## Avoid ambiguity! (If you can) (2006)

### BibTeX

@MISC{Marghetis06avoidambiguity!,

author = {Tyler Marghetis and Rafael Núñez and Jamie Alexandre and Rachel I. Mayberry and Pamela Witcher and Eileen R. Cardillo and Kim Plunkett and Jennifer Aydelott and Victor S. Ferreira},

title = {Avoid ambiguity! (If you can)},

year = {2006}

}

### OpenURL

### Abstract

Evidence from co-speech gesture during mathematical proving

### Citations

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The contemporary theory of metaphor
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Citation Context ...ts are created and understood via a number of fundamental cognitive processes that extend the inferential structure of our bodily experiences. These processes include conceptual metaphor and metonymy =-=[16]-=-, conceptual blending [4], and fictive motion [30]. Using the tools of Cognitive Linguistics, Lakoff and Núñez [17] argued that even mathematical concepts rely on these cognitive processes. While the ... |

111 |
Visible Action as Utterance
- Kendon
- 2004
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Citation Context ... environmentally coupled gestures elaborate meaning and direct local practices. How are we to understand the various ways in which participants used gesture to represent mathematical concepts? Kendon =-=[13]-=- distinguishes three varieties of gestural representation: enactment, depiction, and modeling. In enactment, the motor action is meant to reproduce some features of the activity being represented. For... |

102 |
Flowing waters or teeming crowds: Mental models of electricity
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Citation Context ...describe electricity, for instance, as “water running through a pipe,” effectively mapping intuitions about water volume and pressure onto the more abstract concepts of electrical current and voltage =-=[6]-=-. The use of this pedagogical scaffold, however, does not imply that electrical current is in reality the flow of water particles. Certainly, the expert physicist may call on such metaphors while inst... |

60 |
Action and embodiment within sit- uated human interaction
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Citation Context ...mentation of local mathematical practices — the study of mathematics has ignored the rich meaning-making practices of flesh-and-blood mathematicians, and collapsed multi-agent and multimodal practice =-=[11]-=- into a single idealized agent working within a single written modality. In order to account for the exceptional traits of mathematics — objectivity, necessity, precision, stability – we must remember... |

26 |
Constructing meaning from space, gesture and speech
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(Show Context)
Citation Context ...tice involves collaboration at a blackboard [28, 7], such gestures are referentially ambiguous, anchored either to the inscription itself or to the mathematical entity represented by that inscription =-=[12]-=-. By restricting our attention to representational gestures, we avoided this complication. Future research will explore the ways in which environmentally coupled gestures elaborate meaning and direct ... |

26 | On metaphoric representation
- Murphy
- 1996
(Show Context)
Citation Context ...often object that metaphorical expressions in mathematical discourse may be “dead metaphors,” expressions that once reflected underlying psychological processes but that are now entirely conventional =-=[20, 21]-=-. Certainly, mathematical co-speech gesture exhibits particular signs of conventionalization. In the two examples of gestures co-produced with the lexical affiliate increasing, both participants exhib... |

25 |
Embodied cognition as grounding for situatedness and context
- Nuñéz, Edwards, et al.
- 1999
(Show Context)
Citation Context ...thought, however, is incredibly robust. Mathematical discourse is rife with fictive motion in the absence of diagrams altogether, as demonstrated by corpus studies of purely formal analysis textbooks =-=[25, 24]-=-. In Example 2 above, the participant produces a dynamic gesture after writing a series of static inequalities; the blackboard is covered with static notations, with not a diagram in sight, and yet hi... |

23 |
Illuminating mental representation through speech and gesture
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- 1999
(Show Context)
Citation Context ... with abstract thinking, gestures parallel the metaphorical mappings exhibited linguistically [19, 2, 26], and give us insight into the representation of mathematical concepts and solution strategies =-=[1, 5]-=-. In particular, Núñez [21, 22] demonstrated that mathematicians’ gestures in pedagogical contexts supply converging evidence for the metaphorical and embodied nature of mathematical concepts. Previou... |

19 | Explaining math: Gesturing lightens the load
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(Show Context)
Citation Context ...on requires the deployment of quantitative methods. Goldin-Meadow and her associates have successfully employed statistical methods, but these studies have been limited to simple arithmetic reasoning =-=[1, 7, 10, 9]-=-. Contrary to the results of the present study, they concluded that gestures have propositional mental representations. However, they elicited gesture during the explanation of a simple arithmetic tas... |

18 |
What the teacher’s hands tell the student’s mind about math
- Goldin-Meadow, Kim, et al.
- 1999
(Show Context)
Citation Context ...e, that is, motor action co-produced with speech and thought in real time. Gesture is universal, unconscious, and essential to communication. Most importantly, gesture offers a “window into the mind” =-=[8]-=-. When co-produced with abstract thinking, gestures parallel the metaphorical mappings exhibited linguistically [19, 2, 26], and give us insight into the representation of mathematical concepts and so... |

16 |
With the future behind them: convergent evidence from Aymara language and gesture in the crosslinguistic comparison of spatial construals of time
- Núñez, Sweetser
- 2006
(Show Context)
Citation Context ...ssential to communication. Most importantly, gesture offers a “window into the mind” [8]. When co-produced with abstract thinking, gestures parallel the metaphorical mappings exhibited linguistically =-=[19, 2, 26]-=-, and give us insight into the representation of mathematical concepts and solution strategies [1, 5]. In particular, Núñez [21, 22] demonstrated that mathematicians’ gestures in pedagogical contexts ... |

14 |
The Way We Think, Basic Books
- Fauconnier, Turner
- 2003
(Show Context)
Citation Context ...ood via a number of fundamental cognitive processes that extend the inferential structure of our bodily experiences. These processes include conceptual metaphor and metonymy [16], conceptual blending =-=[4]-=-, and fictive motion [30]. Using the tools of Cognitive Linguistics, Lakoff and Núñez [17] argued that even mathematical concepts rely on these cognitive processes. While the details of the various co... |

12 |
What did Weierstrass really define? The cognitive structure of natural and e–d continuity
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- 1998
(Show Context)
Citation Context ...heir proof or the 40 minutes had passed, the participants explained their proof to the experimenter. The entire session was videorecorded. 3 Coding Based on previous research in Cognitive Linguistics =-=[30, 25, 21]-=-, we generated a list of lexical items thought to elicit fictive motion or metaphorical construals. These included mathematical terms (e.g. function, continuity, limit, contain), verbs of motion (e.g.... |

10 |
Metaphoric gestures and some of their relations to verbal metaphoric expressions
- Cienki
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(Show Context)
Citation Context ...ssential to communication. Most importantly, gesture offers a “window into the mind” [8]. When co-produced with abstract thinking, gestures parallel the metaphorical mappings exhibited linguistically =-=[19, 2, 26]-=-, and give us insight into the representation of mathematical concepts and solution strategies [1, 5]. In particular, Núñez [21, 22] demonstrated that mathematicians’ gestures in pedagogical contexts ... |

10 |
How our hands help us learn
- Goldin-Meadow, Wagner
- 2005
(Show Context)
Citation Context ...on requires the deployment of quantitative methods. Goldin-Meadow and her associates have successfully employed statistical methods, but these studies have been limited to simple arithmetic reasoning =-=[1, 7, 10, 9]-=-. Contrary to the results of the present study, they concluded that gestures have propositional mental representations. However, they elicited gesture during the explanation of a simple arithmetic tas... |

9 |
Gesture offers insight into problem-solving in adults and children
- Garber, Goldin-Meadow
- 2002
(Show Context)
Citation Context ... with abstract thinking, gestures parallel the metaphorical mappings exhibited linguistically [19, 2, 26], and give us insight into the representation of mathematical concepts and solution strategies =-=[1, 5]-=-. In particular, Núñez [21, 22] demonstrated that mathematicians’ gestures in pedagogical contexts supply converging evidence for the metaphorical and embodied nature of mathematical concepts. Previou... |

8 |
Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics
- Núñez
- 2006
(Show Context)
Citation Context ...r the embodiment of mathematics has been drawn largely from mathematical language, using techniques in Cognitive Linguistics, although recent research has included some qualitative studies of gesture =-=[21]-=-. This paper reports on the results of an ongoing research project on the nature of mathematical proof. In particular, we focus on the co-speech gesture produced by graduate mathematics students while... |

5 | Gesturing gives children new ideas about math
- Goldin-Meadow, Cook, et al.
- 2009
(Show Context)
Citation Context ...on requires the deployment of quantitative methods. Goldin-Meadow and her associates have successfully employed statistical methods, but these studies have been limited to simple arithmetic reasoning =-=[1, 7, 10, 9]-=-. Contrary to the results of the present study, they concluded that gestures have propositional mental representations. However, they elicited gesture during the explanation of a simple arithmetic tas... |

4 |
Mental movements without magnitude? A study of spatial biases in symbolic arithmetic
- Pinhas, Fischer
- 2008
(Show Context)
Citation Context ...tive mechanisms of conceptual blending and metaphor [23], and a similar conceptual association between number and space has been shown to have cognitive reality in the context of arithmetic reasoning =-=[18, 27, 15]-=-. This shows that even a near-universal construal requires individual cognitive elaboration and has measurable implications for reasoning. Furthermore, as we saw above, the phrase “to the left” was tr... |

2 |
Dehaene S, Dehaene-Lambertz G. Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception and Psychophyics
- McCrink
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Citation Context ...tive mechanisms of conceptual blending and metaphor [23], and a similar conceptual association between number and space has been shown to have cognitive reality in the context of arithmetic reasoning =-=[18, 27, 15]-=-. This shows that even a near-universal construal requires individual cognitive elaboration and has measurable implications for reasoning. Furthermore, as we saw above, the phrase “to the left” was tr... |

2 |
No innate number line in the human brain
- Núñez
- 2011
(Show Context)
Citation Context ..., and the first frame of Example 4, in which the handshape stamps out a region “to the left,” are both depictions of numerical intervals that exploit the metaphorical mapping between number and space =-=[23]-=-. In modeling, the gesturing body part stands in for another object, as when a fist represents a stone. Both specimens of dynamic gesture above, Examples 1 and 2, involve the modelling of a mathematic... |

2 |
Gesture and beyond. Unpublished manuscript
- Smith
- 2003
(Show Context)
Citation Context ... the diagram a bit higher on the blackboard”). While deictic gestures are undeniably an important part of mathematical practice, particularly when that practice involves collaboration at a blackboard =-=[28, 7]-=-, such gestures are referentially ambiguous, anchored either to the inscription itself or to the mathematical entity represented by that inscription [12]. By restricting our attention to representatio... |

1 |
Gestures and conceptual integration
- Edwards
- 2009
(Show Context)
Citation Context ...lem solving. In these settings, gestures were found to be dynamic — in line with the predictions of Cognitive Linguistics, and suggesting that mathematical concepts are metaphorical in those settings =-=[22, 3]-=-. But would we expect any other behavior? It is standard pedagogical practice to use “real world” examples of abstract concepts, to ground the abstruse in the everyday. Physics teachers might describe... |

1 | Some reflections on the relationship between ’gesture’ and ’sign”, Gesture - Kendon - 2008 |

1 |
Stanislas Dehaene, ‘Recruitment of an area involved in eye movements during mental arithmetic
- Knops, Thirion, et al.
- 2009
(Show Context)
Citation Context ...tive mechanisms of conceptual blending and metaphor [23], and a similar conceptual association between number and space has been shown to have cognitive reality in the context of arithmetic reasoning =-=[18, 27, 15]-=-. This shows that even a near-universal construal requires individual cognitive elaboration and has measurable implications for reasoning. Furthermore, as we saw above, the phrase “to the left” was tr... |

1 |
the ultimate challenge to embodiment: Truth and the grounding of axiomatic systems
- Núñez, ‘Mathematics
- 2008
(Show Context)
Citation Context ...ures parallel the metaphorical mappings exhibited linguistically [19, 2, 26], and give us insight into the representation of mathematical concepts and solution strategies [1, 5]. In particular, Núñez =-=[21, 22]-=- demonstrated that mathematicians’ gestures in pedagogical contexts supply converging evidence for the metaphorical and embodied nature of mathematical concepts. Previous research on mathematical gest... |

1 |
Conceptual resources for constructing the concepts of electricity: the role of models, analogies and imagination
- Taber, Trafford, et al.
- 2006
(Show Context)
Citation Context ... learning of physics — one story goes — is marked by the gradual abandonment of these metaphorical construals, replacing such didactic scaffolds with genuine intuitions about basic physical phenomena =-=[29]-=-. Thus, while the evidence for dynamic gesture in mathematical pedagogy and communication is suggestive, it does not directly address the nature of mathematical practice — or of mathematics itself. In... |

1 |
Towards a Cognitive Semantics, volume 1, chapter 3: How Language Structures Space
- Talmy
- 2000
(Show Context)
Citation Context ...amental cognitive processes that extend the inferential structure of our bodily experiences. These processes include conceptual metaphor and metonymy [16], conceptual blending [4], and fictive motion =-=[30]-=-. Using the tools of Cognitive Linguistics, Lakoff and Núñez [17] argued that even mathematical concepts rely on these cognitive processes. While the details of the various construals underlying mathe... |