When the Classroom Floor Becomes the Complex Plane: Addition and Multiplication as Ways of Bodily Navigation

REFERENCES

• Alibali , M. W. and DiRusso , A. A. 1999 . The function of gesture in learning to count: More than keeping track . Cognitive Development , 14 : 37 – 56 .
   Web of Science ®Google Scholar
• Alibali , M. W. and Goldin-Meadow , S. 1993 . Gesture-speech mismatch and mechanisms of learning: What the hands reveal about a child's state of mind . Cognitive Psychology , 25 : 468 – 523 .
   PubMed Web of Science ®Google Scholar
• Alibali , M. W. and Nathan , M. J. 2007 . “ Teachers' gestures as a means of scaffolding students' understanding: Evidence from an early algebra lesson ” . In Video research in the learning sciences , Edited by: Goldman , R. , Pea , R. , Barron , B. and Derry , S. J. 349 – 365 . Mahwah , NJ : Erlbaum .
   Google Scholar
• Bakhtin , M. M. 1981 . The dialogic imagination: Four essays , Austin : University of Texas Press .
   Google Scholar
• Berti , A. and Frassinetti , F. 2000 . When far becomes near: Remapping of space by tool use . Journal of Cognitive Neuroscience , 12 : 415 – 420 .
   PubMed Web of Science ®Google Scholar
• Cobb , P. 2000 . “ Conducting teaching experiments in collaboration with teachers ” . In New methodologies in mathematics and science education , Edited by: Lesh , R. and Kelly , E. 307 – 333 . Mahwah , NJ : Erlbaum .
   Google Scholar
• Erickson , F. 1996 . “ Ethnographic mycroanalysis ” . In Sociolinguistics and language teaching , Edited by: Berger , N. H. and McKay , S. 283 – 306 . Cambridge , England : Cambridge University Press .
   Google Scholar
• Erickson , F. 2004 . Talk and social theory , Cambridge , England : Polity Press .
   Google Scholar
• Farne , A. , Bonifazi , S. and Ladavas , E. 2005 . The role played by tool-use and tool-length on the plastic elongation of peri-hand space: A single case study . Cognitive Neuropsychology , 22 : 408 – 418 .
   PubMed Web of Science ®Google Scholar
• Gallese , V. and Lakoff , G. 2005 . The brain's concepts: The role of the sensory-motor system in conceptual knowledge . Cognitive Neuropsychology , 22 : 455 – 479 .
   PubMed Web of Science ®Google Scholar
• Gibson , J. J. 1966 . The senses considered as perceptual systems , Westport , CT : Greenwood Press .
   Google Scholar
• Gibson , J. J. 1986 . The ecological approach to visual perception , Hillsdale , NJ : Erlbaum .
   Google Scholar
• Goodale , M. A. , Jakobson , L. S. and Keillor , J. M. 1994 . Differences in the visual control of pantomimed and natural grasping movements . Neuropsychologia , 32 : 1159 – 1178 .
   PubMed Web of Science ®Google Scholar
• Goodwin , C. 2000 . Action and embodiment within situated human interaction . Journal of Pragmatics , 32 : 1489 – 1522 .
   Web of Science ®Google Scholar
• Goodwin , C. 2003 . “ The semiotic body in its environment ” . In Discourses of the body , Edited by: Coupland , J. and Gwyn , R. 19 – 42 . New York , NY : Palgrave/Macmillan .
   Google Scholar
• Hall , R. and Stevens , R. 1995 . “ Making space: A comparison of mathematical work in school and professional design practices ” . In The cultures of computing , Edited by: Star , S. L. 118 – 145 . Oxford , England : Blackwell .
   Google Scholar
• Husserl , E. 1983 . Ideas pertaining to a pure phenomenology and to a phenomenological philosophy: First book , Hingham , MA : Martinus Nijhoff . (Original work published 1913)
   Google Scholar
• Johnson-Frey , S. 2003 . What's so special about human tool use? . Neuron , 39 ( 2 ) : 201 – 204 .
   PubMed Web of Science ®Google Scholar
• Klatzky , R. L. 1998 . “ Allocentric and egocentric spatial representations: Definitions, distinctions, and interconnections ” . In Spatial cognition—An interdisciplinary approach to representation and processing of spatial knowledge , Edited by: Freksa , C. , Habel , C. and Wender , K. F. 1 – 17 . Berlin , Germany : Springer-Verlag .
   Google Scholar
• Lakoff , G. and Núñez , R. E. 1997 . “ The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics ” . In Mathematical reasoning: Analogies, metaphors, and images , Edited by: English , L. D. 21 – 89 . Mahwah , NJ : Erlbaum .
   Google Scholar
• Lakoff , G. and Núñez , R. E. 2000 . Where mathematics comes from: How the embodied mind brings mathematics into being , New York , NY : Basic Books .
   Google Scholar
• Levine , J. 1983 . Materialism and qualia: The explanatory gap . Pacific Philosophical Quarterly , 64 : 354 – 361 .
   Web of Science ®Google Scholar
• Moll , J. , de Oliveira Souza , R. , Passman , L. J. , Cunha , F. C. , Souza Lima , F. and Andreiuolo , P. A. 2000 . Functional MRI correlates of real and imagined tool-use pantomimes . Neurology , 54 : 1331 – 1336 .
   PubMed Web of Science ®Google Scholar
• Myers , N. 2008 . Molecular embodiments and the body-work of modeling in protein crystallography . Social Studies of Science , 38 ( 2 ) : 163 – 199 .
   Web of Science ®Google Scholar
• Nagel , T. 1974 . What is it like to be a bat? . The Philosophical Review , 83 : 435 – 450 .
   Web of Science ®Google Scholar
• Nemirovsky , R. and Ferrara , F. 2009 . Mathematical imagination and embodied cognition . Educational Studies of Mathematics , 70 ( 2 ) : 159 – 174 .
   Web of Science ®Google Scholar
• Noë , A. 2006 . Action in perception , Cambridge , MA : MIT Press .
   Google Scholar
• Penrose , R. 2004 . The road to reality , New York , NY : Alfred Knopf .
   Google Scholar
• Petitot , J. , Varela , F. , Pachoud , B. and Roy , J.-M. 1999 . Naturalizing phenomenology: Issues in contemporary phenomenology and cognitive science , Stanford , CA : Stanford University Press .
   Google Scholar
• Poincaré , H. 1952 . Science and hypothesis , New York , NY : Dover .
   Google Scholar
• Radford , L. 2003 . Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization . Mathematical Thinking and Learning , 5 ( 1 ) : 37 – 70 .
   Google Scholar
• Radford , L. 2009 . Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings . Educational Studies of Mathematics , 70 : 111 – 126 .
   Web of Science ®Google Scholar
• Radford , L. 2010 . The eye as a theoretician: Seeing structures in generalizing activities . For the Learning of Mathematics , 30 ( 2 ) : 2 – 7 .
   Google Scholar
• Rasmussen , C. and Conner , E. February 2009 . Prospective secondary school teachers' understandings of complex number , February , Orlando , FL : Paper presented at the Thirteenth Annual Conference of the Association of Mathematics Teacher Educators .
   Google Scholar
• Roth , W.-M. , Bowen , G. M. and Masciotra , D. 2002 . From thing to sign and ‘natural object’: Toward a genetic phenomenology of graph interpretation . Science, Technology, & Human Values , 27 : 327 – 356 .
   Web of Science ®Google Scholar
• Roth , W.-M. and Welzel , M. 2001 . From activity to gestures and scientific language . Journal of Research in Science Teaching , 38 ( 1 ) : 103 – 136 .
   Web of Science ®Google Scholar
• Sfard , A. 1991 . On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin . Educational Studies in Mathematics , 22 ( 1 ) : 1 – 36 .
   Google Scholar
• Smith , D. and McIntyre , R. 1982 . Husserl and intentionality , London , England : D. Reidel .
   Google Scholar
• Stivers , T. and Sidnell , J. 2005 . Multimodal interaction . Semiotica , 156 ( 1/4 ) : 1 – 20 .
   Web of Science ®Google Scholar
• Streeck , J. and Mehus , S. 2005 . “ Microethnography: The study of practices ” . In Handbook of language and social interaction , Edited by: Fitch , K. L. and Sanders , R. E. 381 – 404 . Mahwah , NJ : Erlbaum .
   Google Scholar
• Tall , D. 2004 . Introducing three worlds of mathematics . For the Learning of Mathematics , 23 ( 3 ) : 29 – 33 .
   Google Scholar