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Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics [chapter]

Rafael Núñez
18 Unconventional Essays on the Nature of Mathematics  
The main goal of this pi ece is to show, using techniques in cognitive science such as cognitive semantics and gestures studies, that concepts and human abstraction in general (as it is exemplified in  ...  In this chapter, while fully endorsing an embodied oriented approach to cognition, I will address the question of the nature of mathematics itself, that is, mathematics not as an application to some area  ...  New York: Springer-Verlag (in press) Conclusion We can now go back to the original question asked in the title of this chapter: Do real numbers really move?  ... 
doi:10.1007/0-387-29831-2_9 fatcat:esmhplscwbgpbmwr36a5fiq66y

Action's Influence on Thought: The Case of Gesture

Susan Goldin-Meadow, Sian L. Beilock
2010 Perspectives on Psychological Science  
Gesture thus has the potential to serve as a unique bridge between action and abstract thought.  ...  We then show that the action features in gesture do not just reflect the gesturer's thinking--they can feed back and alter that thinking.  ...  Acknowledgments This study was supported by National Institute of Child Health and Human Development Grant R01 HD47450 and National Science Foundation Award BCS-0925595 (to Susan Goldin-Meadow) and National  ... 
doi:10.1177/1745691610388764 pmid:21572548 pmcid:PMC3093190 fatcat:jslcs3prdvhd3hnrwutjsh3tre

Using space to talk and gesture about numbers: Evidence from the TV News Archive

2014 Gesture  
The results of our analysis show that gestures reveal the metaphorical and spatial nature of numerical thinking.  ...  This points to the flexibility of how metaphors can become expressed in gesture, and how domains such as number and quantity can be conceptualized through multiple compatible source domains.  ...  Journal of the Learning Sciences, 21 (2), 287–323. DOI: 10.1080/10508406.2011.611445 Núñez, Rafael E. (2004). Do real numbers really move?  ... 
doi:10.1075/gest.13.3.06win fatcat:wqz5d2ubxjbuljz2k2no7anbk4

Embodiment in Mathematics Teaching and Learning: Evidence From Learners' and Teachers' Gestures

Martha W. Alibali, Mitchell J. Nathan
2012 The Journal of the Learning Sciences  
R305H060097 from the Institute of Education Sciences and by Grant No. DRL-0816406 from the National Science Foundation.  ...  We would like to thank Matthew Wolfgram, Breckie Church, and Eric Knuth for their contributions to this line of research.  ...  Representational Gestures Manifest Simulations of Action and Perception A number of contemporary theorists have argued that simulated action is the basis of many cognitive processes, including language  ... 
doi:10.1080/10508406.2011.611446 fatcat:fhwk6hsmxjeu5lpq2nsjd3m4a4

Gesture, sign, and language: The coming of age of sign language and gesture studies

Susan Goldin-Meadow, Diane Brentari
2015 Behavioral and Brain Sciences  
The goal of this review is to elucidate the relationships among sign language, gesture, and spoken language.  ...  How does sign language compare with gesture, on the one hand, and spoken language on the other? Sign was once viewed as nothing more than a system of pictorial gestures without linguistic structure.  ...  However, we do not have a foundation for the acquisition of gesture that is as extensive as what we know about the acquisition of spoken or signed language.  ... 
doi:10.1017/s0140525x15001247 pmid:26434499 pmcid:PMC4821822 fatcat:c6gugoyrrna67ak2xhy34ycx5a

Mathematical Thinking Process of Autistic Students in Terms of Representational Gesture

Sriyanti Mustafa, Toto Nusantara, Subanji Subanji, Santi Irawati
2016 International Education Studies  
<p class="apa">The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach.  ...  Results of this study describes the process of mathematical thinking in terms of a gesture of students with autism in three categories, namely correctly processed, partially processed, and contradictory  ...  Do Real Numbers Really Move? Language, Thinking, and Gesture: The Embodied Cognitive Foundations of Mathematics.  ... 
doi:10.5539/ies.v9n6p93 fatcat:cr4uba3nrvdq3ptj6fhkd5l44u

Enabling the blind to see gestures

Francis Quek, Francisco Oliveira
2013 ACM Transactions on Computer-Human Interaction  
Mathematics instruction and discourse typically involve two modes of communication: speech and graphical presentation.  ...  We want to make the SBVI aware of the deictic gestures performed by the teacher over the graphic in conjunction with speech.  ...  Language, gesture and thought In this section, we will show the deep connection between language, gesture and thought.  ... 
doi:10.1145/2442106.2442110 fatcat:ndikoihz2rclrfx5ryoab7gaaq

Diagrams, gestures and formulae in music

Guerino Mazzola, Moreno Andreatta
2007 Journal of Mathematics and Music - Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance  
Acknowledgements We would like to thank Yves André and the anonymous reviewers for their accurate reading of the manuscript and their precious suggestions concerning a better presentation of the topic.  ...  Category theory is more than a useful universal language, eventually providing the theoretical setting for the foundations of mathematics.  ...  Such a number represents the tangent of length t at the point m of the affine line A over the reals.  ... 
doi:10.1080/17459730601137716 fatcat:bgegmcq6wbg4fa5ckqmplx4lae

Diagrams, gestures and formulae in music

Guerino Mazzola, Moreno Andreatta
2007 Journal of Mathematics and Music - Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance  
Acknowledgements We would like to thank Yves André and the anonymous reviewers for their accurate reading of the manuscript and their precious suggestions concerning a better presentation of the topic.  ...  Category theory is more than a useful universal language, eventually providing the theoretical setting for the foundations of mathematics.  ...  Such a number represents the tangent of length t at the point m of the affine line A over the reals.  ... 
doi:10.1080/17459730701774269 fatcat:jptcolfronee3nxbzg6xnxevoe

Moving Ahead With Human-Machine Communication

Leopoldina Fortunati, Autumn Edwards
2021 Human-Machine Communication  
As a collection, these articles move forward the HMC project by touching on four layers of important discourse: (1) updates to theoretical frameworks and paradigms, including Computers as Social Actors  ...  In this essay, we introduce the 10 articles comprising Volume 2 (2021) of Human-Machine Communication, each of which is innovative and offers a substantial contribution to the field of human-machine communication  ...  These creative forms are at the base, he continues, of language and mathematics, the majority of cultural practices and artifacts, and cultural learning.  ... 
doi:10.30658/hmc.2.1 fatcat:uqgiroaaovhvpeuznwzkwc2jva

How Meaning Moves: Tan Sitong on Borrowing across Cultures

Leigh K. Jenco
2012 Philosophy East & West  
Rather it gestures toward the mutual co-appearance of each and therefore implies a relationship of dynamic adjustment and change.  ...  or "the real thing."  ... 
doi:10.1353/pew.2012.0007 fatcat:tj3tckveo5fihg3a5fasf7lpdq

Communicative Musicality or Stories of Truth and Beauty in the Sound of Moving

Colwyn Trevarthen
2015 Signata - Annals of Semiotics  
of thought, and receptiveness to beauty and humane feeling.  ...  presence of other embodied lives moving with corresponding principles of control (Trevarthen, 2015) .  ... 
doi:10.4000/signata.1075 fatcat:xpgyutvflbetpfrvhroq53zvye

Representational disfluency in algebra: evidence from student gestures and speech

Kristen N. Bieda, Mitchell J. Nathan
2009 ZDM: Mathematics Education  
Understanding the causes and varieties of representational fluency and disfluency contributes directly to our understanding of mathematics knowledge, learning and adaptive forms of reasoning.  ...  These findings also provide implications for mathematics instruction and assessment.  ...  Educational Research Initiative, an alliance of the National Science Foundation, the US Department of Education's Institute of Educational Sciences, and the National Institute of Child Health and Human  ... 
doi:10.1007/s11858-009-0198-0 fatcat:h2w6g7kcsnfknejp7a3tjlflca

Support of mathematical thinking through embodied cognition: Nondigital and digital approaches

Cathy Tran, Brandon Smith, Martin Buschkuehl
2017 Cognitive Research  
Our paper introduces the embodied cognition research in the context of manipulatives, hand gestures, and whole-body movement so that educators and scientists can leverage that foundational knowledge to  ...  Much of this work has been rooted in the use of manipulatives, gestures, and body movements.  ...  Acknowledgements The authors would like to thank Susanne Jaeggi for her helpful comments on an earlier version of this manuscript.  ... 
doi:10.1186/s41235-017-0053-8 pmid:28280771 pmcid:PMC5321706 fatcat:6wwi6onblbebhadj2kxndyjj2y

Doing science by waving hands: Talk, symbiotic gesture, and interaction with digital content as resources in student inquiry

Bor Gregorcic, Gorazd Planinsic, Eugenia Etkina
2017 Physical Review Physics Education Research  
They juxtaposed talk with gestures and resources in the environment to communicate ideas that they initially were not able to express using words alone.  ...  In this paper, we investigate some of the ways in which students, when given the opportunity and an appropriate learning environment, spontaneously engage in collaborative inquiry.  ...  ACKNOWLEDGMENTS The authors acknowledge financial support from the Swedish Research Council (Project No. 2016-04113) and the Slovenian Research Agency (research core funding No. P1-0060).  ... 
doi:10.1103/physrevphyseducres.13.020104 fatcat:xm6xsvh3urbijmt6p56y2y2qoa
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