Mathematics Education in the Early Years: Results from the POEM4 Conference, 2018

✍ Scribed by Martin Carlsen; Ingvald Erfjord; Per Sigurd Hundeland

• Tongue: English
• Leaves: 453
• Category: Library

✦ Table of Contents

Mathematics Education in the Early Years
Introduction
Children’s Mathematical Reasoning
Early Years Mathematics Teaching
Parents’ Role in Children’s Mathematical Development
Contents
About the Editors
Chapter 1: Early Years Mathematics: Semiotic and Cultural Mediation
1.1 Introduction
1.1.1 What Does Early Years Mathematics Mean?
1.1.2 My Personal Trajectory
1.2 Some Outcomes of the Preschool Program
1.2.1 The Giant Slavonic Abacus
1.2.1.1 Task 1: The First Impact (The Narrator’s Voice)
1.2.1.2 Task 2: The Structure of the Artifact (The Constructor’s Voice)
1.2.1.3 Task 3: The Use of the Artifact (The User’s Voice)
1.2.1.4 Task 4: The Justification for Use (The Theoretician’s Voice)
1.2.1.5 Task 5: New Problems (The Problem Poser and Solver’s Voice)
1.2.2 The Time Tube
1.2.3 Semiotic Mediation at the Preschool Level
1.3 The Shift to Toddler Centers (and to Prelinguistic Kids)
1.3.1 From Semiotic Mediation to Cultural Mediation
1.3.2 The Newborn Experience in a Cultural Context
1.3.3 Vygotsky’s Hints to Non-Verbal Mediation: The Inner Visual Field
1.3.4 Vygotsky’s Analysis of the Pointing Gesture
1.3.5 A Replica of a Classical Experiment: Learning to Drink from a Cup
1.3.6 The Effects of Social Relationships
1.4 Concluding Remarks
References
Chapter 2: Young Children’s Early Mathematical Competencies: The Role of Mathematical Focusing Tendencies
2.1 Introduction
2.2 SFON
2.3 SFONS
2.4 SFOR
2.5 SFOP
2.6 Conclusion and Discussion
2.6.1 Conceptual Issues
2.6.2 Measurement Issues
2.6.3 Developmental Issues
2.6.4 Promotion of Mathematical Focusing Tendencies
References
Chapter 3: Play and the Production of Subjectivities in Preschool
3.1 Introduction
3.2 The Production of Individuals In and Through Play
3.3 Semiotic Systems of Cultural Signification
3.4 Being, Becoming, and Subjectivity
3.5 Playing a Mathematical Game
3.6 The Inscription of the Children in the Social World
3.6.1 The Role of Rules
3.6.2 The Role of the Mathematical Content
3.6.3 The Teacher as the Embodiment of an Ideal Form
3.7 Synthesis and Concluding Remarks
References
Part I: Children’s Mathematical Reasoning
Chapter 4: Copying and Comparing Repeating Patterns: Children’s Strategies and Descriptions
4.1 Introduction
4.2 Duplicating, Copying, and Comparing Patterns
4.3 Methodology
4.3.1 Data Analysis
4.4 Findings
4.4.1 Copying and Comparing AB-Structured Necklaces
4.4.2 Copying and Comparing AAB-Structured Necklaces
4.4.3 Comparing the AB and AAB Patterns
4.5 Discussion
References
Chapter 5: Patterning as a Mathematical Activity: An Analysis of Young Children’s Strategies When Working with Repeating Patterns
5.1 Introduction
5.2 Repeating Patterns and Mathematics
5.3 Patterning Strategies
5.4 Method
5.4.1 Setting and Participants
5.4.2 Tasks and Materials
5.4.3 Data Collection and Analysis
5.5 Results
5.6 Discussion
References
Chapter 6: Preschoolers’ Ways of Using Fingers in Numerical Reasoning
6.1 Background and Aim
6.2 Research Review
6.3 The Study
6.4 Analysis
6.5 Results
6.5.1 Fingers as an Image of Numbers
6.5.2 Fingers to Create Numbers of Single Units
6.5.3 Fingers to Visualize the Structure of Numbers
6.6 Conclusions
References
Chapter 7: Young Children’s Cross-Domain Mapping of Numerosity in Path Navigation
7.1 Introduction and Background
7.2 Theoretical Framework
7.3 Methodology
7.3.1 The Intervention and Case Selection
7.3.2 Procedure of the Navigation Task
7.3.3 Operationalisation and Data Analysis
7.4 Results
7.4.1 General Results
7.4.2 Rich Description of Three Groups of Task Solutions
7.5 Discussion
7.6 Summary and Concluding Remarks
References
Chapter 8: Mathematical Problem-Solving Visualised in Outdoor Activities
8.1 Introduction
8.2 Theoretical Frameworks About Mathematical Problem-Solving
8.3 Methodology
8.4 Data
8.4.1 A Child-Initiated, Problem-Solving Activity
8.5 Analysis and Discussion
8.5.1 An Analysis and Discussion of the Measurement Understanding
8.5.2 An Analysis and Discussion Using Copley’s Characteristics of an Effective Problem Solver
8.5.3 An Analysis and Discussion Using Polya’s Problem-Solving Stages
8.5.4 An Analysis and Discussion Using the Didaktic Space
8.6 Implication for the Kindergarten Teacher’s Role
8.7 Conclusion
References
Chapter 9: Making Choices and Explaining Them: An Experiment with Strategy Games in Kindergarten
9.1 Introduction
9.2 Theoretical Framework
9.3 The Teaching Experiment
9.3.1 The Thirteen Buttons Game
9.3.2 The Didactical Choices
9.4 Data Analysis
9.4.1 Phase 1: Introduction to the “Thirteen Buttons Game”
9.4.2 Phase 2. The Discovery of the “Magic Buttons”
9.4.3 Phase 3: The Dinosaur Goes on Holiday
9.5 Conclusion
References
Chapter 10: Measuring Rice in Early-Childhood Education Activities: A Bridge Across Discrete and Continuous Magnitudes
10.1 Introduction
10.2 Theoretical Background of the Study
10.3 Methodology
10.4 Analyses
10.4.1 Strategies Before Introduction of the Artifacts
10.4.1.1 Evaluation of Numerosity
10.4.1.2 Evaluation of Surface
10.4.1.3 Evaluation of Volume
10.4.2 Strategies with Artifacts
10.5 Conclusions and Future Perspectives
References
Chapter 11: The Semiotic Resources Children Use in Their Explanations of Hypothetical Situations
11.1 Introduction
11.2 Semiotic Resources and Explanations
11.3 Methodology
11.4 Results
11.4.1 Introducing an Imaginary Layout
11.4.2 Adapting Gestures
11.4.3 Clarifying What Is Discussed
11.4.4 Alternative Support for Deductive Explanations
11.4.5 Explicit Explanation
11.5 Discussion
11.6 Conclusion
References
Chapter 12: Drawings, Gestures and Discourses: A Case Study with Kindergarten Students Discovering Lego Bricks
12.1 Introduction
12.2 Theoretical Framework
12.3 Research Methodology
12.4 Overview of the Teaching Sequence
12.5 Analysis and Preliminary Results
12.5.1 Different Points of View of Matilde, Laura and Elio
12.5.1.1 Episode 1
12.5.1.2 Episode 2
12.5.1.3 Episode 3
12.6 Conclusions
References
Chapter 13: Perceiving and Using Structures When Determining the Cardinality of Sets: A Child’s Learning Story
13.1 Introduction
13.2 Role of Structures for Numerical and Arithmetical Development
13.3 Research Question
13.4 Design of the Study
13.4.1 Tasks
13.4.2 Implementation
13.4.3 Aspects of Data Analysis
13.4.4 Data Analysis by the Use of Eye-Tracking Technology
13.4.5 Example from the Data Analysis
13.5 Results of the Learning Story of “Luca”
13.6 Summary and Discussion
References
Chapter 14: “A Triangle Is Like a Tent”: Children’s Conception of Geometric Shapes
14.1 Introduction
14.2 Theoretical Background
14.2.1 Explaining Shapes
14.2.2 Drawing Shapes
14.2.3 Identifying Shapes
14.2.4 Coherence
14.3 Research Question
14.4 Design of the Study
14.4.1 Tasks
14.4.2 Analysis
14.5 Results
14.5.1 Explaining Shapes
14.5.2 Drawing Triangles
14.5.3 Coherence Between the Children’s Explanations and Drawings
14.5.4 Identifying Circles, Squares, and Triangles
14.5.5 Coherence Between Children’s Explanations and Identifications
14.6 Summary and Discussion
14.7 Conclusion
References
Chapter 15: Framing Mathematics Teaching with Narratives: The Ambiguity of Goldilocks
15.1 Introduction
15.2 Narratives as Pedagogical Tools
15.3 Methodology
15.4 Two Empirical Examples
15.4.1 Example 1
15.4.2 Example 2
15.5 Content Analysis of the Goldilocks Story
15.5.1 What Mathematical Challenges Does the Story Impose?
15.6 Discussion
Appendix: The Story of Goldilocks and the Three Bears
References
Chapter 16: Kindergarten Teacher’s Knowledge to Support a Mathematical Discussion with Pupils on Measurement Strategies and Procedures
16.1 Introduction
16.2 Theoretical Framework
16.3 Context and Method
16.4 Analysis and Discussion
16.4.1 Episode 1: Ordering by Length Vs. Height
16.4.2 Episode 2: The Magnitude of Length
16.4.3 Final Comments
References
Chapter 17: The Materialisation of Children’s Mathematical Thinking Through Organisation of Turn-Taking in Small Group Interactions in Kindergarten
17.1 Introduction
17.2 Theoretical Framework
17.3 Methodology
17.4 Results
17.4.1 Segment 1, from Kindergarten 1 (K1)
17.4.2 Segment 2.1, from Kindergarten 2 (K2)
17.4.3 Segment 2.2, from Kindergarten 2 (K2)
17.5 Discussion
17.5.1 The Characterisation of Children’s Turn-Taking: Similarities and Differences in the Three Segments
17.5.2 The Role of Children’s Organisation of Turn-Taking for the Materialisation of Children’s Mathematical Thinking in the Joint Activity
References
Chapter 18: Mathematical Activity in Early Childhood and the Role of Generalization
18.1 Introduction
18.2 Analysis of Mathematical Activity in Early Years
18.3 Development of Mathematical Ideas and Generalization
18.4 A Teaching Approach Encouraging Generalization
18.5 Closing
References
Part II: Early Years Mathematics Teaching
Chapter 19: Situational Perception in Mathematics (SPiM)—Results of a Cross-Country Study in Austria and Norway
19.1 Introduction
19.2 Situation-Specific Skills: An Essential Part of Kindergarten Teachers’ Competence
19.3 Kindergarten Teachers’ Situational Perception of Mathematics
19.4 Research Questions
19.5 Methods
19.5.1 Sample
19.5.2 Data Collection
19.5.3 Data Analysis and Analytical Process
19.6 Identified Categories from the Analysed Data
19.7 Discussion
References
Chapter 20: How to Support Kindergarten Children in Spontaneous Measuring Activities
20.1 Background
20.1.1 Measuring
20.1.2 The Knowledge Quartet
20.1.3 The Purpose of Education: Biesta
20.2 Methodology
20.2.1 Limitations of the Study
20.3 Analysis
20.3.1 The Quantitative Data
20.3.2 The Qualitative Data
20.3.3 Relative Heights—Dorothea’s Observation
20.3.4 Who Is Tallest?—Turid’s Observation
20.3.5 Selling Water—Astrid’s Observation
20.3.6 An Empty Cardboard Box—Lina’s Observation
20.3.7 Santa Hats—Lars’s Observation
20.4 Discussion
20.4.1 Reflecting on Practise with the Quartet Knowledge
20.4.2 The Active-Passive Dilemma
20.5 Conclusion
References
Chapter 21: Kindergarten Teachers’ Stories About Young Children’s Problem Posing and Problem Solving
21.1 Introduction
21.2 Methodology
21.3 Results
21.3.1 Goldilocks and the Three Bears
21.3.2 Train Crash
21.3.3 Counting Orange Boats
21.3.4 Packing the Police Car
21.4 Discussion
21.5 Conclusion
References
Chapter 22: ‘You Are Already Bigger Than the Giraffe!’—The Use of Adjectives in Measurement Activities in Kindergarten
22.1 Introduction
22.2 Measuring Length and Weight
22.3 Learning Opportunities: Adjectives
22.4 Research Design and Analysing Methods
22.5 Analysis and Interpretation of Empirical Data
22.6 Empirical Examples for Learning Opportunities
22.7 Conclusion
References
Chapter 23: The Complexity of Teaching Mathematics in Kindergarten: A Case Study and Conceptualization
23.1 Introduction
23.2 Theoretical Background
23.3 Design of the Study
23.4 Tasks of Teaching Mathematics in Kindergarten
23.4.1 Initiating Mathematical Discussions
23.4.2 Responding to Unexpected Questions
23.4.3 Dealing with Wrong Answers
23.4.4 Using Representations
23.4.5 Positioning Children as Valuable Contributors
23.4.6 Asking Productive Mathematical Questions
23.5 Discussion
23.6 Conclusion
References
Part III: Parents’ Role in Children’s Mathematical Development
Chapter 24: Parents’ Valuing of Mathematics for Young Children
24.1 Introduction
24.2 Theoretical Perspective
24.2.1 Narrative Approach to the Learning of Mathematics
24.3 Methodology
24.3.1 Analysis of the Data
24.4 Results
24.4.1 Yahtzee and Ludo, the Value of Learning Numbers
24.4.2 Everyday Activities, the Value of Learning Counting Skills
24.4.3 Length, Volume, Time, and the Value of Learning Measurement Skills
24.4.4 Money and the Valuing of Equivalence
24.5 Discussion
24.6 Conclusion
References
Chapter 25: “Pedagogical” Mathematics During Play at Home: An Exploratory Study
25.1 Introduction
25.2 Theoretical Framework
25.3 Background Literature
25.4 Method
25.4.1 Data Sources
25.5 Results
25.5.1 Establishing the Mathematics Goal
25.5.2 Sustaining the Mathematics Goal
25.5.3 Addressing Each Child’s Role in Play-Based Mathematics
25.5.4 Beyond Pedagogical Moves: Mother-as-Teacher and Funds of Knowledge
25.6 Conclusion
Appendix
References
Index