ZDM

, Volume 42, Issue 1, pp 63–76 | Cite as

Charting the microworld territory over time: design and construction in mathematics education

Original Article

Abstract

The study discusses the development of theoretical ideas and constructs related to digital microworlds within the mathematics education community and their implications for interpretations of mathematics learning. Starting from Papert’s introduction of the concept during ICME 2 in 1972, we trace the evolution of theoretical approaches concerning the essence of the idea in an attempt to situate the notion of constructionism in the light of contemporary frameworks. We argue that microworlds, and the search for a learnable mathematics, have a continued relevance to mathematics education, but that the lens research attention has shifted over time, with the current foci on communal design, situated and embodied approaches and artefacts whose use crosses boundaries between different practices. To illustrate these shifts and the challenges that still remain, we present examples from our current work involving the use of microworlds for learning and teaching through communication, design and construction.

Keywords

Microworlds Communal design Body and ego synonicity Boundary objects 

Notes

Acknowledgments and projects

We would like to thank Guilherme Rodrigues Margalhães, Maisa Aparecida Sigueira Rodrigues, Elen Graciele Martins, Franklin Rodrigues de Souza and Amarilis Reto Ferreira for their ongoing contributions to the design of the musiCALcolorida microworld and FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for their financial support in this endeavour (grant nos. 2004/15109-9 and 2005/60655-4). Our thanks are also due to Costis Kontogiannis, Vassilis Tsitsos, Stassini Frangou, Nikoleta Yiannoutsou and the Psychico College students for their engagement with the Juggler microworld. We acknowledge too the support received in relation to the research projects reported in the paper, ‘ReMath’—Representing Mathematics with Digital Media FP6, IST-4, STREP 026751 (2005–2008) and “SEED”: “Seeding cultural change in the school system through the generation of communities engaged in integrated educational and technological innovation”, European Community, IST, School of Tomorrow, IST-2000-25214. (2001–2004).

References

  1. Agalianos, A. S. (1997). A cultural studies analysis of logo in education, unpublished doctoral thesis, Institute of Education, Policy Studies and Mathematical Sciences, London.Google Scholar
  2. 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. doi:10.1023/A:1022103903080.CrossRefGoogle Scholar
  3. Arzarello, F., & Robutti, O. (2004). Approaching functions through motion experiments (video paper). Educational sudies in mathematics PME special issue (Vol. 57(3)). Berlin: Springer.Google Scholar
  4. Blikstein, P., & Cavallo, D. (2002). Technology as a Trojan Horse in school environments: The emergence of the learning atmosphere (II). In M. Auer & A. Auer (Eds.), Proceedings of the interactive computer aided learning international workshop (pp. 1–22). Villach: Carinthia Technology Institute.Google Scholar
  5. Bottino, R. M., & Kynigos, C. (2009) Mathematics education & digital technologies: Facing the challenge of networking European research teams. International Journal of Computers for Mathematical Learning (in press). Google Scholar
  6. Clements, D., & Sarama, J. (1997). Research on logo: A decade of progress. Computers in the Schools, 14(1–2), 9–46. doi:10.1300/J025v14n01_02.CrossRefGoogle Scholar
  7. diSessa, A. (1997). Open toolsets: New ends and new means in learning mathematics and science with computers. In E. Pehkonen (Ed.), Proceedings of the 21st conference of the international group for the psychology of mathematics education, 1 (Vol. 2, pp. 47–62). Lahti, Finland.Google Scholar
  8. diSessa, A. (2000). Changing minds, computers, learning and literacy. Cambridge: MIT Press.Google Scholar
  9. Drijvers, P., Kieran, C., & Mariotti, M. A. (in press). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J. B. Lagrange (Eds.), Digital technologies and mathematics education: Rethinking the terrain. Berlin: Springer.Google Scholar
  10. Drijvers, P., & Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In K. Heid & G. Blume (Eds.), Research on technology and the teaching and learning of mathematics (Vol. 2, pp. 363–392). Charlotte: Information Age.Google Scholar
  11. Edwards, L. D. (1995). Microworlds as representations. In A. diSessa, C. Hoyles, & R. Noss (Eds.), Computers and exploratory learning (pp. 127–154). Berlin: Springer.Google Scholar
  12. Fuglestad, A.-B., Healy, L., Kynigos, C., & Monaghan, J. (in press). Working with teachers: Context and culture. In C. Hoyles & J. B. Lagrange (Eds.), Digital technologies and mathematics education: Rethinking the terrain. Berlin: Springer.Google Scholar
  13. Guin, D., Ruthven, K., & Trouche, L. (2004). The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument. New York: Springer.Google Scholar
  14. Healy, L. (2006a). Constructing simulations to express developing statistical knowledge. In A. Ross, & B. Chance (Eds) Proceedings of the 7th international conference for the teaching of statistics (ICOTS7), Salvador, Brazil. http://www.stat.auckland.ac.nz/~iase/publications/17/7G1_HEAL.pdf. Accessed 24 Oct 2008.
  15. Healy, L. (2006b). A developing agenda for research into digital technologies and mathematics education: A view from Brazil. In L. H. Son, N. Sinclair, J. B. Lagrange, & C. Hoyles (Eds.), Proceedings of the ICMI 17 study conference: Background papers for the ICMI-17 study (pp. 213–220). Hanoi University of Technology, Hanoi, Vietnam.Google Scholar
  16. Healy, L. (2008). Topic Study Group 15: Technology and mathematics education. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematics education (ICME-10) (pp. 355–358). Roskilde University, Denmark.Google Scholar
  17. Healy, L., & Fernandes, S. (2008). The role of gestures in the mathematical practices of blind learners. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojana, & A. Sepulveda (Eds.), Proceedings of the 32nd conference of the international group for the psychology of mathematics education (Vol. 3, pp. 137–144). Morelia, Mexico.Google Scholar
  18. Healy, L., Jahn, A-P., Frante, J.B. (submitted). Digital Technologies and the challenge of constructing an inclusive school mathematics. ZDM—The International Journal on Mathematics Education.Google Scholar
  19. Healy, L., & Sinclair, N. (2007). If this is our mathematics, what are our stories? International Journal of Computers for Mathematical Learning, 12(1), 3–21.CrossRefGoogle Scholar
  20. Hoyles, C. (1993). Microworlds/Schoolworlds: The transformation of an innovation. In C. Keitel, & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology NATO ASI, series F: Computer and systems sciences (Vol. 121, pp. 1–17). Heidelburg: Springer. Google Scholar
  21. Hoyles, C. (1995). Exploratory software, exploratory cultures? In A. A. diSessa, C. Hoyles, R. Noss, & L. D. Edwards (Eds.), Computers and exploratory learning (pp. 199–220). Berlin: Springer.Google Scholar
  22. Hoyles, C., Noss, R., & Adamson, R. (2002). Rethinking the microworld idea. Journal of Educational Computing Research, Special issue on: Microworlds in mathematics education, 27(1–2), 29–53.Google Scholar
  23. Hoyles, C., Noss, R., & Kent, P. (2004). On the integration of digital technologies into mathematics classrooms. International Journal of Computers for Mathematical Learning, 9(3), 309–326.CrossRefGoogle Scholar
  24. Kafai, Y., & Resnick, M. (Eds.). (1996). Constructionism in practice. Mahwah: Lawrence Erlbaum Associates Publishers.Google Scholar
  25. Kaput, J. (2004) Technology becoming infrastructural in mathematics education. Paper presented in Topic Study Group 15: Technology and Mathematics Education. 10th International Congress on Mathematics Education, Denmark.Google Scholar
  26. Kynigos, C. (2002). Generating cultures for mathematical microworld development in a multi-organisational context. Journal of Educational Computing Research, 27(1–2), 183–209.Google Scholar
  27. Kynigos, C. (2004). Black and white box approach to user empowerment with component computing. Interactive Learning Environments, 12(1–2), 27–71.CrossRefGoogle Scholar
  28. Kynigos, C. (2007a). Half-Baked logo microworlds as boundary objects in integrated design. Informatics in Education, 2007, 6(2), 1–24.Google Scholar
  29. Kynigos, C. (2007b). Half-baked microworlds in use in challenging teacher educators’ knowing. International Journal of Computers for Mathematical Learning, 12(2), 87–111.CrossRefGoogle Scholar
  30. Kynigos, C., Philippou, G., Potari, D., Sakonidis, C. (in press) Research in mathematics education. In Greece and Cyprus, Proceedings of the 33rd conference of the international group for the psychology of mathematics education. Thessaloniki, Greece.Google Scholar
  31. Laborde, C., Kynigos, C., Hollebrands, K., & Strasser, R. (2006). Teaching and learning geometry with technology. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275–304). Rotterdam: Sense.Google Scholar
  32. Lagrange, J.-B. (2000/2001). L’intégration d’instruments informatiques dans l’enseignement: Une approche par les techniques. Educational Studies in Mathematics, 43(1), 1–30.Google Scholar
  33. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. New York: Basic Books.Google Scholar
  34. Mariotti, M. A. (2001). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44, 25–53.CrossRefGoogle Scholar
  35. Moreno, L. A., & Sriraman, B. (2005). Structural stability and dynamic geometry: Some ideas on situated proofs. ZDM—The International Journal on Mathematical Education, 37(3), 130–139.CrossRefGoogle Scholar
  36. Nemirovsky, R., & Borba, M. (2004). Bodily activity and imagination in mathematics. Educational Studies in Mathematics, 57(3), 303–321.CrossRefGoogle Scholar
  37. Noss, R. (1991). The social shaping of computing in mathematics education. In D. Pimm & E. Love (Eds.), The teaching and learning of school mathematics (pp. 205–219). London: Hodder and Stoughton.Google Scholar
  38. Noss, R., & Hoyles, C. (1996). Windows on mathematical meaning: Learning cultures and computers. Dordrecht: Kluwer.Google Scholar
  39. Nunes, T. (2004). Teaching mathematics to deaf children. Whurr Publishers, London.Google Scholar
  40. Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. London: Harvester Press.Google Scholar
  41. Papert, S. (1991). Situating constructionism. In I. Harel, & S. Papert (Eds.), Constructionism (pp. 1–11). Norwood, NJ: Ablex Publishing Corporation.Google Scholar
  42. Papert, S. (2002). The Turtle’s long slow trip: Macro-educological perspectives on microworlds. Journal of Educational Computing Research, 27(1), 7–28.CrossRefGoogle Scholar
  43. Papert, S. (2006). From Math Wars to the New New Math. Plenary Lecture at the 17th ICMI Study Conference, Digital technologies and mathematics teaching and learning: Rethinking the terrain. Hanoi, Vietnam.Google Scholar
  44. Penner, D. (2001). Cognition, computers and synthetic science: Building knowledge and meaning through modelling. In W. Secade (Ed.), Review of research in education (pp. 17–30), Washington: American Educational Research Association, Frontiers/Berlin: SpringerGoogle Scholar
  45. Radford, L., Bardini, C., Sabena, C., Diallo, P., Simbagoye, A (2005). On embodiment, artifacts, and signs: a semiotic-cultural perspective on mathematical thinking. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th conference of the Iinternational group for the psychology of mathematics education (Vol. 4, pp. 113–120). University of Melbourne, Australia.Google Scholar
  46. Sarama, J., & Clements, D. (2002). Design of microworlds in mathematics and science education. Journal of Educational Computing Research, 27(1), 1–3.CrossRefGoogle Scholar
  47. Sinclair, N. (2001). The aesthetic is relevant. For the Learning of Mathematics, 21(1), 25–32.Google Scholar
  48. Sinclair, N., Healy, L., & Sales, C. O. R. (in press). Time for telling stories: Narrative thinking with dynamic geometry. ZDM—The International Journal on Mathematics Education, 41(4).Google Scholar
  49. Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, ‘translations’ and boundary objects: Amateurs and professionals in Berkeley’s museum of vertebrate zoology, 1907–1939. Social Studies of Science, 19, 387–420.CrossRefGoogle Scholar
  50. Thompson, P. W. (1987). Mathematical microworlds and intelligent computer-assisted instruction. In G. Kearsley (Ed.), Artificial intelligence and education (pp. 83–109). New York: Addison-Wesley.Google Scholar
  51. Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrument activity. European Journal of Psychology in Education, 9(3), 77–101.CrossRefGoogle Scholar
  52. Vygotsky, L. S. (1978). Mind in society. Cambridge: Harvard University Press.Google Scholar
  53. Vygotsky, L. S. (1981). The instrumental method in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 134–143). Armonk: M.E. Sharpe.Google Scholar
  54. Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. New York/Cambridge: Cambridge University Press.Google Scholar
  55. Wilensky, U. (2006). Agent-based restructurations for modeling change. Contribution to the Plenary Panel on Connectivity at the ICMI Study Conference, Digital technologies and mathematics teaching and learning: Rethinking the terrain. Hanoi, Vietnam.Google Scholar

Copyright information

© FIZ Karlsruhe 2009

Authors and Affiliations

  1. 1.Bandeirante University of São Paulo, Post-Graduate Programme in Mathematics EducationSão PauloBrazil
  2. 2.Educational Technology Lab, Department of Pedagogy, School of Philosophy, Faculty of Philosophy, Pedagogy and PsychologyUniversity of Athens PanepistimiopolisIlissiaGreece

Personalised recommendations