Gestures and conceptual integration in mathematical talk

Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately.

[1]  Susan Goldin-Meadow,et al.  From children's hands to adults' ears: gesture's role in the learning process. , 2003, Developmental psychology.

[2]  L. Radford,et al.  The Seen, the Spoken, and the Written: A Semiotic Approach to the Problem of Objectification of Mathematical Knowledge. , 2002 .

[3]  E. Hutchins.  Material anchors for conceptual blends , 2005 .

[4]  G. Lakoff,et al.  Where mathematics comes from : how the embodied mind brings mathematics into being , 2002 .

[5]  Lyn D. English,et al.  Mathematical reasoning : analogies, metaphors, and images , 1997 .

[6]  Marina Basu.  The Embodied Mind: Cognitive Science and Human Experience , 2004 .

[7]  David Lee.  Cognitive Linguistics: An Introduction , 2001 .

[8]  S. Goldin-Meadow,et al.  What the teacher's hands tell the student's mind about math. , 1999 .

[9]  M. Alibali,et al.  Gesture and the process of speech production: We think, therefore we gesture , 2000 .

[10]  S. Kita.  Pointing: Where language, culture, and cognition meet , 2003 .

[11]  Ornella Robutti,et al.  Motion, Technology, Gestures in Interpreting Graphs , 2006 .

[12]  Susan Goldin-Meadow,et al.  Transitional knowledge in the acquisition of concepts , 1988 .

[13]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[14]  S. Goldin-Meadow,et al.  The mismatch between gesture and speech as an index of transitional knowledge , 1986, Cognition.

[15]  Ricardo Nemirovsky,et al.  Body Motion and Graphing , 1998 .

[16]  Eve Sweetser,et al.  What we mean by meaning: Conceptual integration in gesture analysis and transcription , 2005 .

[17]  Michele Cerulli,et al.  Calculators, Graphs, Gestures and the Production of Meaning. , 2003 .

[18]  Luciana Bazzini,et al.  From Grounding Metaphors to Technological Devices: A Call for Legitimacy in School Mathematics , 2001 .

[19]  Norma C. Presmeg,et al.  Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics , 1992 .

[20]  R. Núñez,et al.  Embodied cognition as grounding for situatedness and context in mathematics education , 1999 .

[21]  David Pimm.  Metaphor and Analogy in Mathematics. , 1981 .

[22]  D. McNeill.  Hand and Mind: What Gestures Reveal about Thought , 1992 .

[23]  Reuben Hersh,et al.  18 Unconventional Essays on the Nature of Mathematics , 2013 .

[24]  Nancy K. Mack,et al.  Learning Fractions with Understanding: Building upon Informal Knowledge. , 1988 .

[25]  Richard Lesh,et al.  Rational number, ratio and proportion , 1992 .

[26]  D. McNeill.  Gesture and Thought , 2005 .

[27]  Sotaro Kita,et al.  How representational gestures help speaking , 2000 .

[28]  Ferdinando Arzarello,et al.  Semiosis as a multimodal process , 2006 .

[29]  G. Fauconnier,et al.  The Way We Think: Conceptual Blending and the Mind''s Hidden Complexities. Basic Books , 2002 .

[30]  A. Sfard.  On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin , 1991 .

[31]  D. McNeill.  Language and Gesture: Gesture in action , 2000 .

[32]  Valerie Walkerdine,et al.  The Mastery of Reason , 1988 .

[33]  Laurie D. Edwards.  A natural history of mathematical gesture , 2003 .

[34]  T. Graham,et al.  The role of gesture in children's learning to count. , 1999, Journal of experimental child psychology.

[35]  M. Alibali,et al.  The function of gesture in learning to count: more than keeping track * , 1999 .

[36]  Rafael Núñez,et al.  Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics , 2003, Embodied Artificial Intelligence.

[37]  Norma Presmeg,et al.  Semiotics and the “Connections” Standard: Significance of Semiotics for Teachers of Mathematics , 2006 .

[38]  Robert A. Reeve,et al.  Gesture in collaborative mathematics problem-solving , 2001 .

[39]  L. Radford.  Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization , 2003 .