Metaphor Activation in Multimodal Discourse

Maciej Rosiński

Metaphor Activation in Multimodal Discourse

Case studies on the emergence of geometrical concepts

ISBN 978-83-7507-284-6
Semper Publishers, Warsaw 2019
Size B5, 202 pages, illustrations

The book examines the phenomenon of metaphor activation in the context of mathematics. Throughout the case studies it is shown how study participants, who needed to explain simple geometrical concepts, express metaphorical thought in speech, gesture and drawings, thus fully engaging their embodied minds with the problems at hand. The goal of the book is to show that metaphors in mathematics, rather than being dead, have the potential to organise the discourse of mathematics, and mathematics education. The study received an award from the Polish Cognitive Linguistics Association for the best doctoral dissertation, defended in 2018.

Maciej Rosiński is an assistant professor at the Institute of English Studies, University of Warsaw, where he researches scientific and educational discourse, focusing on figurative thought and multimodality. He also teaches courses on cognitive linguistics and discourse analysis.

Table of Contents

Acknowledgements

Transcript convention and abbreviations

0 Introduction

1 Metaphor: From conceptual mappings to the dynamics of discourse

1.1 Metaphors in everyday life and metaphors in mathematics

1.1.1 Experiential grounding of metaphors

1.1.2 Where does mathematics come from?

1.1.3 Metonymy

1.1.4 How metaphors in uence the understanding of concepts

1.2 Metaphor in multiple modalities

1.2.1 Metaphor in gesture

1.2.2 Gesture in mathematics

1.2.3 Pictorial metaphor

1.2.4 Diagrams in mathematics

1.3 Metaphor in discourse

1.3.1 Dea or alive?

1.3.2 Dynamic View and Conceptual Metaphor Theory

1.3.3 Metaphor shifts in discourse

1.3.4 Priming and on-line metaphor construction

2 The role of metaphors in mathematics

2.1 Why do you need metaphors for something you can see?

2.2 Metaphors and models

2.3 Mathematics as an embodied material practice

3 Methodology, research design and goals

3.1 Interview design

3.2 Research assumptions and goals

3.3 Multimodal metaphor analysis

3.3.1 Speech

3.3.2 Gesture

3.3.2.1 Coding gesture form

3.3.2.2 Gesture interpretation

3.3.2.3 Gesture and metaphor

3.3.3 Drawings

3.3.4 Use of instruments

4 Emergence of geometrical concepts in discourse. Case studies

4.1 Angle as a figure, angle as rotation

4.1.1 Static angles

4.1.2 Dynamic angles

4.1.3 Addition and subtraction of angles

4.1.4 Negative angles, negotiation of meaning

4.1.5 Conclusion

4.2 Angles in gesture space, angles in imagery

4.2.1 Describing through imagery

4.2.2 Constructions in gesture space

4.2.3 Rotation in imagery

4.2.4 Conclusion and insights from other case studies

4.3 Line and point symmetries

4.3.1 Folds and reflections

4.3.2 Point reflections

4.3.3 Conclusion and insights from other interviews

4.4 Symmetry: transformations and invariants

4.4.1 Invariants

4.4.2 Other transformations

4.4.3 Area as an invariant of reflection

4.4.4 Conclusion and insights from other interviews

4.5 Area calculation strategies

4.5.1 Covering surfaces with rectangle

4.5.2 Triangles

4.5.3 Other polygons

4.5.4 Closed curves

4.5.5 Conclusion and insights from other interviews

4.6 Units of measure

4.6.1 Squares as units

4.6.2 Cutting up units

4.6.3 Angle units

4.6.4 Conclusion and insights from other interviews

4.7 Supplement: Area in educational discourse

4.7.1 Counting units

4.7.2 Figures which take up space

4.7.3 Conclusion

4.8 Final remarks

5 Emergence through metaphor

References

Streszczenie (Summary in Polish)