Dialogical Education and Learning Mathematics Online from Teachers

  • Marcelo C. Borba
  • Rúbia B.A. Zulatto
Part of the Mathematics Teacher Education book series (MTEN, volume 5)


In this chapter we intend to show how we learned mathematics in the process of teaching teachers online how to use geometry software in face-to-face classrooms. We emphasize that we need to be open to risks and being pushed beyond our “comfort zone” if we want to use information and communication technology. In particular, we emphasize that the risk is greater once the decision has been made to adopt an interactive-dialogical approach for an online course, but that once the virtual community has become dialogical, the risks diminish. We suggest that one can grow accustomed to the risk and feel more comfortable with it. Before presenting one example about conics, we present our theoretical perspective regarding the use of information and communication technology based on the theoretical construct humans-with-media. We discuss our understanding of dialogical teaching education and the context of the online course. We then show how the problem-solving dynamic we set up for the course led one of the teacher/students to pose a problem that initially none of the participants knew how to solve – a situation that lead to mathematics learning on the part of everyone, including the teachers of the course.


Mathematics Education Mathematics Teacher Online Environment Risk Zone Comfort Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Although they are not responsible for the content of this chapter, we would like to thank Antonio Olimpio and Ricardo Scucuglia, members of our research group GPIMEM, for comments on earlier versions of this chapter. We would also like to thank Anne Kepple for her careful and insightful review of the English. Finally, we would like to thank, in memoriam, Geraldo Duarte, a colleague of the mathematics Department at UNESP, for chatting with us about the possible ways of solving the problem that was at center stage in this chapter.


  1. Alrø, H., & Skovsmose, O. (2002). Dialogue and learning in mathematics education: Intention, reflection, critique. Dordrecht: Kluwer Academic Publishers.Google Scholar
  2. Borba, M. C. (1993). Students Understanding of Transformations of Functions Using Multi-Representational Software. Dissertation in Mathematics Education. Ithaca: Cornell University.Google Scholar
  3. Borba, M. C. (1995). Overcoming limits of software tools: A student’s solution for a problem involving transformation of functions. In L. Meira & D. Carraher (Eds.), Proceedings of the PME, 19(2), 248–255.Google Scholar
  4. Borba, M., & Gadanidis, G. (2008). Virtual communities and networks of practising mathematics teachers: The role of technology in collaboration. In T. Wood & K. Krainer (Eds.), International handbook of mathematics teacher education: (Vol. 3). Participants in mathematics teacher education: individuals, teams, communities, and networks. Rotterdam: Sense Publishers.Google Scholar
  5. Borba, M. C., Malheiros, A. P. S., & Zulatto, R. B. A. (2007). Educação a distância online. Belo Horizonte: Editora Autêntica.Google Scholar
  6. Borba, M. C., & Penteado, M. G. (2001). Informática e Educação Matemática. Belo Horizonte: Editora Autêntica.Google Scholar
  7. Borba, M. C., & Santos S. C. (2005). Educação Matemática: Propostas e Desafios, Pesquisa Educacional e Cotidiano Escolar, 7(2), 291–312.Google Scholar
  8. Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, visualization and experimentation. Dordrecht: Kluwer Academic Publishers.Google Scholar
  9. Borba, M. C., & Zulatto, R. B. A. (2006). Different media, different types of collective work in online continuing teacher education: Would you pass the pen, please? In Proceedings of the PME, 30(2): 201–208.Google Scholar
  10. Confrey, J. (1991). Function Probe©. Apple Macintosh® Computer. Designed by J. Confrey, F. Carroll, S. Cato, P. Davis, and E. Smith.Google Scholar
  11. Freire, P. (2005). Pedagogia do oprimido, 45. Ed., Editora Paz e Terra Rio de Janeiro.Google Scholar
  12. 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). Hillsdale, NJ: Erlbaum.Google Scholar
  13. Levy, P. (1993). As Tecnologias da Inteligência: o futuro do pensamento na era da informática. Rio de Janeiro: Editora 34.Google Scholar
  14. Penteado, M. G. (2000). Possibilidades para a formação de professores de matemática. In M. G. Penteado & M. C. Borba (Eds.), A informática em ação: Formação de professores, pesquisa e extensão. Editora Olho d’Água.Google Scholar
  15. Penteado, M. G. (2001). Computer-based learning environments: Risks and uncertainties for teacher. Ways of Knowing Journal, 1(2), 23–35.Google Scholar
  16. Sadolin, V. (2000). Geometricks. Software de Geometria Dinâmica com fractais.Google Scholar
  17. Santos, S. C. & Borba, M. C. (2008). Internet e softwares de Geometria Dinâmica como atores na Produção Matemática On-Line. Zetetiké, 16(29), 93–116.Google Scholar
  18. Tikhomirov, O. K. (1981). The psychological consequences of computerization. In J. V. Wertsch (Ed.), The concepto f activity in soviet psychology (pp. 256–278). New York: M.E. Sharpe Inc.Google Scholar
  19. Wagner, H. R. (1979). Fenomenologia e relações sociais. Textos Escolhidos de Alfred Schutz. Rio de Janeiro: Zahar Editores.Google Scholar
  20. Zulatto, R. B. A. (2002). Professores de Matemática que utilizam softwares de geometria dinâmica: suas características e perspectivas. Máster thesis. Rio Claro. Brasil: Universidade Estadual Paulista.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.GPIMEM and UNESPRio Claro-SPBrazil
  2. 2.GPIMEM, FIEL and FAALLimeira-SPBrazil

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