The Impact of Scale on Children’s Spatial Thought: A Quantitative Study for Two Settings in Geometry Education (Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik)

In this book, Cathleen Heil addresses the question of how to conceptually understand children's spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps.In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children's spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children's spatialthought in those two settings both at a manifest and latent level. Danksagung Abstract Contents List of Figures List of Tables 1 Introduction [DELETE] Part I Theoretical Background 2 Conceptualizing Spatial Cognition [DELETE] 2.1 Space in Cognition 2.1.1 Physical and Psychological Space 2.1.2 Spatial Cognition 2.1.3 Scale as a Psychological Construct 2.2 Spatial Representations and Spatial Behavior 2.2.1 The Concept of Representation 2.2.2 Palmer's Model of (Spatial) Representations 2.2.3 Liben's Model of Spatial Representations 2.2.4 Spatial Behavior 2.3 Encoding and Maintainance of Spatial Knowledge 2.3.1 Frames of Reference 2.3.2 Primary and Secondary Sources of Spatial Knowledge 2.3.3 The Architecture of Spatial Memory 2.4 Spatial Abilities 2.4.1 Definition of Spatial Abilities at Different Scales of Space 2.4.2 Conceptual Distinctions 3 Understanding Spatial Abilities at Different Scales of Space 3.1 Spatial Behavior at Different Scales of Space 3.1.1 Object Manipulation in Small-Scale Spaces 3.1.2 Map-Based Navigation in Real Space 3.2 Cognitive Analysis of Small-Scale Spatial Abilities 3.2.1 Representation of Small-Scale Spatial Information 3.2.2 Mental Transformations of Small-Scale Spatial Information 3.2.3 Maintenance of Small-Scale Spatial Information in Working Memory 3.3 Cognitive Analysis of Large-Scale Spatial Abilities 3.3.1 Understanding Maps 3.3.2 Representation of Large-Scale Spatial Information 3.3.3 Cognitive Processes of Map-Based Orientation 3.3.4 Maintenance of Large-Scale Spatial Information in Working Memory 3.4 Comparison of Spatial Abilities at Different Scales of Space 4 Reviewing Empirical Findings of Spatial Abilities at Different Scales of Space 4.1 The Dissociation of Two Subclasses of Small-Scale Spatial Abilities 4.1.1 The Psychometric Literature 4.1.2 The Individual Differences Literature 4.1.3 The Developmental Literature 4.2 The Dissociation of Two or More Subclasses of Large-Scale Spatial Abilities 4.2.1 The Psychometric Literature 4.2.2 The Individual Differences Literature 4.2.3 The Developmental Literature 4.3 The Relationship Between Small-Scale and Large-Scale Spatial Abilities 4.3.1 Studies Without Maps 4.3.2 Studies Involving Maps Part II Empirical Study 5 Design of the Empirical Study [DELETE] 5.1 Research Questions, Latent Constructs, and Research Design 5.1.1 Research Questions 5.1.2 Latent Constructs 5.1.3 Hypotheses 5.1.4 Research Design 5.2 Methodological Framework 5.2.1 Psychometrics 5.2.2 Structural Equation Modeling 5.2.3 Treatment of Missing Data 5.3 Planning of the Empirical Study 5.3.1 Location and Organizational Framework 5.3.2 Requirements Regarding the Sample and Testing Material 6 Testing Material for Small-Scale Spatial Abilities [DELETE] 6.1 Development of a Set of Paper-and-Pencil Tasks 6.1.1 Preliminary Considerations 6.1.2 Tasks Measuring OB 6.1.3 Tasks Measuring EGO 6.2 Pilot Study 6.2.1 Sample, Material, and Procedure 6.2.2 Preliminary Analysis 6.2.3 Detailed Analysis of All Measures 6.2.4 Confirmatory Factor Analyses 6.2.5 Implications for the Main Study 7 Testing Material for Large-Scale Spatial Abilities [DELETE] 7.1 Development of a Set of Map-Based Orientation Tasks 7.1.1 Preliminary Considerations 7.1.2 Conceptual Choices 7.1.3 Methodical Choices 7.2 Presentation of the Map-Based Orientation Tests 7.2.1 Tasks Measuring MapEnvSelf 7.2.2 Tasks Measuring SurveyMap 8 Additional Testing Material 8.1 The Corsi Block Test 8.1.1 Materials 8.1.2 Procedure 8.1.3 Scoring 8.2 PTSOT-C 8.2.1 Design of the Adopted Instrument 8.2.2 Framework for Item Construction and Analysis 8.2.3 Testing Procedure 9 Data Collection 9.1 Participants 9.2 Materials 9.3 Experimenters 9.4 Procedure 9.4.1 Testing Procedure for the Small-Scale Spatial Abilities Test 9.4.2 Testing Procedure for the Large-Scale Spatial Abilities Test 9.5 Documentation 9.6 Data Treatment 9.6.1 Encoding and Scoring 9.6.2 Treatment of Missing Data Part III Results and Discussion 10 Children's Small-Scale Spatial Abilities [DELETE] 10.1 Analyses of Items and Measures 10.1.1 Summary of Item Analyses 10.1.2 Descriptive Statistics 10.1.3 Reliabilities 10.2 On the Dissociation of Two Subclasses of Small-Scale Spatial Abilities 10.2.1 Class Clustering Effects 10.2.2 Analysis of Pearson Correlations 10.2.3 Confirmatory Factor Analysis 10.3 The Role of Visuospatial Working Memory 10.3.1 Descriptive Analysis of Different Corsi Block Test Measures 10.3.2 Analysis of Pearson Correlations 10.3.3 An Extended Model Involving VSWM 10.4 Item Analysis for the PTSOT-C 10.5 Discussion of the Empirical Findings 11 Children's Large-Scale Spatial Abilities [DELETE] 11.1 Analyses of the Items and Measures 11.1.1 Detailed Analysis of Individual Measures 11.1.2 Summary: Psychometric Properties of All Items 11.1.3 Summary: Descriptive Statistics of the Measures 11.1.4 Reliabilities 11.2 On the Dissociation of Three Subclasses of Large-Scale Spatial Abilities 11.2.1 Analysis of Results From Multiple Imputation Procedure 11.2.2 Class Clustering Effects 11.2.3 Analysis of Pearson Correlations 11.2.4 Confirmatory Factor Analyses 11.3 The Influence of Visuospatial Working Memory 11.3.1 Analysis of Pearson Correlations 11.3.2 An Extended Model Involving VSWM 11.4 Discussion of the Empirical Findings 12 Relations Between Children's Small-Scale and Large-Scale Spatial Abilities 12.1 Results at the Manifest Level 12.1.1 Zero-Order Correlation Analysis 12.1.2 Semipartial Correlation Analyses 12.1.3 Hierarchical Multiple Regression Analyses 12.2 Results at the Latent Level 12.2.1 Results From Structural Equation Modeling 12.2.2 Latent Regression Models 12.2.3 The Role of Visuospatial Working Memory 12.3 Discussion of the Empirical Findings 13 Discussion, Limitations, and Implications 13.1 Discussion of the Empirical Findings 13.1.1 Children's Individual Differences in Spatial Abilities at Different Scales of Space 13.1.2 The Relation Between Small-Scale and Large-Scale Spatial Abilities 13.1.3 The Role of Subclasses of Spatial Abilities 13.1.4 The Role of Visuospatial Working Memory 13.1.5 An Extended Model of Spatial Abilities at Different Scales of Space 13.2 Limitations 13.2.1 Basic Assumptions and Design of the Study 13.2.2 Experimental Setup 13.2.3 Methodology 13.2.4 Neglected Covariates 13.3 Implications 13.3.1 Implications for Research in Mathematics Education 13.3.2 Implications for Research in Psychology 13.3.3 Implications for Geometry Education in Primary Schools 14 Conclusion [DELETE] A Small-Scale Spatial Abilities Test Extra Tables References