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Microworlds as Representations

  • Conference paper
Computers and Exploratory Learning

Part of the book series: NATO ASI Series ((NATO ASI F,volume 146))

Abstract

This paper examines in detail the category of open-ended exploratory computer environments which have been labeled “microworlds.” One goal of the paper is to review the various ways in which the term “microworld” has been used within the mathematics and science education communities, and to analyze a number of examples of computer microworlds. Two definitions or ways of describing microworlds are proposed: a “structural” definition which focuses on design elements shared by the environments, and a “functional” definition which highlights commonalities in how students learn with microworlds. In the final section of the paper, the notion that computer microworlds, or symbol systems in general, can be said to “embody” mathematical or scientific ideas is examined within a broader consideration of ideas about representation.

It is as though, in becoming electronic, our beautiful old astrolabes, sextants, surveyor's compasses, observatories, orreries, slide rules, mechanical clocks, drawing instruments and fromwork, maps and plans—physical things all, embodiments of the purest geometry, their sole work to make us at home in space—become environments themselves, the very framework of what they once only measured. —M. Benedickt

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References

  • Abelson, H. and diSessa, A. (1981) Turtle Geometry: The Computer as a Medium for Exploring Mathematics, Cambridge, MA: MIT Press

    MATH  Google Scholar 

  • Adams, S. and diSessa, A. (1991) Learning by “cheating”: Students’ inventive ways of using a Boxer motion microworld, Journal of Mathematical Behavior, 10/1, 79–90

    Google Scholar 

  • Benedickt, M. (1991) (ed.) Cyberspace: First Steps, Cambridge, MA: MIT Press

    Google Scholar 

  • Ben-Sefer, D. (1989) Hebrew grammar explained to non-Hebrew speakers that do know Logo, in U. Leron, and N. Krumholtz (eds.) Proceedings of the Fourth International Conference for Logo and Mathematics Education, 13–24, Haifa, Israel: The Israeli Logo Centre, Technion

    Google Scholar 

  • Berger, P. and Luckman, T. (1966) The Social Construction of Reality: A Treatise in the Sociology of Knowledge, New York: Irvington Publishers, Inc.

    Google Scholar 

  • Bloor, D. (1976) Knowledge and Social Imagery, London: Routledge and Kegan Paul

    Google Scholar 

  • Cobb, P., Yakel, E, Wood, T. (1992) A constructivist alternative to the representational view of mind in mathematics education, Journal for Research in Mathematics Education, 23/1, 2–33

    Article  Google Scholar 

  • Cruickshank, D. (1993) The real science behind Jurassic Park, IRIS Universe, 25, 12–19

    Google Scholar 

  • diSessa, A. (1979) On learnable representations of knowledge:A meaning for the computational metaphor, in J. Lochhead and J. Clement (eds.) Cognitive Process Instruction: Research on Teaching Thinking Skills, 239–266, Philadelphia: The Franklin Institute Press

    Google Scholar 

  • diSessa, A. (1982) Unlearning Aristotelian physics: A study of knowledge-based learning, Cognitive Science, 6, 37–75

    Article  Google Scholar 

  • diSessa, A. (1985) A principled design for an integrated computational environment, Human-Computer Interaction, 1, 1–47

    Article  Google Scholar 

  • diSessa, A. (1986) Models of computation, in D. Norman and S. Draper (eds.) User Centered System Design: New Perspectives on Human-Computer Interaction, 201–218, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • diSessa, A. (1993) Toward an epistemology of physics, Cognition and Instruction, 10/2-3, 105–225

    Article  Google Scholar 

  • diSessa, A. (1989) Computational Media as a Foundation for New Learning Cultures, Boxer Group Technical Report-G5, Berkeley, CA; The Boxer Group

    Google Scholar 

  • diSessa, A. (1990) Social niches for future software, in A. diSessa, M. Gardner, J. Greeno, A. Schoenfeld and E. Stage (eds.) Toward a Scientific Practice of Science Education, 301–322, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • diSessa, A. and Abelson, H. (1986) Boxer: A reconstructible computational medium, Communications of the ACM, 29/9, 859–868

    Article  Google Scholar 

  • Dugdale, S. and Kibbey, D. (1990) Beyond the evident content goals: Part I, Tapping the depth and flow of the educational undercurrent, Journal of Mathematical Behavior, 9, 201–228

    Google Scholar 

  • Dugdale, S. (1981) Green Globs: A Microcomputer Application for Graphing of Equations, CERL Report E-21, Urbana, Illinois: University of Illinois

    Google Scholar 

  • Edwards, L. (1988) Children’s learning in a transformation geometry microworld, in A. Borbas (ed.) Proceedings of the XII Conference of the International Group for the Psychology of Mathematics Education, 1,263–270, Vezprem, Hungary

    Google Scholar 

  • Edwards, L. (1990) The role of microworlds in the construction of conceptual entities, in G. Booker, P. Cobb and T. de Mendicuti (eds.) Proceedings of the XIV Conference of the International Group for the Psychology of Mathematics Education, 1, 235–242, Mexico City, Mexico

    Google Scholar 

  • Edwards, L. (1991) Children’s learning in a computer microworld for transformation geometry, Journal for Research in Mathematics Education, 22/2, 122–137

    Article  Google Scholar 

  • Edwards, L. (1992a) A Logo microworld for transformation geometry, In C. Hoyles and R. Noss (eds.) Learning Logo and Mathematics, 127–155, Cambridge, MA: MIT Press

    Google Scholar 

  • Edwards, L. (1992b) A comparison of children’s learning in two interactive computer environments, Journal of Mathematical Behavior, 11/1, 73–82

    Google Scholar 

  • Edwards, L. (in press) The design and analysis of a mathematical microworld, Journal for Educational Computing Research

    Google Scholar 

  • Fey, J. (1989) Technology and mathematics education: A survey of recent developments and important problems, Educational Studies in Mathematics, 20, 237–272

    Article  Google Scholar 

  • Goldin, G. (1988) The development of a model for competence in mathematical problem solving based on systems of cognitive representation, in A. Borbas (ed.) Proceedings of the XII Conference of the International Group for the Psychology of Mathematics Education II, 358–365, Vezprem, Hungary

    Google Scholar 

  • Goldin, G. (1991) The IGPME working group on representations, in F. Furinghetti (ed.) Proceedings of the XV Conference of the International Group for the Psychology of Mathematics Education, 1, xxii, Assisi, Italy

    Google Scholar 

  • Greeno, J. (1991) Number sense as situated knowledge in a conceptual domain, Journal for Research in Mathematics Education, 22/3, 170–218

    Article  Google Scholar 

  • Groen, G. and Kieran, C. (1983) In search of Piagetian mathematics, in H. Ginsburg (ed.) The Development of Mathematical Thinking, 352–375, New York: Academic Press

    Google Scholar 

  • Hadamard, J. (1945) An Essay on the Psychology of Invention in the Mathematical Field, Princeton, NJ: Princeton University Press

    Google Scholar 

  • Harel, I. (1991) Children Designers, Norwood, NJ: Ablex

    Google Scholar 

  • Hillel, J. (1987) (ed.) Proceedings of the Third International Conference for Logo and Mathematics Education, Montreal: Department of Mathematics,Concordia University

    Google Scholar 

  • Hoyles, C. (1985) Developing a context for Logo in school mathematics, in Logo 85: Theoretical Papers, 23–42, Cambridge, MA: MIT

    Google Scholar 

  • Hoyles, C. (1993) Micro worlds/School worlds: The transformation of an innovation, in C. Keitel and K. Ruthven (eds.) Learning from Computers: Mathematics Education and Technology, 1–17, NATO ASI Series F, Vol. 121, Berlin: Springer-Verlag

    Chapter  Google Scholar 

  • Hoyles, C. and Noss, R. (1987a) Children working in a structured Logo environment: From doing to understanding, Recherches en Didactiques des Mathematiques, 8/12, 131–174

    Google Scholar 

  • Hoyles, C. and Noss, R. (1987b) Synthesizing mathematical conceptions and their formalization through the construction of a Logo-based school mathematics curriculum, Internationaljournal of Mathematics, Science and Technology, 18/4, 581–595

    Article  Google Scholar 

  • Hoyles, C. and Noss, R. (1992) A pedagogy for mathematical microworlds, Educational Studies in Mathematics, 23/1, 31–57

    Article  Google Scholar 

  • Hoyles, C. and Noss, R. (1993) Deconstructing microworlds, in D. L. Ferguson (ed.) Advanced Educational Technologies for Mathematics and Science, 415–438, NATO ASI Series F, Vol. 107, Berlin; Springer-Verlag

    Google Scholar 

  • Hutchins, E., Hollan, J. and Norman, D. (1986) Direct manipulation interfaces, in D. Norman and S. Draper (eds.) User Centered System Design: New Perspectives on Human-Computer Interaction, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Janvier, C. (1987) (ed.) Problems of Representation in the Teaching and Learning of Mathematics, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Kaput, J. (1987) Representation systems and mathematics, in C. Janvier (ed.) Problems of Representation in the Teaching and Learning of Mathematics, 19–26, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Kitcher, P. (1987) The Nature of Mathematical Knowledge, NY: Oxford University Press

    Google Scholar 

  • Lakoff, G. (1987) Women, Fire and Dangerous Things: What Categories Reveal about the Mind, Chicago: University of Chicago Press

    Google Scholar 

  • Lakoff, G. (1988) Cognitive semantics, in U. Eco, M. Santambrogio and P. Violi (eds.) Meaning and Mental Representation, 119–154, Bloomington, IN: Indianna University Press

    Google Scholar 

  • Lakoff, G. (1993) The contemporary theory of metaphor, in A. Ortony (ed.) Metaphor and Thought, 202–251, Cambridge, England: Cambridge University Press

    Chapter  Google Scholar 

  • Lakoff, G. and Johnson, M. (1980) Metaphors We Live by, Chicago: U. of Chicago Press

    Google Scholar 

  • Lave, J. and Wenger, E. (1991) Situated Learning: Legitimate Peripheral Participation, Cambridge, UK: Cambridge University Press

    Book  Google Scholar 

  • Leron, U. and Krumholtz, N. (1989) (eds.) Proceedings of the Fourth International Conference for Logo and Mathematics Education, Haifa, Israel: The Israeli Logo Centre, Technion

    Google Scholar 

  • McArthur, D. and Lewis, M. (1991) Overview of object-oriented microworlds for learning mathematics through inquiry, in L. Birnbaum (ed.) Proceedings of the International Conference on the Learning Sciences, 315–321, Charlottesville, VA: AACE

    Google Scholar 

  • Mehan, H. (1989) Microcomputers in classrooms: Educational technology or social practice? Anthropology and Education Quarterly, 20/1, 4–22

    Google Scholar 

  • Meira, L. (1991) On the transparency of material displays, paper presented at the Annual Meeting of the American Educational Research Association (April), Chicago, Illinois

    Google Scholar 

  • Noss, R. (1986) Constructing a conceptual framework for elementary algebra through Logo programming, Educational Studies in Mathematics, 17, 335–357

    Article  Google Scholar 

  • Noss, R. and Hoyles, C. (1992) Looking forward and looking back, in C. Hoyles and R. Noss (eds.) Learning Logo and Mathematics, 431–468, Cambridge, MA: MIT Press

    Google Scholar 

  • Ohlsson, S. (1987) Sense and reference in the design of interactive illustrations for rational numbers, in R. Lawler and M. Yazdani (eds.) Artificial Intelligence and Education: Volume One: Learning Environments and Tutoring Systems, 308–344, Norwood, NJ: Ablex

    Google Scholar 

  • Papert, S. (1980) Mindstorms, New York: Basic Books

    Google Scholar 

  • Papert, S. (1987) Microworlds: Transforming education, in R. Lawler and M. Yazdani (eds.) Artificial Intelligence and Education: Volume One: Learning Environments and Tutoring Systems, 79–94, Norwood, NJ: Ablex

    Google Scholar 

  • Pea, R. (1987) Integrating human and computer intelligence, in R. Pea and K. Sheingold (eds) Mirrors of Minds: Patterns of Experience in Educational Computing,128–146, Norwood, NJ: Ablex

    Google Scholar 

  • Pea, R. and Sheingold, K. (1987) (eds.) Mirrors of Minds: Patterns of Experience in Educational Computing, Norwood, NJ: Ablex

    Google Scholar 

  • Pimm, D. (1987) Speaking Mathematically, London: Routledge and Kegan Paul

    MATH  Google Scholar 

  • Pirolli, R. and Greeno, J. (1988) The problems space of instructional design, in J. Psotka, D. Massey, and S. Mutter (eds.) Intelligent Tutoring Systems: Lessons Learned, 181–201, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Pratt, D. (1991) The design of Logo microworlds, in L. Nevile (ed.) Proceedings of the Fifth international Logo and Mathematics Education Conference, 25–41, Cairns, Australia

    Google Scholar 

  • Preibisius, E. (1993) “What’s this button for?” California Mathematics Council Communicator, 17/4, 26

    Google Scholar 

  • Rauenbusch, F and Bereiter, C. (1991) Making reading more difficult: A degraded text microworld for teaching reading comprehension strategies, Cognition and Instruction, 8/2,181–206

    Article  Google Scholar 

  • Reddy, M. (1993) The conduit metaphor, in A. Ortony (ed.) Metaphor and Thought, 164–201, Cambridge, England: Cambridge University Press

    Chapter  Google Scholar 

  • Resnick, L. (1991) Shared cognition: Thinking as social practice, in L. Resnick, J. Levine and S. Teasley (eds.) Perspectives on Socially-Shared Cognition, 1–22, Washington, DC: American Psychological Association

    Chapter  Google Scholar 

  • Santambrogio, M. and Violi, P. (1988) Introduction, in U. Eco, M. Santambrogio and P. Violi (eds.) Meaning and Mental Representation, 1–22, Bloomington, IN: Indianna University Press

    Google Scholar 

  • Sherin, B., diSessa, A. and Hammer, D. (1993) Dynaturtle revisited: Learning physics via collaborative design of a computer model, Interactive Learning Environments, 3/2, 91–118

    Article  Google Scholar 

  • Shute, V and Glaser, R. (1990) A large-scale evaluation of an intelligent discovery world: Smithtown, Interactive Learning Environments, 1/1, 51–77

    Article  Google Scholar 

  • Skemp, R. (1987) The Psychology of Learning Mathematics, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Strohecker, C. (1991) Elucidating styles of thinkingabout topology through thinking about knots, in I. Harel and S. Papert (eds.) Constructionism, 215–234, Norwood, NJ: Ablex

    Google Scholar 

  • Tall, D. and Vinner, S. (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity, Educational Studies in Mathematics, 12, 151–169

    Article  Google Scholar 

  • Thompson, P. (1985) Experience, problem solving and learning mathematics: Considerations in developing mathematics curricula, in E. Silver (ed.) Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Hillsdale, NJ: Lawrence Erlbaum

    Google Scholar 

  • Thompson, P. (1987) Mathematical microworlds and intelligent computer-assisted instruction, in G. Kearsley (ed.) Artificial Intelligence and Instruction: Applications and Methods, 83–109, Reading, MA: Addison Wesley

    Google Scholar 

  • Thompson, P. (1992) Notations, conventions, and constraints: Contributions to effective uses of concrete materials in elelmentary mathematics, Journal for Research in Mathematics Education, 23/2, 123–147

    Article  Google Scholar 

  • Trowbridge, D. (May, 1989) Graphs and Tracks: An application of manipulable graphics, Academic Computing, 24–49

    Google Scholar 

  • Wenger, E. (1987) Artificial Intelligence and Tutoring Systems: Computational and Cognitive Approaches to the Communication of Knowledge, Los Altos, CA: Morgan Kaufman

    Google Scholar 

  • White, B. (1981) Designing Computer Games to Facilitate Learning, AI-TR-619, Artificial Intelligence Laboratory, MIT

    Google Scholar 

  • White, B. and Frederiksen. (1987) Qualitative models and intelligent learning environments. In R. Lawler and M. Yazdani (eds.) Artificial Intelligence and Education: Volume One: Learning Environments and Tutoring Systems, 281–305, Norwood, NJ: Ablex

    Google Scholar 

  • White, L. (1956) The locus of mathematical reality: An anthropological footnote, in J. Newman (ed.) The World of Mathematics, 4, 2348–2364, New York: Simon and Schuster

    Google Scholar 

  • Wilensky, U. (1993) Connected mathematics—Building concrete relationships with mathematical knowledge, Unpublished doctoral dissertation, MIT

    Google Scholar 

  • Vinner, S. and Dreyfus, T. (1989) Images and definitions for the concept of function, Journal for Research in Mathematics Education, 20, 356–366

    Article  Google Scholar 

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Authors and Affiliations

  1. Crown College, University of California, 95064, Santa Cruz, CA, USA

    Laurie D. Edwards

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  1. Laurie D. Edwards
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Editors and Affiliations

  1. Graduate School of Education, University of California at Berkeley, 4533 Tolman Hall, 94720-1670, Berkeley, CA, USA

    Andrea A. diSessa

  2. Department of Mathematics, Statistics and Computing, University of London, Institute of Education, 20 Bedford Way, WC1H 0AL, London, UK

    Celia Hoyles  & Richard Noss  & 

  3. Crown College, University of California at Santa Cruz, 95064, Santa Cruz, CA, USA

    Laurie D. Edwards

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Edwards, L.D. (1995). Microworlds as Representations. In: diSessa, A.A., Hoyles, C., Noss, R., Edwards, L.D. (eds) Computers and Exploratory Learning. NATO ASI Series, vol 146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57799-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-57799-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63359-1

  • Online ISBN: 978-3-642-57799-4

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