Advertisement

ZDM

, Volume 50, Issue 1–2, pp 129–142 | Cite as

Expansive movements in the development of mathematical modeling: analysis from an Activity Theory perspective

  • Jeannette Galleguillos
  • Marcelo de Carvalho Borba
Original Article
First Online:

Abstract

This research was conducted during an online continuing education course for mathematics teachers, whose core focus was modeling and applications. We studied the interactions of one group of two teachers, who worked collectively in posing and solving a modeling problem through a closed group on the social network Facebook. The research question guiding this paper was how the development of mathematical modeling occurs from an Activity Theory perspective, recognizing tensions that occur, and its evolution in the process of posing and solving a modeling problem. The researchers took a qualitative approach, analyzing discursive manifestations in the modeling process. In the discussion, contradictions emerged in the group through events such as dilemma and conflict. The results indicate that the modeling task acted as an artifact that brought to light inner contradictions, and thus, allowed teachers to move from a conflict to the formulation of an open problem, and from a dilemma to the construction of a model and a pedagogic strategy.

Keywords

Mathematics teacher education Mathematical modelling Cultural-historical Activity Theory Online distance learning 
This is a preview of subscription content, log in to check access.

References

  1. Anthony, G., Hunter, R., & Thompson, Z. (2014). Expansive learning: Lessons from one teacher’s learning journey. ZDM Mathematics Education, 46(2), 279–291.  https://doi.org/10.1007/s11858-013-0553-z.CrossRefGoogle Scholar
  2. Araújo, JdeL. (2013). Ser crítico em projetos de modelagem em uma perspectiva crítica de educação matemática. Bolema Boletim de Educação Matemática, 26(43), 839–859.CrossRefGoogle Scholar
  3. Ärlebäck, J. (2009). Mathematical modelling in upper secondary mathematics education in Sweden: A curricula and design study (Unpublished Doctoral Thesis). Linköping University, Linköping, Sweden.Google Scholar
  4. Bassanezi, R. C. (2002). Ensino-aprendizagem com modelagem matemática. São Paulo: Editora Contexto.Google Scholar
  5. Blum, W. (2012). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The proceedings of the 12th international congress on mathematical education (pp. 73–98). Seoul: Springer.Google Scholar
  6. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects: State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.  https://doi.org/10.1007/BF00302716.CrossRefGoogle Scholar
  7. Bonotto, C. (2007). How to replace word problems with activities of realistic mathematical modelling. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 185–192). New York: Springer.CrossRefGoogle Scholar
  8. Borba, M. C. (1987). Um estudo de etnomatemática e sua incorporação na elaboração de uma proposta pedagógica para o “Núcleo-escola” da Favela da Vila Nogueira-São Quirino (Unpublished Master’s Thesis). UNESP, Rio Claro, São Paulo.Google Scholar
  9. Borba, M. C. (2009). Potential scenarios for internet use in the mathematics classroom.. ZDM Mathematics Education, 41(4), 453–465.CrossRefGoogle Scholar
  10. Borba, M. C. (2012). Humans-with-media and continuing education for mathematics teachers in online environments. ZDM Mathematics Education, 44, 801–814.CrossRefGoogle Scholar
  11. Borba, M. C., Malheiros, A. P. S., & Zulatto, R. B. A. (2010). Online distance education. Rotterdam: Sense Publishers.Google Scholar
  12. Borba, M. C., Villarreal, M., & Soares, D. S. (2016). Modeling using data available on the internet. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 143–152). Reston: National Council of Teachers of Mathematics.Google Scholar
  13. Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, experimentation and visualization. New York: Springer.Google Scholar
  14. Caldeira, A. D. (2009). Modelagem matemática: Um outro olhar. ALEXANDRIA Revista de Educação em Ciência e Tecnologia, 2(2), 33–54.Google Scholar
  15. Cordero, F. (2006). La modellazione e la rappresentazione grafica nell’insegnamento-apprendimento della matematica. La Matematica e la sua Didattica, pp. 59–79.Google Scholar
  16. Cunha, M. I. (1989). O bom professor e a sua prática (Coleção Magistério: Formação e trabalho Pedagógico). Campinas: Papirus.Google Scholar
  17. Daniels, H. (2003). Vygotsky e a pedagogia. Brasil: Edições Loyola. English edition: Daniels, H. (2001). Vygotsky and pedagogy. London: Routledge: São Paulo.Google Scholar
  18. Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.Google Scholar
  19. Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen & R.-L. Punamäki (Eds.), Perspectives on Activity Theory (pp. 19–38). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  20. Engeström, Y. (2000). Activity Theory as a framework for analyzing and redesigning work. Ergonomics, 43(7), 960–974.CrossRefGoogle Scholar
  21. Engeström, Y. (2001). Expansive learning at work: Toward an activity theoretical reconceptualization. Journal of Education and Work, 14, 133–156.CrossRefGoogle Scholar
  22. Engeström, Y. (2006). Activity Theory and expansive design. In S. Bagnara & G. C. Smith (Eds.), Theories and practice of interaction design (pp. 3–23). Hillsdale: Lawrence Erlbaum.Google Scholar
  23. Engeström, Y., & Sannino, A. (2011). Discursive manifestations of contradictions in organizational change efforts. Journal of Organizational Change Management, 368–387.Google Scholar
  24. Goodchild, S., & Jaworski, B. (2005). Using contradictions in a teaching and learning development project. In H. L. Chick & J. L. Vincent (Eds.) Proceedings of de 29th conference of the International Group for the Psychology of Mathematics Education, (Vol. 3, pp. 41–48). Melbourne: PME.Google Scholar
  25. Hardman, J. (2005). An exploratory case study of computer use in a primary school mathematics classroom: New technology, new pedagogy? Research: Information and Communication Technologies. Perspectives in Education, 23(4), 99–111.Google Scholar
  26. Holzkamp, K. (1993). Lernen: Subjektwissenschaftliche grundlegung. Frankfurt: M: Campus.Google Scholar
  27. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302–310.CrossRefGoogle Scholar
  28. Langemeyer, I. (2005). Contradictions in expansive learning: Towards a critical analysis of self-dependent forms of learning in relation to contemporary socio-technological change. Forum Qualitative Social Research, 7(1), Art. 12.Google Scholar
  29. Leont’ev, A. N. (1981). The problem of activity in psychology. In J. V. Wertsh (Ed.), The concept of activity in Soviet psychology. New York: M. E. Sharpe. Inc.Google Scholar
  30. Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 3–32). New York: Springer.CrossRefGoogle Scholar
  31. Potari, D. (2013). The relationship of theory and practice in mathematics teacher professional development: An Activity Theory perspective. ZDM The International Journal on Mathematics Education, 45(4), 507–519.  https://doi.org/10.1007/s11858-013-0498-2.CrossRefGoogle Scholar
  32. Rosa, M., & Orey, D. (2013). Ethnomodeling as a research theoretical framework on ethnomathematics and mathematical modeling. Journal of Urban Mathematics Education, 6(2), 62–80.Google Scholar
  33. Roth, W.-M. (2013). Contradictions and uncertainty in scientifics’ mathematical modeling and interpretation of data. Journal of Mathematical Behavior, 32, 593–612.CrossRefGoogle Scholar
  34. Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  35. Saviani, D. (1985). Do senso comum a consciência filosófica. Brasil: Cortez Editora.Google Scholar
  36. Silva, M. (2000). Sala de aula interativa. Rio de Janeiro: Quartet.Google Scholar
  37. Soares, D. S., & Souto, D. L. P. (2014). Tensões no processo de análise de modelos em um curso de cálculo diferencial e integral. Revista de Matemática, Ensino e Cultura, pp. 44–74.Google Scholar
  38. Souto, D. L. P., & Borba, M. C. (2015). Movimentos, estagnações, tensões e transformações na aprendizagem da matemática on-line. In Seminário Internacional de Pesquisa em Educação Matemática (Vol. 6, pp. 1–12). Pirenópolis: Sociedade Brasileira de Educação Matemática.Google Scholar
  39. Souto, D. L. P., & Borba, M. C. (2016). Seres humanos-com-internet ou internet-com-seres humanos: Uma troca de papéis?. Revista Latinoamericana de Investigación en Matemática Educativa.  https://doi.org/10.12802/relime.13.1924.Google Scholar
  40. Vygotsky, L. (1978). Mind and society. Cambridge: Harvard University Press.Google Scholar
  41. Williams, J., & Goos, M. (2013). Modelling with mathematics and technology. In M. A. Clements, A. Bishop, C. Keitel-Kreidt, J. Kilpatrick & F. K.-S. Leung (Eds.), Third international handbook of mathematics education (pp. 549–569). New York: Springer.Google Scholar
  42. Yamagata-Lynch, L. C. (2010). Activity systems analysis methods. Boston: Springer.CrossRefGoogle Scholar
  43. Zevenbergen, R., & Lerman, S. (2007). Pedagogy and interactive whiteboard: Using an activity theory approach to understand tensions in practice. In J. Watson & K. Beswick (Eds.), Mathematics education research group of Australasia (MERGA) Conference (Vol. 30, pp. 853–862). Hobart: MERGA, Inc.Google Scholar

Copyright information

© FIZ Karlsruhe 2017

Authors and Affiliations

  1. 1.Universidad de ValparaísoValparaísoChile
  2. 2.São Paulo State University (UNESP)Rio ClaroBrazil

Personalised recommendations

Cite article

Buy options