Children's Mathematics

Making Marks, Making Meaning

AvElizabeth Carruthers,Maulfry Worthington

Inbunden, Engelska, 2006

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Beskrivning

'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.

Produktinformation

Utgivningsdatum:2006-08-07
Mått:170 x 242 x 21 mm
Vikt:620 g
Format:Inbunden
Språk:Engelska
Antal sidor:280
Upplaga:2
Förlag:SAGE Publications
ISBN:9781412922821

Utforska kategorier

Pedagogisk metodik inom Psykologi och pedagogik

Recensioner i media

′ 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

Innehållsförteckning

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