Table Of ContentEarly Mathematics Learning and Development
Virginia Kinnear
Mun Yee Lai
Tracey Muir Editors
Forging
Connections in
Early Mathematics
Teaching and
Learning
Early Mathematics Learning and Development
Series editor
Lyn D. English
Queensland University of Technology, School of STM Education
Brisbane, QLD, Australia
More information about this series at http://www.springer.com/series/11651
Virginia Kinnear Mun Yee Lai
(cid:129)
Tracey Muir
Editors
Forging Connections in Early
Mathematics Teaching
and Learning
123
Editors
Virginia Kinnear Tracey Muir
Schoolof Education, Collegeof Education, FacultyofEducation,CollegeofArts,Law
PsychologyandSocial Work andEducation
Flinders University University of Tasmania
Bedford Park,SA Launceston,TAS
Australia Australia
MunYee Lai
Faculty of Education andArts,
Schoolof Education
Australian Catholic University
Fitzroy, VIC
Australia
ISSN 2213-9273 ISSN 2213-9281 (electronic)
EarlyMathematics Learning andDevelopment
ISBN978-981-10-7151-5 ISBN978-981-10-7153-9 (eBook)
https://doi.org/10.1007/978-981-10-7153-9
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Contents
1 Forging Connections in Early Mathematics: Perspectives
and Provocations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Virginia Kinnear, Mun Yee Lai and Tracey Muir
2 Early Mathematics Education: A Plea for Mathematically
Founded Conceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Virginia Kinnear and Erich Ch. Wittmann
3 Powerful Frameworks for Conceptual Understanding . . . . . . . . . . 37
Camilla Björklund
4 Building Connections Between Children’s Representations
and Their Conceptual Development in Mathematics. . . . . . . . . . . . 55
Janette Bobis and Jennifer Way
5 Geometry Learning in the Early Years: Developing
Understanding of Shapes and Space with a Focus on
Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
IliadaElia,MarjavandenHeuvel-PanhuizenandAthanasiosGagatsis
6 A Possible Learning Trajectory for Young Children’s
Experiences of the Evolution of the Base-10 Positional
Numeral System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Mun Yee Lai and Chun Ip Fung
7 From Cradle to Classroom: Exploring Opportunities to Support
the Development of Shape and Space Concepts in Very Young
Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Aisling Leavy, Jennifer Pope and Deirdre Breatnach
8 Mathematizing Basic Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Allen Leung and Simon Hung
v
vi Contents
9 Connecting the Mathematics Identity of Early Childhood
Educators to Classroom Experiences for Young Children . . . . . . . 155
Sandra M. Linder and Amber M. Simpson
10 Using Mathematics to Forge Connections Between Home and
School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Tracey Muir
11 Young Children’s Reasoning Through Data Exploration . . . . . . . . 191
Gabrielle Oslington, Joanne T. Mulligan and Penny Van Bergen
12 Making Connections to Realize Learning Potential in Early
Childhood Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Aubrey H. Wang and James P. Byrnes
13 Funds of Knowledge: Children’s Cultural Ways of Knowing
Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Maulfry Worthington
14 Making Connections Using Multiplication and Division
Contexts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Jennifer Young-Loveridge and Brenda Bicknell
15 Slow Maths: A Metaphor of Connectedness for Early Childhood
Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Steve Thornton
Contents vii
Chapter Titleandauthor Keywords
number
1 ForgingConnectionsinEarly Connections;Mathematicallearning;
Mathematics:Perspectivesand Purposeful;Mathematicsideas;
Provocations Children’slives;Mathematicsculture
VirginiaKinnear,MunYeeLaiand
TraceyMuir
2 EarlyMathematicsEducation:APlea Mathematicalstructure;Conceptual
forMathematicallyFounded understanding;Design;Mathematics
Conceptions activities;Play;Pureandapplied
VirginiaKinnearandErichCh. mathematics;Earlychildhood
Wittmann
3 PowerfulFrameworksforConceptual Conceptualunderstanding;Half;
Understanding Attention;Preschool;Structure;
CamillaBjörklund Learningintention;Variationtheoryof
learning;Preschool
4 BuildingConnectionsBetween Representations;Gesture;Drawing;
Children’sRepresentationsandTheir Conceptualunderstanding;Earlyyears
ConceptualDevelopmentin ofschool
Mathematics
JanetteBobisandJenniferWay
5 GeometryLearningintheEarly Geometry;Visualization;Shape
Years:DevelopingUnderstandingof transformation;Imaginaryperspective
ShapesandSpacewithaFocuson taking;Spatialconcepts;Gesture;Early
Visualization years
IliadaElia,Marjavanden
Heuvel-PanhuizenandAthanasios
Gagatsis
6 APossibleLearningTrajectoryfor Base-10positionalnumeralsystem;
YoungChildren’sExperiencesofthe Conceptofplacevalue;Teachingfor
EvolutionoftheBase-10Positional mathematizing;Earlyyearsofschool
NumeralSystem
MunYeeLaiandChunIpFung
7 FromCradletoClassroom: Geometry;Spatialawareness;Shape;
ExploringOpportunitiestoSupport Learningtrajectories;Play;Gesture;
theDevelopmentofShapeandSpace Home;Community;Language;Birthto
ConceptsinVeryYoungChildren 8years
AislingLeavy,JenniferPopeand
DeirdreBreatnach
8 MathematizingBasicAddition Mathematizing;Addition;Counting;
AllenLeungandSimonHung Subitizing;Guidedreinvention;Early
yearsofschool
9 ConnectingtheMathematicsIdentity Identity;Professionaldevelopment;
ofEarlyChildhoodEducatorsto Mathematics;Phenomenology;
ClassroomExperiencesforYoung Prior-to-school
Children
SandraM.LinderandAmberM.
Simpson
viii Contents
Chapter Titleandauthor Keywords
number
10 UsingMathematicstoForge Mathematics;Homeschoolpartnership;
ConnectionsBetweenHomeand Numeracy;Parents;Earlyyearsof
School school
TraceyMuir
11 YoungChildren’sReasoning Giftededucation;Statisticalreasoning;
ThroughDataExploration Modelbuilding;Datamodelling;
GabrielleOslington,JoanneT.Mulligan Representations;Classification;Early
andPennyVanBergen yearsofschool
12 MakingConnectionstoRealize Opportunity-Propensityframework;
LearningPotentialinEarly Opportunityfactors;Propensityfactors;
ChildhoodMathematics Structuralequationmodeling;
AubreyH.WangandJamesP.Byrnes Mathematicslearning;Earlychildhood
13 FundsofKnowledge:Children’s Culturalknowledge;Children’s
CulturalWaysofKnowing interests;Pretend-play;Preschool;
Mathematics Informalmathematics
MaulfryWorthington
14 MakingConnectionsUsing Counting;Multiplicationanddivision;
MultiplicationandDivisionContexts Representations;Materials;Placevalue;
JenniferYoung-LoveridgeandBrenda Earlyyearsofschool
Bicknell
15 SlowMaths:AMetaphorof Connections;Slow;Disciplinarynorms;
ConnectednessforEarlyChildhood History;Culture;Realworld;Metaphor
Mathematics
SteveThornton
Contents ix
3 g
1 n
Home 7,9,10,12, Learningtrajectories 6,7,13 Mathematizi 4,6,8,12
13, ons 3,
FundsofKnowledge 10,13 Pedagogy 2,3,4,7,8, ’ChildrensGraphicRepresentati 4,5,8,11,114
Priorknowledgeandmathematics 2,4,8,10,11,12,14 Curriculum 2,7,10,12,13,14 ObjectsandMaterials 2,3,4,5,7,8,14
Everydayexperiencesandknowledge 2,3,7,8,11,13,14 Environmentalandtaskdesign 2,3,6,7,8,11 Drawing 4,5,11,13
Play 2,3,4,7,9,13 MathematicalStructure 2,3,4,6,11,14 Gesture 4,5,7,8
EarlyChildhood 2,4,5,7,12 Mathematicalprocesses 4,5,6,8,9,11,14 Visualization 5,7,8
school 14 concepts 14
yyearsof 8,10,11, hematical 4,5,6,7, metry
Earl 4,6, Mat 2,3, Geo 5,7
Preschool 3,13 Mathematicallanguage 5,6,7,8,12,13 Counting 6,8,14
Prior-to-school 2,10 MathematicalorstatisticalReasoning 3,5,7,11,12,11,14 Number 3,4,6,7,8,10,14
