Drawing space: Mathematicians' kinetic conceptions of eigenvectors

Educational Studies in Mathematics

Volumn 74, Issue 3, 2010, Pages 223-240

  Sinclair, Nathalie ^a   Tabaghi, Shiva Gol ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Conceptual mathematics; Diagram; Gesture; Language; Linear algebra; Metaphor; Motion; Time

Indexed keywords

EID: 77953719504     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-010-9235-8     Document Type: Article

References (36)

1. Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics (translated by Pimm D.). In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216-235). London: Hodder and Stoughton.
2. Burton, L. (2004). Mathematicians as enquirers: Learning about learning mathematics. Dordrecht: Kluwer.
3. Châtelet, G. (1993). Les enjeux du mobile. Paris: Seuil [English translation by R. Shore & M. Zagha: Figuring space: Philosophy, mathematics and physics, Dordrecht: Kluwer, 2000].
4. Courant, R., & Robbins, H. (1978). What is mathematics? New York: Oxford University Press.
5. Goldin-Meadow, S. (2003). Gesture: How our hands help us think. Cambridge: Harvard University Press.
6. Harris, M. (2008). Why mathematics? You might ask. In T. Gowers, J. Barrow-Green, & I. Leader (Eds.), The Princeton companion to mathematics. Princeton: Princeton University Press.
7. Hawkins, T. (1975). Cauchy and the spectral theory of matrices. Historia Mathematica, 2, 1-29.
8. Healy, L. (2009). Relationships between sensory activity, cultural artefacts and mathematical cognition. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education. Thessaloniki: PME.
9. Keller, H. (1969). The story of my life. New York: Collier-Macmillan.
10. Lakoff, G., & Núñez, R. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. New York: Basic Books.
11. Lay, D. C. (2006). Linear algebra and its application. USA: Pearson Addison Wesley.
12. Mancosu, P. (1996). Philosophy of mathematics and mathematical practice in the seventeenth century. NewYork: Oxford University Press.
13. Nemirovsky, R., & Borba, M. (2003). Perceptuo-motor activity and imagination in mathematics learning. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, 1 (pp. 103-135). Manoa: University of Hawaii.
14. Netz, R. (2009). Ludic mathematics: Greek mathematics and the Alexandrian aesthetic. Cambridge: Cambridge University Press.
15. Núñez, R. (2006). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. In R. Hersh (Ed.), 18 Unconventional essays on the nature of mathematics (pp. 160-181). New York: Springer.
16. Ochs, E., Gonzales, P., & Jacobyet, S. (1996). When I come down I'm in the domain state: Grammar and graphic representation in the interpretive activity of physicists. In E. Ochs, E. A. Schegloff, & S. A. Thompson (Eds.), Interaction and grammar (pp. 328-369). Cambridge: Cambridge University Press.
17. Palmieri, P. (2009). Superposition: On Cavalieri's practice of mathematics. Archive for History of Exact Sciences, 63, 471-495.
18. Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. New York: Basic Books.
19. Pimm, D. (2006). Drawing on the image in mathematics and art. In N. Sinclair, D. Pimm, & W. Higginson (Eds.), Mathematics and the aesthetic: New approaches to an ancient affinity (pp. 160-189). New York: Springer.
20. Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
21. Radford, L. (2009). No! He starts walking backward!: Interpreting motion graphs and the question of space, place and distance. ZDM the International Journal on Mathematics Education, 41, 467-480.
22. Robutti, O. (2006). Motion, technology, gesture in interpreting graphs. The International Journal for Technology in Mathematics Education, 13(30), 117-126.
23. Rotman, B. (2008). Becoming beside ourselves: The alphabet, ghosts, and distributed human beings. Durham: Duke University Press.
24. Russell, B. (1903). The principles of mathematics. Cambridge: Cambridge University Press.
25. Schiralli, M., & Sinclair, N. (2003). A constructive response to where mathematics comes from. Educational Studies in Mathematics, 52(1), 79-91.
26. Seitz, J. A. (2000). The bodily basis of thought. New Ideas in Psychology, 18, 23-40.
27. Seitz, J. A. (2005). The neural, evolutionary, developmental, and bodily basis of metaphor. New Ideas in Psychology, 23, 74-95.
28. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.
29. Sfard, A. (2009). What's all the fuss about gestures? A commentary. Educational Studies in Mathematics, 70(2), 191-200.
30. Sinclair, N. (2010). Knowing more than we can tell. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers, advances in mathematics education (pp. 591-608). New York: Springer.
31. Sinclair, N., Healy, L., & Sales, C. O. R. (2009). Time for telling stories: Narrative thinking with dynamic geometry. ZDM, 41, 441-452.
32. Solomon, Y., & O'Neill, J. (1998). Mathematics and narrative. Language and Education, 12(3), 210-221.
33. Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.
34. Talmy, L. (1996). Fictive motion in language and caption. In P. Bloom, M. Peterson, L. Nadel, & M. Garrett (Eds.), Language and space (pp. 212-273). Cambridge: MIT Press.
35. Thurston, W. P. (1994). On proof and progress in mathematics. The American Mathematical Society, 30(2), 161-177.
36. Wright, T. (2001). Karen in motion: The role of physical enactment in developing an understanding of distance, time, and speed. Journal of Mathematical Behavior, 20, 145-162.