Making a circle: Tool use and the spaces where we live

Cognition and Instruction

Volumn 24, Issue 4, 2006, Pages 387-437

  Noble, Tracy ^a   DiMattia, Cara ^a   Nemirovsky, Ricardo ^a   Barros, Apolinario ^b  

^a TERC   (United States)

^b Boston Public Schools ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845349265     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1207/s1532690xci2404_1     Document Type: Article

References (29)

1. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245-274.
2. Chassapis, D. (1999). The mediation of tools in the development of formal mathematical concepts: The compass and the circle as an example. Educational Studies in Mathematics, 37, 275-293.
3. Cobb, P., & Bauersfeld, H. (1995). Introduction: The coordination of psychological and sociological perspectives in mathematics education. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 1-24). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
4. Confrey, J., & Smith, E. (1991, October). A framework for functions: Prototypes, multiple representations, and transformations. Paper presented at the 13th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education, Blacksburg, VA.
5. Ginsburg, H. P. (1997). Entering the child's mind: The clinical interview in psychological research and practice. New York: Cambridge University Press.
6. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195-227.
7. Heidegger, M. (1962). Being and time (J. Macquarrie & E. Robinson, Trans.). New York: Harper & Row. (Original published in 1927)
8. Hutchins, E. (1995). Cognition in the wild. Cambridge, MA: MIT Press.
9. Iriki, A., Tanaka, M., & Iwamura, Y. (1996). Coding of modified body schema during tool use by macaque postcentral neurones. Cognitive Neuroscience and Neuropsychology NeuroReport, 7(14), 2325-2330.
10. Jordan, B., & Henderson, A. (1995). Interaction analysis: Foundations and practice. Journal of the Learning Sciences, 4(1), 39-103.
11. Kaput, J. J. (1998). Representations, inscriptions, descriptions of learning: A kaleidoscope of windows. Journal of Mathematical Behavior, 17(2), 265-281.
12. Keller, C. M., & Keller, J. D. (1996). Cognition and tool use: The blacksmith at work. Cambridge, England: Cambridge University Press.
13. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, England: Cambridge University Press.
14. Mariotti, M. A. (2002). The influence of technological advances on students' mathematics learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 695-723). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
15. Moustakas, C. (1994). Phenomenological research methods. Thousand Oaks, CA: Sage.
16. Nemirovsky, R., DiMattia, C., Ribiero, B., & Lara-Meloy, T. (2005). Talking about teaching episodes. Journal of Mathematics Teacher Education, 8(5), 363-392.
17. Nemirovsky, R., & Noble, T. (1997). Mathematical visualization and the place where we live. Educational Studies of Mathematics, 33(2), 99-131.
18. Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and graphing. Cognition and Instruction, 16(2), 119-172.
19. Noble, T., Nemirovsky, R., DiMattia, C., & Wright, T. (2004). Learning to see: Making sense of the mathematics of change in middle school. International Journal of Computers for Mathematical Learning, 9(2), 109-167.
20. Noss, R., Healy, L., & Hoyles, C. (1997). The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics, 33(2), 203-233.
21. Packer, M. J., & 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.
22. Pozzi, S., Noss, R., & Hoyles, C. (1998). Tools in practice, mathematics in use. Educational Studies in Mathematics, 36, 105-122.
23. Presmeg, N. (1986). Visualisation in high school mathematics. For the Learning of Mathematics, 6, 42-46.
24. Rogoff, B., Paradise, R., Arauz, R. M., Correa-Chávez, M., & Angelillo, C. (2003). Firsthand learning through intent participation. Annual Review of Psychology, 54, 175-203.
25. Sacks, H., Schegloff, E. A., & Jefferson, G. (1974). A simplest systematics for the organization of turn-taking for conversation. Language, 50(4), 696-731.
26. Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77-101.
27. Yamamoto, S., & Kitazawa, S. (2001). Sensation at the tips of invisible tools. Nature Neuroscience, 4(10), 979-980.
28. Yerushalmy, M., & Chazan, D. (1990). Overcoming visual obstacles with the aid of the Supposer. Educational Studies in Mathematics, 21, 199-219.
29. Zazkis, E., Dubinsky, E., & Dautermann, J. (1996). Coordinating visual and analytic strategies: A study of students' understandings of the group D4. Journal for Research in Mathematics Education, 27(4), 435-457.