, Volume 40, Issue 2, pp 287–301 | Cite as

A networking method to compare theories: metacognition in problem solving reformulated within the Anthropological Theory of the Didactic

  • Esther Rodríguez
  • Marianna BoschEmail author
  • Josep Gascón
Original article


An important role of theory in research is to provide new ways of conceptualizing practical questions, essentially by transforming them into scientific problems that can be more easily delimited, typified and approached. In mathematics education, theoretical developments around ‘metacognition’ initially appeared in the research domain of Problem Solving closely related to the practical question of how to learn (and teach) to solve non-routine problems. This paper presents a networking method to approach a notion as ‘metacognition’ within a different theoretical perspective, as the one provided by the Anthropological Theory of the Didactic. Instead of trying to directly ‘translate’ this notion from one perspective to another, the strategy used consists in going back to the practical question that is at the origin of ‘metacognition’ and show how the new perspective relates this initial question to a very different kind of phenomena. The analysis is supported by an empirical study focused on a teaching proposal in grade 10 concerning the problem of comparing mobile phone tariffs.


Mathematics Education Mathematical Activity Study Process Metacognitive Strategy Didactic Contract 
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.


  1. Adibnia, A., & Putt, I. J. (1998). Teaching problem solving to year 6 students: a new approach. Mathematics Education Research Journal, 10(3), 42–58.Google Scholar
  2. Barbé, J., Bosch, M., Espinoza, L., & Gascón, J. (2005). Didactic restrictions on the teacher’s practice: the case of limits of functions in Spanish high schools. Educational Studies in Mathematics, 59, 235–268.CrossRefGoogle Scholar
  3. Barquero, B., Bosch, M., & Gascón, J. (2008). Using research and study courses for teaching mathematical modelling at university level. In D. Pitta-Pantazi, & G. Pilippou (Eds.), Proceedings of the fifth congress of the European society for research in mathematics education (pp. 2050–2059). Cyprus: University of Cyprus.Google Scholar
  4. Bosch, M., & Gascón, J. (2005). La praxéologie comme unité d’analyse des processus didatiques. In A. Mercier, & C. Margolinas (Coord.), Balises en Didactique des Mathématiques (pp. 107–122). Grenoble: La Pensée Sauvage.Google Scholar
  5. Brousseau, G. (1997). Theory of didactical situations in mathematics. Didactique des Mathématiques 1970–1990. Dordrecht: Kluwer.Google Scholar
  6. Chevallard, Y. (1999). L’analyse de pratiques professorales dans la théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–266.Google Scholar
  7. Chevallard, Y. (2004), Vers une didactique de la codisciplinarité. Notes sur une nouvelle épistémologie scolaire. Journées de didactique comparée. Lyon (3–4 mai 2004).
  8. Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.) Proceedings of the IV Congress of the European Society for Research in Mathematics Education (CERME 4) (pp. 1254–1263). Barcelona: FUNDEMI IQS.Google Scholar
  9. Chevallard, Y. (2008). Readjusting didactics to a changing epistemology. Invited panel session at the European conference on education research, Genève, 13–15 September 2006 (in press).Google Scholar
  10. Chevallard, Y., Bosch, M., & Gascón, J. (1997). Estudiar matemáticas. El eslabón perdido entre la enseñanza y el aprendizaje. Barcelona: ICE/Horsori.Google Scholar
  11. Clarke, D. J., Stephens, W. M., & Waywood, A. (1992). Communication and the learning of mathematics. In T. A. Romberg (Ed.), Mathematics assessment and evaluation: imperatives for mathematics educators. (pp. 184–212). New York: The State University of New York Press.Google Scholar
  12. Douglas, M. (1987). How institutions think. London: Routledge & L. Kegan Paul.Google Scholar
  13. Fan, L., & Zhu, Y. (2007). From convergence to divergence: the development of mathematical problem solving in research, curriculum, and classroom practice in Singapore. ZDM—The International Journal on Mathematics Education, 39(5–6), 491–501.CrossRefGoogle Scholar
  14. Flavell, J.H. (1976), Metacognitive aspects of problem solving. In L.B. Resnick (Ed.). The nature of intelligence (pp. 231–236). Hillsdale: Erlbaum.Google Scholar
  15. García, F. J., Gascón, J., Ruiz Higueras, L., & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM—The International Journal on Mathematics Education, 38(3), 226–246.CrossRefGoogle Scholar
  16. Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176.CrossRefGoogle Scholar
  17. Gascón, J. (2003). From the cognitive to the epistemological programme in the didactics of mathematics: two incommensurable scientific research programmes? For the Learning of Mathematics, 23(2), 44–55.Google Scholar
  18. Goos, M. (1995). Metacognitive decision-making and social interactions during paired problem solving. Mathematics Education Research Journal, 6(2), 144–165.Google Scholar
  19. Kaune, C. (2006). Reflection and metacognition in mathematics education—tools for the improvement of teaching quality. ZDM—The International Journal on Mathematics Education, 38(4), 350–360.CrossRefGoogle Scholar
  20. Kilpatrick, J. (1985). A retrospective account of the past twenty-five years of research on teaching mathematical problem solving. In E. Silver (Ed.), Teaching and learning mathematical problem solving: multiple research perspectives (pp. 1–15). Hillsdale: Erlbaum.Google Scholar
  21. Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.Google Scholar
  22. Lester, F.K., & Garofalo, J. (1982). Mathematical problem solving: issues in research. Philadelphia: Franklin Institute Press.Google Scholar
  23. Lester, F. (1994). Musings about mathematical problem-solving research: The first 25 years in JRME. Journal for Research in Mathematics Education, 25(6), 660–675.CrossRefGoogle Scholar
  24. McAfee, O., & Leong, D. J. (1994). Assessing and guiding young children’s development and learning. Boston: Allyn & Bacon.Google Scholar
  25. Niss, M. (1999). Aspects of the nature and state of research in mathematics education. Educational Studies in Mathematics, 40, 1–24.CrossRefGoogle Scholar
  26. Pólya, G. (1981). Mathematical discovery. On understanding, learning, and teaching problem solving. New York: Wiley (Combined paperback edition).Google Scholar
  27. Rodríguez, E. (2005). Metacognición, matemáticas y resolución de problemas: una propuesta integradora desde el enfoque antropológico. Doctoral dissertation. Universidad Complutense de Madrid, Madrid.Google Scholar
  28. Rodríguez, E., Bosch, M., & Gascón, J. (2008). An anthropological approach to ‘Metacognition’: the research and study courses. In D. Pitta-Pantazi, & G. Pilippou (Eds.), Proceedings of the fifth congress of the European society for research in mathematics education (pp. 1798–1807). Cyprus: University of Cyprus.Google Scholar
  29. Ruiz, N., Bosch, M., & Gascón, J. (2008). The functional algebraic modelling at secondary level. In D. Pitta-Pantazi, & G. Pilippou (Eds.), Proceedings of the fifth congress of the European society for research in mathematics education (pp. 2170–2179) Cyprus: University of Cyprus.Google Scholar
  30. Schoenfeld, A. H. (1985a). Mathematical problem solving. San Diego: Academic Press.Google Scholar
  31. Schoenfeld, A. H. (1985b). Metacognitive and epistemological issues in mathematical understanding. In E. Silver (Ed.), Teaching and learning mathematical problem-solving: multiple research perspectives (pp. 361–380). Hillsdale: Erlbaum.Google Scholar
  32. Schoenfeld, A. H. (1985c). Making sense of “out loud” problem-solving protocols. Journal of Mathematical Behaviour, 4, 171–191.Google Scholar
  33. Schoenfeld, A. H. (1987). Cognitive science and mathematics education. Hillsdale: Erlbaum.Google Scholar
  34. Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: MacMillan.Google Scholar
  35. Schoenfeld, A. H. (2007). Problem solving in the United States, 1970–2008: research and theory, practice and politics. ZDM—The International Journal on Mathematics Education, 39(5–6), 537–551.CrossRefGoogle Scholar
  36. Silver, E. (1985). The teaching and assessing of mathematical problem solving. Reston: National Council of Teachers of Mathematics (NCTM).Google Scholar
  37. Silver, E., & Herbst, P. (2007). Theory in mathematics education scholarship. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 39–67). Charlotte: Information Age Publishing.Google Scholar
  38. Silver, E., & Marshall, S. (1990). Mathematical and scientific problem solving: findings, issues, and instructional implications. In B. F. Jones & L. Idol (Eds.), Dimensions of thinking and cognitive instruction (pp. 265–290). Hillsdale: Erlbaum.Google Scholar
  39. Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48.Google Scholar

Copyright information

© FIZ Karlsruhe 2008

Authors and Affiliations

  • Esther Rodríguez
    • 1
  • Marianna Bosch
    • 2
    Email author
  • Josep Gascón
    • 3
  1. 1.Universidad Complutense de MadridMadridSpain
  2. 2.Universitat Ramon LlullBarcelonaSpain
  3. 3.Universitat Autònoma de BarcelonaBarcelonaSpain

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