This book focusses on teaching and learning in elementary and middle school mathematics and suggests practices for teachers to help children be successful mathematical thinkers. Contributions from diverse theoretical and disciplinary perspectives are explored. Topics include the roles of technology, language, and classroom discussion in mathematics learning, the use of creativity, visuals, and teachers’ physical gestures to enhance problem solving, inclusive educational activities to promote children’s mathematics understanding, how learning in the home can enhance children’s mathematical skills, the application of mathematics learning theories in designing effective teaching tools, and a discussion of how students, teachers, teacher educators, and school boards differentially approach elementary and middle school mathematics.
This book and its companion, Mathematical Cognition and Understanding, take an interdisciplinary perspective to mathematical learning and development in the elementary and middle school years. The authors and perspectives in this book draw from education, neuroscience, developmental psychology, and cognitive psychology. The book will be relevant to scholars/educators in the field of mathematics education and also those in childhood development and cognition. Each chapter also includes practical tips and implications for parents as well as for educators and researchers.
Author(s): Katherine M. Robinson, Donna Kotsopoulos, Adam K. Dubé
Publisher: Springer
Year: 2023
Language: English
Pages: 233
City: Cham
Contents
Contributors
Abbreviations
Chapter 1: An Introduction to Mathematics Teaching and Learning in the Elementary and Middle School Years
1.1 An Introduction to Mathematics Teaching and Learning in the Elementary and Middle School Years
References
Part I: Pedogical Approaches to Teaching
Chapter 2: Instructional Supports for Mathematical Problem Solving and Learning: Visual Representations and Teacher Gesture
2.1 Introduction
2.2 Teacher Gesture as an External Support for Attending to Instructionally Relevant Information
2.3 Do Teachers’ Gestures Help Students Encode Instructionally Relevant Information?
2.4 Diagrams as External Supports for Discerning Structure
2.5 Implications for Educational Practice
References
Chapter 3: Equilibrated Development Approach to Word Problem Solving in Elementary Grades: Fostering Relational Thinking
3.1 Introduction
3.2 Theoretical Background
3.2.1 Operational Paradigm
3.2.2 Insights from Neuro-education and the Developmental Aspects of Learning
3.2.3 Relational Paradigm
3.3 Equilibrated Development Approach
3.3.1 Activities to Promote Relational Thinking and Modeling
3.3.1.1 Activity 1. Communicating the Mathematical Structure of a Problem: The Captain’s Game
3.3.1.2 Activity 2. Mathematically Impossible Situations (MIS)
3.3.1.3 Activity 3. Working in a Computer Environment
3.3.1.4 Activity 4. Differentiation Between Additive and Multiplicative Relationships
3.4 How It Works in Class
3.5 Conclusion
References
Chapter 4: Experiences of Tension in Teaching Mathematics for Social Justice
4.1 Introduction
4.2 Background and Context
4.2.1 The Colegio Context
4.2.2 Introducing Nora
4.3 Methodology and Data
4.3.1 Nora’s Orientation to Mathematics Teaching and Learning
4.4 Teaching Math for Social Justice
4.4.1 Tensions in Teaching Math for Social Justice
4.5 Nora’s Tensions
4.5.1 Student Tensions: Fostering Success and Changing Orientation
4.5.2 Collegial Tensions: Changing Orientation and Mathematical Being
4.6 Implications for Teaching
4.6.1 Elicited and Eliciting Tensions
4.6.2 Preparing for Sticky Situations
References
Chapter 5: Designing Inclusive Educational Activities in Mathematics: The Case of Algebraic Proof
5.1 Introduction
5.2 Theoretical Framework
5.2.1 Multimodal Approach
5.2.2 Universal Design for Learning
5.2.3 Formative Assessment
5.2.4 Algebraic Proof
5.3 Method: A Design-Based Approach
5.4 From Theoretical Tools to Design: An Educational Sequence on Isoperimetric Rectangles
5.5 The Teaching and Learning Sequence: An Overview
5.6 Analysis
5.7 Discussion
5.8 Implications and Conclusions
References
Chapter 6: A Sustained Board Level Approach to Elementary School Teacher Mathematics Professional Development
6.1 Introduction
6.2 Professional Development (PD) Programming
6.3 Assessing Mathematics Professional Development
6.4 Provincial Context
6.5 The Professional Development Sessions
6.6 Results
6.6.1 Changes in Mathematical Achievement
6.6.2 Teacher Perceptions
6.7 Discussion
6.7.1 Success of the Professional Development Programming
6.7.2 Limitations and Next Steps
6.8 Implications for School Boards
References
Part II: Mathematical Learning
Chapter 7: A Digital Home Numeracy Practice (DHNP) Model to Understand the Digital Factors Affecting Elementary and Middle School Children’s Mathematics Practice
7.1 Introduction
7.2 Digital Home Numeracy Practice (DHNP)
7.2.1 Theoretical Underpinnings for DHNP
7.2.1.1 Cognitive-Communicative Model (CCM)
7.2.1.2 Affordance Theory
7.2.1.3 Embodied Cognition
7.2.2 Design Features of Effective Educational Media
7.2.2.1 Virtual Manipulatives
7.2.2.2 Digital Feedback
7.2.2.3 Digital Scaffolding
7.3 The DHNP Model
7.3.1 DHNP Outer Model
7.3.1.1 Home Learning Environment (HLE)
7.3.1.2 Home Numeracy Environment (HNE)
7.3.1.3 Implicit Components of the HNE: Parental Factors, Child Factors and Parent-Child Relationships
7.3.1.4 Explicit Components of the HNE
7.3.2 DHNP Inner Model
7.3.2.1 DHNP Components
7.4 How Does the Proposed DHNP Model Contribute to Middle School Mathematics Education?
7.5 Potential Avenues for Practical Implications on DHNP
7.6 Summary
References
Chapter 8: How Number Talks Assist Students in Becoming Doers of Mathematics
8.1 Introduction
8.2 Conceptual Framework
8.2.1 A Situative Perspective on Knowing and Learning
8.2.2 The Role of Mental Computation During Number Talks
8.2.3 Developing Sociomathematical Norms for Doing Mathematics
8.3 Study Context
8.4 How Did Number Talks Assist Ms. Jones’ Students in Becoming Doers of Mathematics?
8.4.1 Building Agency by Establishing Sociomathematical Norms
8.4.2 Shifting Authority Through Small Group Number Talks
8.4.3 Learning How to Share Mathematical Reasoning During Whole Group Number Talks
8.5 Discussion
8.6 Implications for Teaching and Learning
References
Chapter 9: Language Matters: Mathematical Learning and Cognition in Bilingual Children
9.1 Introduction
9.2 Biological and Cultural Evolution of Mathematical Skills
9.3 Bilingual Brains Process Information Differently
9.4 Bilingual Mathematical Development
9.5 Insights from Bilingual Mathematical Education in USA and Other Countries
9.5.1 Frequency of Language Use
9.6 Evidence-Based Recommendations
9.6.1 Allowing Code-Switching
9.6.2 Allowing Other ‘Off-loading’ Strategies
9.6.3 Strengthen Retrieval of Mathematical Facts in Both Languages
9.6.4 Incorporating Home and Cultural Contexts
9.6.5 Mathematics Instruction in the Home Language
9.6.6 Immersive Bilingual Programs or Structured Immersive Sessions
9.6.7 Feedback and Culturally Relevant Mathematics Instruction
9.6.8 Discussions About Mathematics and Culture
9.6.9 Making Connections Between Mathematics and Aspects of Children’s Lives
9.6.10 Confirmations from Non-USA Contexts
9.6.11 Need for More Innovation and Research
9.7 Conclusion
References
Chapter 10: Mathematical Creativity of Learning in 5th Grade Students
10.1 Introduction
10.2 Mathematical Creativity
10.3 Creativity Techniques
10.4 Workshop Model to Stimulate Creative Thinking in Mathematics
10.5 Application of Mathematical Creativity
10.6 Data Sources
10.7 Results and Discussion
10.8 Considerations and Implications
References
Chapter 11: Symbolic Mathematics Language Literacy: A Framework and Evidence from a Mixed Methods Analysis
11.1 Symbolic Mathematics in Curriculum
11.2 Symbolic Mathematics Language Literacy (SMaLL)
11.3 Empirical Exploration of SMaLL Variations
11.3.1 Quantitative Strand: Cognitive Evidence of SMaLL
11.3.2 Qualitative Strand: Metacognitive Evidence of SMaLL
11.3.3 Mixed Methods Integration: Multilevel Evidence of SMaLL
11.4 Discussion and Conclusions
References
Chapter 12: Grasping Patterns of Algebraic Understanding: Dynamic Technology Facilitates Learning, Research, and Teaching in Mathematics Education
12.1 Theories of Perceptual Learning and Embodied Cognition
12.2 Leveraging Perceptual and Embodied Learning Within Graspable Math
12.2.1 Perceptual Features Guide Students’ Attention to Notational Structures
12.2.2 Transforming Abstract Symbols into Objects Makes Algebra Concrete for Learners
12.2.3 Immediate Visual Feedback Informs Students’ Problem Solving
12.3 Graspable Math: A Tool to Advance Theory, Research, and Practice
12.4 Research on Mathematical Cognition and Student Learning
12.4.1 Evidence of Student Learning in Graspable Math and From Here to There!
12.4.2 Analyzing Students’ Problem-Solving Processes in Graspable Math
12.5 Implications for Research and Education
12.6 Conclusion
References
Index
