Learning to see: Making sense of the mathematics of change in middle school

International Journal of Computers for Mathematical Learning

Volumn 9, Issue 2, 2004, Pages 109-167

  Noble, Tracy ^a   Nemirovsky, Ricardo ^a   Dimattia, Cara ^a   Wright, Tracey ^a  

^a TERC   (United States)

Author keywords

Case study; Graphs; Mathematics of change; Middle school; Visual representations

Indexed keywords

COMPUTER AIDED INSTRUCTION; COMPUTER MONITORS; COMPUTER SOFTWARE; GRAPH THEORY; MATHEMATICAL TECHNIQUES;

CASE STUDIES; MIDDLE SCHOOL; VISUAL REPRESENTATIONS;

EDUCATION;

EID: 4444363091     PISSN: 13823892     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:IJCO.0000040891.50250.7e     Document Type: Article

References (48)

1. Battista, M.T. (1999). The importance of spatial structuring in geometric reasoning. Teaching Children Mathematics 6(3): 170-177.
2. Bishop, A. (1989). Review of research on visualization in mathematics education. Focus on Learning Problems in Mathematics 11(1): 7-16.
3. Casey, E.S. (1987). Remembering, A phenomenological study. Bloomington and India-napolis, IN: Indiana University Press.
4. Chun, M.M. and Nakayama, K. (2000). On the functional role of implicit visual memory for the adaptive deployment of attention across scenes. Visual Cognition 7(1-3): 65-81.
5. Clements, D., Nemirovsky, R. and Sarama, J. (1995). Trips©. California: Dale Seymour Publications.
6. Cobb, P. and Bauersfeld, H. (1995). Introduction: The coordination of psychological and sociological perspectives in mathematics education. In P. Cobb and H. Bauersfeld (Eds), The Emergence of Mathematical Meaning: Interaction in Classroom Cultures. Hillsdale, NJ: Lawrence Erlbaum.
7. Confrey, J. (1991). Function Probe (Version 2.3.9). Santa Barbara, Ca: Intellimation.
8. Crawford, A.R. and Scott, W.E. (2000). Making sense of slope. The Mathematics Teacher, 93(2): 114-118.
9. DeLaura. (1996). Baby Math Worlds. North Dartmouth: SimCalc Project.
10. Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. Proceedings of the fifteenth Annual Conference of the International Group for the Psychology of Mathematics Education (Assisi), vol. 1, 32-48.
11. Gibson, J.J. (1972). A theory of direct visual perception. In J.R. Royce and W.W. Rozenboom (Eds), The Psychology of Knowing. New York: Gordon & Breach
12. Goodwin, C. (1994). Professional Vision. American Anthropologist 96(3): 606-633.
13. Goodwin, C. (1997). The Blackness of Black: Color Categories as Situated Practice. In L. B. Resnick, R. Saljo, C. Pontecorvo and B. Burge (Eds), Discourse, Tools, and Reasoning: Essays on Situated Cognition (NATO Asi Series. Series F, Computer and Systems Sciences, Vol 160), Berlin: Springer-Verlag.
14. Goody, J. (1977). The Domestication of the Savage Mind. Cambridge, UK: Cambridge University Press.
15. Healy, L. and Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers? Mathematical Thinking and Learning 1(1): 59-84.
16. Horgan, J. (1993). The death of proof. Scientific American (October) 92-103.
17. Intraub, H. (1997). The representation of visual scenes. Trends in Cognitive Sciences 1(6): 217-221.
18. Jastrow, J. (1900). Fact and Fable in Psychology. Boston: Houghton-Mifflin.
19. Jordan, B. and Henderson, A. (1995). Interaction Analysis: Foundations and Practice. The Journal of the Learning Sciences 4(1): 39-103.
20. Kaput, J.J. (1994). Democratizing access to calculus: New routes to old roots. In A. Schoenfeld (Ed.), Mathematical Thinking and Problem Solving (pp. 77-156). Hills-dale, NJ: Erlbaum.
21. Kaput, J.J. (1997), SimCalc MathWorlds. North Dartmouth, MA: SimCalc Project.
22. Kelly, J.A. (1999). Improving problem solving through drawings. Teaching Children Mathematics 6(1): 48-51.
23. Kohler, W. (1947/1975), Gestalt Psychology. New York: Liveright.
24. Marton, F. and Booth, S. (1997), Learning and Awareness. Mahwah, NJ: Lawrence Erlbaum.
25. Nemirovsky, R., & Tierney, C. (2001). Children creating ways to represent changing situations: On the development of homogeneous spaces. Educational Studies in Mathematics 45: 67-102.
26. Nemirovsky, R., Tierney, C. and Wright, T. (1998). Body Motion and Graphing. Cognition and Instruction 16(2): 119-172.
27. Noble, T., Nemirovsky, R., Wright, T. and Tierney, C. (2001). Experiencing change: The mathematics of change in multiple environments. Journal for Research in Mathematics Education 32(1): 85-108.
28. Noss, R., Healy, L. and Hoyles, C. (1997). The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics 33(2): 203-233.
29. Packer, M.J. and Mergendoller, J.R. (1989). The development of practical social understanding in elementary school-age children. In L.T. Winegar (Ed), Social Interaction and the Development of Children's Understanding (pp. 67-94). Norwood, NJ: Ablex.
30. Piaget, J. (1946/1970). The Child's Conception of Movement and Speed (G. E. T. Holloway & M. J. Mackenzie, Trans.), New York: Basic Books.
31. Poincaré, H. (1905/1952). Science and Hypothesis. New York, NY; Dover Publications.
32. Presmeg, N. (1986). Visualisation in high school mathematics. For the Learning of Mathematics 6(42-46).
33. Presmeg, N. (1989). Visualization in multicultural mathematics classrooms. Focus on Learning Problems in Mathematics 11(1): 17-24.
34. Presmeg, N. (1992). Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics. Educational Studies in Mathematics 23: 595-610.
35. Rival, I. (1987), Picture Puzzling: Mathematicians are rediscovering the power of pictorial reasoning. The Sciences, 27: 41-46.
36. Saljo, R. and Bergqvist, K. (1997). Seeing the Light: Discourse and Practice in the Optics Lab. In L. Resnick, R. Saljo, C. Pontecorvo and B. Burge (Eds), Discourse, Tools, and Reasoning: Essays on Situated Cognition (NATO Asi Series. Series F, Computer and Systems Sciences, Vol 160). Berlin: Springer-Verlag.
37. Schwartz, J.L. and Yerushalmy, M. (1988). The Geometric Supposer. Pleasantville, NY: Sunburst Communications.
38. Simons, D.J. and Levin, D.T. (1997). Change blindness. Trends in Cognitive Science, 1(7): 261-267.
39. Stevens, R. and Hall, R. (1998). Disciplined perception: Learning to see in technoscience. In M. Lampert and M.L. Blunk (Eds), Talking Mathematics in School: Studies of Teaching and Learning. Cambridge, UK: Cambridge University Press.
40. Stroup, W. (1997). Function-Based Algebra: Classroom Activities and Materials. Unpublished manuscript.
41. Stroup, W. (2002). Understanding qualitative calculus: A structural synthesis of learning research. International Journal of Computers for Mathematical Learning 7: 167-215.
42. Weiskrantz, L. (1997). Consciousness Lost and Found. Oxford, U.K. Oxford University Press.
43. Wittgenstein. (1953/1997). Philosophical Investigations (G. E. M. Anscombe, Trans.). Malden, MA: Blackwell.
44. Yarbus, A.L. (1967). Eye Movements and Vision. New York: Plenum.
45. Yerushalmy, M. and Chazan, D. (1990). Overcoming Visual Obstacles with the Aid of the Supposer. Educational Studies in Mathematics 21: 199-219.
46. Yerushalmy, M. and Shternberg, B. (in press). Epistemological and Cognitive Aspects of Time: A Tool Perspective, In R. Nemirovsky and D. Carraher (Eds), Journal for Research in Mathematics Education Monograph CD-Rom Special Issue: National Council of Teachers of Mathematics.
47. Zeki, S. (1999). Inner Vision: A Exploration of Art and the Brain. Oxford, UK: Oxford University Press.
48. Zimmerman, W. and Cunningham, S. (1991). Editor's introduction: What is Mathematical Visualization, In W. Zimmerman and S. Cunningham (Eds), Visualization in Teaching and Learning Mathematics (pp. 1-8): Mathematical Association of America.