Learning to graph linear functions: A case study of conceptual change

Cognition and Instruction

Volumn 19, Issue 2, 2001, Pages 215-252

  Chiu, Ming Ming ^c   Kessel, Cathy ^a   Moschkovich, Judit ^b   Muñoz Nuñez, Agustin ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040482995     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1207/S1532690XCI1902_03     Document Type: Article

References (48)

1. Allison, P. D., & Liker, J. K. (1982). Analyzing sequential categorical data on dyadic interaction: A comment on Gottman. Psychological Bulletin, 91, 393-403.
2. Arcavi, A., & Schoenfeld, A. (1992). Mathematics tutoring through a constructivist lens: The challenges of sense-making. Journal of Mathematical Behavior, 11, 321-336.
3. Bakeman, R., & Gottman, J. M. (1986). Observing interaction: An introduction to sequential analysis. Cambridge, England: Cambridge University Press.
4. Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics, 2(1), 34-42.
5. Brophy, J. (1986). Teaching and learning mathematics: Where research should be going. Journal for Research in Mathematics Education, 17, 323-346.
6. Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in basic mathematical skills. Cognitive Science, 4, 397-426.
7. Chiu, M. M. (1996). Exploring the origins, uses, and interactions of student intuitions: Comparing the lengths of paths. Journal for Research in Mathematics Education, 27, 478-504.
8. Chiu, M. M. (2000). Group problem solving processes: Social interactions and individual actions. Journal for the Theory of Social Behavior, 30, 27-50.
9. Clement, J. (1980, April). Algebra word problem solutions: Analysis of a common misconception. Paper presented at the annual meeting of the American Educational Research Association, Boston.
10. Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13, 16-30.
11. Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of Research in Education, 16, 3-56.
12. Confrey, J. (1991). Learning to listen: A student's understanding of powers often. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 111-137). Dordrecht, The Netherlands: Kluwer.
13. Glaser, B., & Strauss, A. (1967). The discovery of grounded theory: Strategies for qualitative research. New York: Aldine de Gruyter.
14. Goldenberg, E. P. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representations of functions. Journal of Mathematical Behavior, 7, 135-173.
15. Guba, E., & Lincoln, Y. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.
16. Hawkins, D., Apelman, M., Colton, R., & Flexner, A. (1982). A report of research on critical barriers to the learning and understanding of elementary science. Washington, DC: National Science Foundation.
17. Herscovics, N. (1989). Cognitive obstacles encountered in the learning of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Vol. 4, pp. 60-86). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
18. Hewson, W. H., & Hewson, M. G. A. (1984). The role of conceptual conflict in conceptual change and the design of science instruction. Instructional Science, 13, 1-13.
19. Kamii, C., & Livingston, S. J. (1994). Young children continue to reinvent arithmetic - 3rd grade: Implications of Piaget's theory. New York: Teachers College Press.
20. Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning and teaching. Review of Educational Research, 60, 1-64.
21. Lobato, J., Moschkovich, J., Chiu, M., Kessel, C., & Muñoz, A. (1993). Persistence and transformation of a student's alternative strategy in the domain of linear functions. In J. Rossi Becker & B. Pence (Eds.), Proceedings of the 15th conference of the North American chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 184-191). San Jose, CA: SJSU Center for Mathematics and Computer Science Education.
22. Lucy, J., & Wertsch, J. (1987). Vygotsky and Whorf: A comparative analysis. In M. Hickmann (Ed.), Social and functional approaches to language and thought (pp. 67-86). Orlando, FL: Academic.
23. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
24. Magidson, S. (1992). From the laboratory to the classroom: A technology-intensive curriculum for functions and graphs. Journal of Mathematical Behavior, 11, 361-376.
25. Matz, N. (1982). Towards a process model for high school algebra errors. In D. Sleeman & J. S. Brown (Eds.), Intelligent tutoring systems (pp. 25-50). New York: Academic.
26. Moschkovich, J. N. (1992a). Making sense of linear graphs and equations: An analysis of students' conceptions and language use. Unpublished doctoral dissertation, University of California, Berkeley.
27. Moschkovich, J. N. (1992b). Students' use of the x-intercept: An instance of a transitional conception. In W. Geeslin & K. Graham (Eds.), Proceedings of the 16th annual meeting of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 128-135). Durham, NH: Program Committee of the 16th Psychology of Mathematics Education Conference.
28. Moschkovich, J. N. (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5, 239-277.
29. Moschkovich, J. N. (1998). Resources for refining conceptions: Case studies in the domain of linear functions. The Journal of the Learning Sciences, 7, 209-237.
30. Moschkovich, J. N. (1999). Students' use of the x-intercept as an instance of a transitional conception. Educational Studies in Mathematics, 37, 169-197.
31. Moschkovich, J. N., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations, and connections among them. In T. Romberg, E. Fennema, & T. Carpenter (Eds.), Integrating research on the graphical representation of function (pp. 69-99). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
32. Osborne, R., & Wittrock, M. (1983). Learning science: A generative process. Science Education, 67, 489-508.
33. Ploetzner, R., & VanLehn, K. (1997). The acquisition of qualitative physics knowledge during textbook-based physics training. Cognition and Instruction, 15, 169-205.
34. Schoenfeld, A. (1985). Mathematical problem solving. Orlando, FL: Academic.
35. Schoenfeld, A. (1990). GRAPHER: A case study of educational technology, research, and development. In M. Gardner, J. Greeno, F. Reif, A. Schoenfeld, A. diSessa, & E. Stage (Eds.), Toward a scientific practice of science education (pp. 281-300). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
36. Schoenfeld, A., Gamoran, M., Kessel, C., Leonard, M., Orbach, R., & Arcavi, A. (1992). Toward a comprehensive model of human tutoring in complex subject matter domains. Journal of Mathematical Behavior, 11, 293-319.
37. Schoenfeld, A., Smith, J., & Arcavi, A. (1993). Learning: The microgenetic analysis of one student's understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 55-175). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
38. Smith, J., diSessa, A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3, 115-163.
39. Stevens, R. (1991). Through mathematical eyes: Perceptual primitives and the evolution of noticing. Unpublished manuscript, University of California, Berkeley.
40. Stevens, R. (1992). The dawning of aspects: A descriptive analysis of one student's activity. Unpublished manuscript, University of California, Berkeley.
41. Stevens, R., & Hall, R. (1998). Disciplined perception: Learning to see in technoscience. In M. Lampert & M. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 107-150). Cambridge, England: Cambridge University Press.
42. Strike, K. A., & Posner, G. J. (1985). A conceptual change view of learning and understanding. In L. H. T. West & A. L. Pines (Eds.), Cognitive structure and conceptual change (pp. 211-231). New York: Academic.
43. Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
44. Vinner, S. (1990). Inconsistencies: Their causes and function in learning mathematics. Focus on Learning Problems in Mathematics, 12, 85-97.
45. Vygotsky, L. S. (1974). Thought and language. Cambridge, MA: MIT Press.
46. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
47. Vygotsky, L. S. (1987). Thinking and speech. In R. Rieber & A. Cartoon (Eds.), The collected works of L. S. Vygotsky (Vol. 1, pp. 39-287). New York: Plenum.
48. Walkerdine, V., & Sinha, C. (1978). The internal triangle: Language, reasoning, and the social context. In I. Markova (Ed.), The social context of language (pp. 150-176). New York: Wiley.