The Body in Mathematics : Theoretical and Methodological Lenses / Laurie D. Edwards and Christina M. Krause.

Format:

Book

Author/Creator:

Edwards, Laurie D., author.

Krause, Christina M., author.

Series:

Mathematics teaching and learning ; Volume 7.

Mathematics Teaching and Learning Series ; Volume 7

Language:

English

Subjects (All):

Critical thinking.

Physical Description:

1 online resource (349 pages)

Edition:

First edition.

Place of Publication:

Leiden, The Netherlands : Koninklijke Brill BV, [2025]

Summary:

This book surveys the landscape of embodied approaches to mathematical thinking, teaching, and learning. It presents cutting edge empirical findings and brings into intellectual contact the most influential theoretical frameworks that center the role of the body in mathematics education.

Contents:

Intro

Contents

Figures and Tables

Notes on Contributors

1. Introduction

1 Introduction

2 Embodiment in Mathematics Education

3 Embodiment in Social and Cultural Context

4 Goals of the Book

5 Theoretical Perspectives

5.1 Phenomenology and Embodiment

5.2 Multimodality and Semiotics in Embodiment

5.3 Cognitive Linguistics and Embodiment

6 Structure of the Book

6.1 Nemirovsky and Brady

6.2 Radford and Alibali

6.3 Shvarts/Abrahamson and Dixon/Peterson/Vaidya

6.4 Gerofsky and Flood

6.5 Edwards and Roth

7 Discussion

Notes

References

2. Bodies, Incorporeals, and the Birth of a Mathematical Diagram

Abstract

Keywords

2 Sense and Emptiness

3 Sense and Emptiness in Mathematics

4 Projecting a Parabola in the Football Field - Three Episodes

4.1 Episode 1: That's Really What It Looks Like?

4.2 Episode 2: Projecting above the Horizon Line

Commentary

4.3 Episode 3: Encountering the Infinite

5 Discussion

Acknowledgements

3. Embodied Experimentation with Alberti's Window

2 Ontologies and Procedural Means of Achieving Shared Access

3 Embodied Experimentation

4 Gooding's Image of Embodied Experimental Practice

5 Re-Interpretation

5.1 Stage 1. How Experiences Are Stabilized in Construals of Experimental Data

5.2 Stage 2. How Inferencing Interacts with Perceiving

5.2.1 The Second Task

5.2.2 Second Phase of the Second Task

5.2.3 Third Phase of the Second Task

5.3 Stage 3. How the Dialogue between Theory and Experiment Fills in Conceptual Constructions

5.3.1 Would the Hyperbolic Projection of All Parabolas Converge or "Close" at the Horizon Line?.

5.3.2 Would the Hyperbolic Projection of All Parabolas Leave a Gap Between the Two Hyperbolic Branches?

5.3.3 What Can We Say about The Hyperbolas Created by Extreme Parabolas?

5.3.4 Summary of Stage 3

6 Discussion

7 Conclusion

4. Sensed Objects, Sensing Subjects

2 Reproducing and Expanding a Figural Sequence

3 Movement

4 Sensuous Cultural-Historical Cognition

5 Reproducing Term 4

6 The Teacher

7 Concluding Remarks

Acknowledgment

5. Action, Attention, and Multimodal Scaffolding

2 Sociocultural Framework

3 Information Processing Framework

4 Data Source

5 Analysis and Interpretation

5.1 Sociocultural Perspective: Scaffolding Nicolas's Building of Term 4

5.2 Information Processing Perspective: Encoding the Diagram and Connecting Representations

6.1 Multi-Modal Scaffolding

6.2 The Roles of Objects and Social Context in Shaping and Constraining Actions

6.3 Conclusion: The Nature of Embodiment

Note

6. Intercorporeal Functional Dynamic System

2 Theoretical Framework: Embodied Mechanisms of the Teaching/Learning Collaboration

2.1 The Functional-System and Complex-Dynamic-Systems Approaches: Coupling and Anticipation

2.2 Functional Dynamic Systems in Mathematics Learning: Action-Based Embodied Design

2.3 An Intercorporeal Functional Dynamic System: A Goal-Oriented Coupling of Two Bodies

2.3.1 Cognitive Mechanisms of Intercorporeal Coupling: Joint Action and Joint Attention

2.3.2 Coupling of Two Bodies into a Functional System

2.4 Teaching/Learning as the Development of an Intercorporeal Functional Dynamic System: Micro-Zones of Proximal Development.

2.4.1 On How the Dynamics of Intercorporeal Systems Develop

2.4.2 An Object of Joint Attention Develops

2.5 Research Questions

3 Methodology

3.1 Dual Eye-Tracking Technology

3.2 Procedure and Participants

3.3 Learning Activity

3.4 Data Analysis

4 Results and Discussion

4.1 Stage 1. An Intercorporeal System and Micro-Zone of Proximal Development: A Focus on the Student's Embodied Actions

4.1.1 Phase 1: Convergence: Establishing Intercorporeal Functional Dynamic System

4.1.2 Phase 2: Divergence: The Tutor Tunes Away to Anticipate an Innovation in the Student's Dynamics

4.1.3 Phase 3: Embodied Discovery: New Dynamic Patterns in the Student's Functional System

4.1.4 Phase 4: Micro-Zone of Proximal Development: Inviting the Student to Reflect on the Fluent Performance

4.2 Stage 2. An Intercorporeal System and Micro-Zone of Proximal Development: Focus on a Tutor's Explanations

5 Summary and Conclusion

Acknowledgments

Appendix 1: Transcription Key

7. Ecological Foundations to the Creation of New Meaning

2 Embodiment and Meaning

3 The Trouble with Novel Meaning for Traditional Approaches

4 Dissipative Structure Theory and Embodied Cognition

4.1 Dissipative Structures Primer

5 Dissipative Structures Adapt to Novel Events

6 Dissipative Structures and Meaning

7 Articulation between Leontievian and Gibsonian Approaches

8 The Classroom as a Complex, Dissipative Structure

9 Summary

8. Experiencing Mathematical Relationships at a Variety of Scales through Body Movement

2 Literature Review on the Importance of Scale in The Embodied Learning of Mathematics

2.1 Defining Small (Micro), Medium (Meso) and Large/Extra-Large (Macro) Experiential Scales.

2.2 Hall, Ma, and Nemirovsky: Walking Scale Geometry Using GPS Tracking

2.3 Tversky: Body Movement and Perception at Different Scales

2.4 Kelton and Ma: Coordination of Many Bodies at Large Scale

2.5 Empirical Studies and Exemplars: Pedagogical Design at Different Scales

3 Working Definitions of Small, Medium and Large Physical Scales

3.1 Moving Back and Forth across Physical Scales (SML) as an Element of Pedagogical Design

4 Case Studies/Examples of Experiencing Mathematical Relationships at a Variety of Scales through Body Movement

4.1 Graphs and Gestures: Gesturing a Graph with Different Qualities of Movement

4.2 Exploring Mathematical Patterns in Weaving at Small, Medium, and Large Scales

4.3 Experiencing Plain Hunt on Four (PH4) in Different Media and Scales

4.4 The Wurzelschnecke or Pythagorean Spiral

4.5 Dancing Euclidean Proofs on the Beach

4.6 Further Examples of Pedagogies That Move across Small, Medium, and Large Physical Scales

5 Qualities of Noticing in Relation to Physical Scale of Body Movement

9. Mathematical Enskilment

2 Co-Operative Action for Understanding Enskilment in Mathematical Taskscapes

2.1 Positioning the World for Perception and Action, Creating Conditions for Noticing

2.2 Attending and Responding to Embodied Action to Socially Calibrate Performance

2.3 Highlighting and Coding Multisensory Phenomena

3 Concluding Remarks

10. Modalities, Image Schemas, and Mathematical Proof

2 Theoretical Context

2.1 Embodiment

2.2 Cognitive Linguistics

2.3 Gesture Studies

2.3.1 Types of Gestures

2.4 Multimodality

2.5 Studies of Proof and Proving

2.6 Studies of Gesture, Multimodality, and Proof

3 Methods.

3.1 Participants and Procedure

3.2 The Conjecture

3.3 Methods of Analysis

3.4 Transcribing and Annotation Conventions

4 Two Students in Search of a Proof: Annotated Transcript

4.1 Summary of the Session as a Whole

4.1.1 Segment A: Sharing Existing Knowledge (00:28)

4.1.2 Segment B: Making Plausible Assertions (01:36)

4.1.3 Segment C: Adding Visual Anchors (00:56)

4.1.4 Segment D: Clarifying the Argument (01:12)

4.1.5 Segment E: Adding Written Symbols (01:08)

4.1.6 Segment F: Attempts at Formalizing (01:33)

4.1.7 Segment G: Restating and Concluding (00:31)

5 Analysis

5.1 Overview of the Modalities

5.2 Functions of the Modalities: Speech and Written Inscriptions

5.3 Functions of the Modalities: Graphic Inscriptions

5.4 Functions of the Modalities: Gesture

5.4.1 Types of Gestures

5.5 How Were the Modalities Related?

5.6 Evidence of Image-Schematic Logic

6.1 How Did the Students Utilize the Different Modalities?

6.2 How Were the Different Modalities Related to Each Other?

6.3 Was There Evidence For "Body-Based Image-Schematic Logic"?

6.4 Questions and Further Inquiry

11. Event as Minimal Unit of Analysis

1.1 Looking Back

1.2 Critiques of the Embodiment Discourse

1.3 A New Theoretical Road Taken

2 Thinking and Speaking vs. Thought and Speech

2.1 Theoretical Prolegomena

2.2 Rereading a Short Section of the Proof Session

3 Transactional, Event-Focused Approach to Collaboration

4 Moving Beyond Dichotomization

12. Discussion

2 Theoretical Frameworks

3 Themes

4 Questions and Directions for Future Inquiry

5 Final Note

Index.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references and index.

ISBN:

90-04-71770-6