Children′s Mathematical GraphicsModelling MathematicsInvolving Parents and FamiliesChildren′s First and Continuing EducatorsThe Home As a Rich Learning EnvironmentWhat Mathematics Do Young Children Do At Home?What Mathematics Do Parents Notice At Home?Parents Observe a Wealth of MathematicsHelping Parents Recognise Children′s Mathematical MarksParents′ Questions about Children′s Mathematical GraphicsConclusionChildren, Teachers and PossibilitiesInclusionChildren′s QuestionsTeachers′ QuestionsIt′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 InspectorPraise 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

• Who Takes Notice of Children′s Own ′Written′ Mathematics?Children′s Mathematical GraphicsInternational FindingsStudies That Relate To Mathematical LiteracyEnquiring into Children′s MathematicsMaking Marks, Making MeaningChildren Making Meaning with MarksDifferent Literacies: Mathematical LiteracyChildren Represent Their Mathematical Actions and Understanding On PaperLearning TheoriesReading and Using Mathematical GraphicsSociocultural Perspectives Contexts in Early Years SettingsTeachers′ BeliefsCreativity in MathematicsSummaryMathematical SchemasWhat Is a Schema?Schemas and MathematicsSchemas and Mark-MakingObserving Schemas in a School SettingMapping Patterns of Schema ExplorationEarly Writing, Early MathematicsThe Significance of Emergent WritingYoung Children Explore SymbolsEarly Writing and Early Mathematical MarksEarly (Emergent) Literacy Is Often MisunderstoodConclusionBridging the Gap between Home and School MathematicsDisconnectionsUnderstanding SymbolsMathematics as a Foreign LanguageBecoming BinumerateTeachers′ DifficultiesConclusionMaking Sense of Children′s Mathematical GraphicsThe Evolution of Children′s Early MarksCategories of Children′s Mathematical GraphicsCommon Forms of Graphical MarksEarly Development of Mathematical MeaningEarly Explorations with Marks′The Beginning Is Everything′Early Written NumeralsNumerals as LabelsRepresentations of Quantities and CountingThe Development of Early Written Number, Quantities and CountingUnderstanding Children′s Developing CalculationsPractical MathematicsThe Fifth Dimension: Written CalculationsRepresentations of Early OperationsCounting ContinuouslyNarrative ActionsSupporting Children′s Own Mathematical MarksSeparating SetsExploring SymbolsStandard Symbolic Calculations with Small NumbersCalculations with Larger Numbers Supported By JottingsThe Development of Children′s Mathematical Graphics: Becoming BinumerateConclusionEnvironments That Support Children′s Mathematical GraphicsRich Mathematical Environments for LearningThe Balance between Adult-Led and Child-Initiated LearningRole-Play and Mark-MakingThe Physical EnvironmentPractical StepsGraphics AreasConclusionCase Studies from Early Childhood SettingsThe Birthday CardsA Number Line′No Entry′Carl′s GarageChildren′s Centres: The Cambridge Learning Network ProjectSpontaneous Dice GameYoung Children Think DivisionA Zoo VisitMathematics and Literacy in Role-Play: The Library VanAaron and the TrainMultiplying Larger NumbersNectarines for a PicnicConclusionDeveloping Children′s Written MethodsThe Assessment of Children′s Mathematical Representations On PaperThe Problem with WorksheetsAssessing Samples of Children′s Own MathematicsExamples of Assessment of Children′s MathematicsThe Pedagogy of Children′s Mathematical GraphicsModelling MathematicsInvolving Parents and FamiliesChildren′s First and Continuing EducatorsThe Home As a Rich Learning EnvironmentWhat Mathematics Do Young Children Do At Home?What Mathematics Do Parents Notice At Home?Parents Observe a Wealth of MathematicsHelping Parents Recognise Children′s Mathematical MarksParents′ Questions about Children′s Mathematical GraphicsConclusionChildren, Teachers and PossibilitiesInclusionChildren′s QuestionsTeachers′ QuestionsIt′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 InspectorPraise 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

• Who Takes Notice of Children′s Own ′Written′ Mathematics?Children′s Mathematical GraphicsInternational FindingsStudies That Relate To Mathematical LiteracyEnquiring into Children′s MathematicsMaking Marks, Making MeaningChildren Making Meaning with MarksDifferent Literacies: Mathematical LiteracyChildren Represent Their Mathematical Actions and Understanding On PaperLearning TheoriesReading and Using Mathematical GraphicsSociocultural Perspectives Contexts in Early Years SettingsTeachers′ BeliefsCreativity in MathematicsSummaryMathematical SchemasWhat Is a Schema?Schemas and MathematicsSchemas and Mark-MakingObserving Schemas in a School SettingMapping Patterns of Schema ExplorationEarly Writing, Early MathematicsThe Significance of Emergent WritingYoung Children Explore SymbolsEarly Writing and Early Mathematical MarksEarly (Emergent) Literacy Is Often MisunderstoodConclusionBridging the Gap between Home and School MathematicsDisconnectionsUnderstanding SymbolsMathematics as a Foreign LanguageBecoming BinumerateTeachers′ DifficultiesConclusionMaking Sense of Children′s Mathematical GraphicsThe Evolution of Children′s Early MarksCategories of Children′s Mathematical GraphicsCommon Forms of Graphical MarksEarly Development of Mathematical MeaningEarly Explorations with Marks′The Beginning Is Everything′Early Written NumeralsNumerals as LabelsRepresentations of Quantities and CountingThe Development of Early Written Number, Quantities and CountingUnderstanding Children′s Developing CalculationsPractical MathematicsThe Fifth Dimension: Written CalculationsRepresentations of Early OperationsCounting ContinuouslyNarrative ActionsSupporting Children′s Own Mathematical MarksSeparating SetsExploring SymbolsStandard Symbolic Calculations with Small NumbersCalculations with Larger Numbers Supported By JottingsThe Development of Children′s Mathematical Graphics: Becoming BinumerateConclusionEnvironments That Support Children′s Mathematical GraphicsRich Mathematical Environments for LearningThe Balance between Adult-Led and Child-Initiated LearningRole-Play and Mark-MakingThe Physical EnvironmentPractical StepsGraphics AreasConclusionCase Studies from Early Childhood SettingsThe Birthday CardsA Number Line′No Entry′Carl′s GarageChildren′s Centres: The Cambridge Learning Network ProjectSpontaneous Dice GameYoung Children Think DivisionA Zoo VisitMathematics and Literacy in Role-Play: The Library VanAaron and the TrainMultiplying Larger NumbersNectarines for a PicnicConclusionDeveloping Children′s Written MethodsThe Assessment of Children′s Mathematical Representations On PaperThe Problem with WorksheetsAssessing Samples of Children′s Own MathematicsExamples of Assessment of Children′s MathematicsThe Pedagogy of Children′s Mathematical GraphicsModelling MathematicsInvolving Parents and FamiliesChildren′s First and Continuing EducatorsThe Home As a Rich Learning EnvironmentWhat Mathematics Do Young Children Do At Home?What Mathematics Do Parents Notice At Home?Parents Observe a Wealth of MathematicsHelping Parents Recognise Children′s Mathematical MarksParents′ Questions about Children′s Mathematical GraphicsConclusionChildren, Teachers and PossibilitiesInclusionChildren′s QuestionsTeachers′ QuestionsIt′s All Very Well - But What About Test Scores?Reflections