Distributed by design: On the promises and pitfalls of collaborative learning with multiple representations

Journal of the Learning Sciences

Volumn 20, Issue 3, 2011, Pages 489-547

  White, Tobin ^a   Pea, Roy ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960379928     PISSN: 10508406     EISSN: None     Source Type: Journal    
DOI: 10.1080/10508406.2010.542700     Document Type: Article

References (82)

1. Ainsworth, S. (1999). The functions of multiple representations. Computers and Education, 33, 131-152.
2. Aronson, E. (1978). The jigsaw classroom. Beverly Hills, CA: Sage.
3. Barron, B. (2003). When smart groups fail. Journal of the Learning Sciences, 12, 307-359.
4. Bazerman, C. (1996). Review of Edwin Hutchins-"Cognition in the wild." Mind, Culture and Activity, 3(1), 51-54.
5. Bereiter, C. (2002). Knowledge outside the mind. In C. Bereiter, Education and mind in the knowledge age (pp. 51-83). Mahwah, NJ: Erlbaum.
6. Brown, A., Ash, D., Rutherford, M., Nakagawa, K., Gordon, A., & Campione, J. (1993). Distributed expertise in the classroom. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations (pp. 188-228). New York, NY: Cambridge University Press.
7. Brown, A., & Campione, J. (1994). Guided discovery in a community of learners. In K.McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 229-270). Cambridge, MA: MIT Press.
8. Burrill, G. (1992). The graphing calculator: A tool for change. In J. T. Fey (Ed.), Calculators in mathematics education: 1992 yearbook (pp. 14-22). Reston, VA: National Council of Teachers of Mathematics.
9. Cleaves, W. (2008). Promoting mathematics accessibility through multiple representations jigsaws. Mathematics Teaching in the Middle School, 13, 446-452.
10. Clement, L. (2004). A model for understanding, using, and connecting representations. Teaching Children Mathematics, 11(2), 97-102.
11. Cobb, P. (1998). Learning from distributed theories of intelligence. Mind, Culture, and Activity, 5(3), 187-204.
12. Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5-43.
13. Cobb, P. (2002). Reasoning with tools and inscriptions. Journal of the Learning Sciences, 11, 187-215.
14. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
15. Cohen, E. (1994). Restructuring the classroom: Conditions for productive small groups. Review of Educational Research, 64(1), 1-35.
16. Danish, J., & Enyedy, N. (2007). Negotiated representational mediators: How young children decide what to include in their science representations. Science Education, 91(1), 1-35.
17. diSessa, A. (2004). Metarepresentation: Naïve competence and targets for instruction. Cognition and Instruction, 22(3), 293-331.
18. diSessa, A., Hammer, D., Sherin, B., & Kolpakowski, T. (1991). Inventing graphing: Metarepresentational expertise in children. Journal of Mathematical Behavior, 10(2), 117-160.
19. Enyedy, N. (2003). Knowledge construction and collective practice: At the intersection of learning, talk, and social configurations in a computer-mediated mathematics classroom. Journal of the Learning Sciences, 12, 361-407.
20. Enyedy, N. (2005). Inventing mapping: Creating cultural forms to solve collective problems. Cognition and Instruction, 23, 427-466.
21. Fey, J. (1989). Technology andmathematics education: A survey of recent developments and important problems. Educational Studies in Mathematics, 20, 237-272.
22. Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. Cuoco & F. Curcio (Eds.), The roles of representation in school mathematics (pp. 1-23). Reston, VA: National Council of Teachers of Mathematics.
23. Goldman, S., Pea, R., & Maldonado, H. (2004). Emerging social engineering in the wireless classroom. In Y. Kafai, W. Sandoval, N. Enyedy, A. S. Nixon, & F. Herrera (Eds.), Embracing diversity in the learning sciences: Proceedings of the Sixth International Conference of the Learning Sciences (pp. 222-230). Mahwah, NJ: Erlbaum.
24. Goldman, S., Pea, R., Maldonado, H., Martin, L., & White, T. (2004). Functioning in the wireless classroom. In J. Roschelle, T.-W. Chan, Kinshuk, & S. J. H. Yang (Eds.), Proceedings of the Third IEEE International Workshop on Wireless and Mobile Technologies in Education (pp. 75-82). New York, NY: IEEE Press.
25. Goodwin, C. (1994). Professional vision. American Anthropologist, 96, 606-633.
26. Greeno, J., & Hall, R. (1997). Practicing representation: Learning with and about representational forms. Phi Delta Kappan, 78, 361-367.
27. Greeno, J. G., McDermott, R., Cole, K., Engle, R. A., Goldman, S., Knudsen, J., ... Linde, C. (1999). Research, reform, and aims in education: Modes of action in search of each other. In E. Lagemann & L. Shulman (Eds.), Issues in education research: Problems and possibilities (pp. 299-335). San Francisco, CA: Jossey-Bass.
28. Hall, R. (1996). Representation as shared activity: Situated cognition and Dewey's cartography of experience. Journal of the Learning Sciences, 5, 209-238.
29. Hall, R., Stevens, R., & Torralba, T. (2002). Disrupting representational infrastructure in conversations across disciplines. Mind, Culture and Activity, 9(3), 179-210.
30. Hanson, N. R. (1958). Patterns of discovery: An inquiry into the conceptual foundations of science. Cambridge, England: Cambridge University Press.
31. Herbel-Eisenmann, B. (2002). Using student contributions and multiple representations to develop mathematical language. Mathematics Teaching in the Middle School, 8(2), 100-105.
32. Hutchins, E. (1993). Learning to navigate. In S. Chaiklin & J. Lave (Eds.), Understanding practice: Perspectives on activity and context (pp. 35-63). New York, NY: Cambridge University Press.
33. Hutchins, E. (1995). Cognition in the wild. Cambridge, MA: MIT Press.
34. Izsák, A. (2003). "We want a statement that is always true": Criteria for good algebraic representations and the development of modeling knowledge. Journal for Research in Mathematics Education, 34(3), 191-227.
35. Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167-194). Reston, VA: National Council of Teachers of Mathematics.
36. Kaput, J. J. (1992). Technology and mathematics education. In D. Grouws (Ed.), A handbook of research on mathematics teaching and learning (pp. 515-556). New York, NY: Macmillan.
37. Kaput, J. J. (1993). The urgent need for proleptic research in the graphical representation of quantitative relationships. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Integrating research in the graphical representation of functions (pp. 279-311). Hillsdale, NJ: Erlbaum.
38. Kaput, J. J. (1995). Creating cybernetic and psychological ramps from the concrete to the abstract: Examples from multiplicative structures. In D. N. Perkins & J. L. Schwartz (Eds.), Software goes to school: Teaching for understanding with new technologies (pp. 130-154). London, England: Oxford University Press.
39. Kaput, J. J. (1998). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows. Journal of Mathematical Behavior, 17(2), 265-281.
40. Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
41. Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra teaching and learning. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 99-152). Boston, MA: Kluwer.
42. Larkin, J., & Simon, H. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65-99.
43. Latour, B. (1990). Drawing things together. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice (pp. 123-152). Cambridge, MA: MIT Press.
44. Latour, B., & Woolgar, S. (1986). Laboratory life: The construction of scientific facts. Princeton, NJ: Princeton University Press.
45. Lee, V., & Sherin, B. (2006). Beyond transparency: How students make representations meaningful. In S. Barab, K. Hay, & D. Hickey (Eds.), Proceedings of the 7th International Conference of the Learning Sciences (pp. 397-403). Mahwah, NJ: Erlbaum.
46. Leinhardt, G., Zaslavsky, O., & Stein, M. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1-64.
47. Lemke, J. L. (2000). Across the scales of time: Artifacts, activities, and meanings in ecosocial systems. Mind, Culture, and Activity, 7(4), 273-290.
48. Lesser, L. (2000). Reunion of broken parts: Experiencing diversity in algebra. Mathematics Teacher, 93(1), 62-67.
49. Meira, L. (1995). The microevolution of mathematical representations in children's activity. Cognition and Instruction, 13, 269-313.
50. Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29(2), 121-142.
51. Moschkovich, J., 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 functions (pp. 69-100). Hillsdale, NJ: Erlbaum.
52. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
53. National Research Council. (2000). How people learn: Brain, mind, experience, and school (Expanded ed.). Washington, DC: National Academies Press.
54. Parnafes, O., & DiSessa, A. (2004). Relations between types of reasoning and computational representations. International Journal of Computers for Mathematical Learning, 9, 251-280.
55. Pea, R. D. (1987). Cognitive technologies for mathematics education. In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 89-122). Hillsdale, NJ: Erlbaum.
56. Pea, R. D. (1992). Augmenting the discourse of learning with computer-based learning environments. In E. de Corte, M. Linn, & L. Verschaffel (Eds.), Computer-based learning environments and problem-solving (NATO Series, Subseries F: Computer and System Sciences, pp. 313-343). New York, NY: Springer-Verlag.
57. Pea, R. D. (1993). Practices of distributed intelligence and designs for education. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations (pp. 47-87). New York, NY: Cambridge University Press.
58. Pea, R. D. (1994). Seeing what we build together: Distributed multimedia learning environments for transformative communications. Journal of the Learning Sciences, 3, 285-299.
59. Peirce, C. S., Hartshorne, C., Weiss, P., & Burks, A. (1935). Collected papers of Charles Sanders Peirce: Volumes 1-6. Cambridge, MA: Harvard University Press.
60. Rider, R. (2007). Shifting from traditional to nontraditional teaching practices using multiple representations. Mathematics Teacher, 100, 494-500.
61. Roschelle, J. (1992). Learning by collaborating: Convergent conceptual change. Journal of the Learning Sciences, 2, 235-276.
62. Roschelle, J. (1996). Designing for cognitive communication: Epistemic fidelity or mediating collaborating inquiry. In D. L. Day & D. K. Kovacs (Eds.), Computers, communication and mental models (pp. 13-25). London, England: Taylor & Francis.
63. Roschelle, J., Pea, R., Hoadley, C., Gordin, D., & Means, B. (2000). Changing how and what children learn in school with computer-based technologies. The Future of Children: Children and Computer Technology, 10(2), 76-101.
64. Roth, W., & McGinn, M. (1998). Inscriptions: Toward a theory of representing as social practice. Review of Educational Research, 68(1), 35-59.
65. Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1993). Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 55-175). Hillsdale, NJ: Erlbaum.
66. Schwartz, D., & Martin, T. (2006). Distributed learning and mutual adaptation. Pragmatics and Cognition, 14, 313-332.
67. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press.
68. Sherin, B. (2000). How students invent representations of motion: A genetic account. Journal of Mathematical Behavior, 19, 399-441.
69. Stahl, G. (2006). Group cognition: Computer support for building collaborative knowledge. Cambridge, MA: MIT Press.
70. Stevens, R., & Hall, R. (1998). Disciplined perception: Learning to see in technoscience. In M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 107-149). New York, NY: Cambridge University Press.
71. Thompson, P. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education, 1 (Issues in Mathematics Education Vol. 4, pp. 21-44). Providence, RI: American Mathematical Society.
72. Thompson, P., & Sfard, A. (1994). Problems of reification: Representations and mathematical objects. In D. Kirshner (Ed.), Proceedings of the annual meeting of the International Group for the Psychology of Mathematics Education-North America, plenary sessions (Vol. 1, pp. 1-32). Baton Rouge: Louisiana State University.
73. Tripathi, P. (2008). Developing mathematical understanding through multiple representations. Mathematics Teaching in the Middle School, 13, 438-445.
74. White, T. (2005). Deciphering students' developing conceptions of functions in a collaborative computing environment. In G. M. Lloyd, M.Wilson, J. L. M.Wilkins, & S. L. Behm (Eds.), Proceedings of the 27th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education, 13, 149-156. Roanoke: Virginia Tech.
75. White, T. (2006). Code talk: Student discourse and participation with networked handhelds. International Journal of Computer-Supported Collaborative Learning, 1, 359-382.
76. White, T. (2008). Debugging an artifact, instrumenting a bug: Dialectics of instrumentation and design in technology-rich learning environments. International Journal of Computers for Mathematical Learning, 13(1), 1-26.
77. White, T. (2009). Encrypted objects and decryption processes: Problem-solving with functions in a learning environment based on cryptography. Educational Studies in Mathematics, 72(1), 17-37.
78. Woolgar, S. (1990). Time and documents in researcher interaction: Some ways of making out what is happening in experimental science. In M. Lynch & S. Woolgar (Eds.), Representation in scientific practice (pp. 123-152). Cambridge, MA: MIT Press.
79. Yerushalmy, M. (1991). Student perceptions of aspects of algebraic function using multiple representation software. Journal of Computer Assisted Learning, 7, 42-57.
80. Yerushalmy, M. (2006). Slower algebra students meet faster tools: Solving algebra word problems with graphing software. Journal for Research in Mathematics Education, 37, 356-387.
81. Yerushalmy, M., & Shternberg, B. (2001). Charting a visual course to the concept of function. In A. Cuoco & F. Curcio (Eds.), The roles of representation in school mathematics (pp. 251-268). Reston, VA: National Council of Teachers of Mathematics.
82. Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive Science, 18(1), 87-122.