, Volume 39, Issue 1–2, pp 127–135 | Cite as

The onto-semiotic approach to research in mathematics education

  • Juan D. GodinoEmail author
  • Carmen Batanero
  • Vicenç Font
Original article


In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.


Mathematical Object Mathematical Practice Language Game Personal Meaning Instructional Process 
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.



This research work has been carried out in the frame of the project, MCYT- FEDER: SEJ2004-00789.


  1. Anderson, M., Sáenz-Ludlow, A., Zellweger, S., & Cifarelli, V. C. (Eds). (2003). Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing. Otawa: Legas.Google Scholar
  2. Batanero, C., Godino J.D., Steiner, H.G., & Wenzelburger, E. (1994). The training of researchers in Mathematics Education. Results from an International study. Educational Studies in Mathematics, 26, 95–102.CrossRefGoogle Scholar
  3. Brousseau G. (1997). Theory of didactical situation in mathematics. Dordrecht: Kluwer.Google Scholar
  4. Cantoral, R., & Farfán, R. M. (2003). Matemática educativa: Una visión de su evolución. Revista Latinoamerica de Investigación en Matemática Educativa, 6(1), 27–40.Google Scholar
  5. Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 73–112.Google Scholar
  6. Contreras, A., Font, V., Luque, L., & Ordóñez, L. (2005). Algunas aplicaciones de la teoría de las funciones semióticas a la didáctica del análisis infinitesimal. Recherches en Didactique des Mathématiques, 25(2), 151–186.Google Scholar
  7. Douady, R. (1986). Jeux de cadres et dialectique outil-objet. Recherches en Didactique des Mathématiques, 7(2), 5–31.Google Scholar
  8. Duval R. (1995). Sémiosis et penseé humaine. Berna: Peter Lang.Google Scholar
  9. Eco, U. (1979). Tratado de semiótica general. Barcelona: Lumen, 1991.Google Scholar
  10. Ernest, P. (1994). Varieties of constructivism: their metaphors, epistemologies and pedagogical implications. Hiroshima Journal of Mathematics Education, 2, 1–14.Google Scholar
  11. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. New York: SUNY.Google Scholar
  12. Font, V. (2001). Processos mentals versus competència, Biaix 19, pp. 33–36.Google Scholar
  13. Font, V. (2002). Una organización de los programas de investigación en Didáctica de las Matemáticas. Revista EMA, 7(2), 127–170.Google Scholar
  14. Godino, J. D. (1996). Mathematical concepts, their meanings, and understanding. In L. Puig, & A. Gutierrez (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (pp. 2-417–424), University of Valencia.Google Scholar
  15. Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, 22(2/3), 237–284.Google Scholar
  16. Godino, J. D. (2003). Teoría de las funciones semióticas. Un enfoque ontológico-semiótico de la cognición e instrucción matemática. Departamento de Didáctica de la Matemática. Universidad de Granada. (Available at
  17. Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325–355.Google Scholar
  18. Godino, J. D., & Batanero, C. (1998). Clarifying the meaning of mathematical objects as a priority area of research in mathematics education. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics Education as a Research Domain: A Search for Identity (pp. 177–195). Dordrecht: KluwerGoogle Scholar
  19. Godino, J. D., & Recio, A. M. (1998). A semiotic model for analysing the relationships between thoughy, language and context in mathematics education. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, vol. 3 1.8. University of Stellenbosch, South Africa.Google Scholar
  20. Godino, J. D., Batanero, C., & Roa, R. (2005). An onto-semiotic analysis of combinatorial problems and the solving processes by university students. Educational Studies in Mathematics, 60(1), 3–36.CrossRefGoogle Scholar
  21. Godino, J. D., Wilhelmi, M. R., & Bencomo, D. (2005). Suitability criteria of a mathematical instruction process. A teaching experience of the function notion. Mediterranean Journal for Research in Mathematics Education, 4.2, 1–26.Google Scholar
  22. Godino, J. D., Contreras, A., & Font, V. (2006). Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, 26(1), 39–88.Google Scholar
  23. Godino, J. D., Font, V., Contreras, A., & Wilhelmi, M. R. (2006). Una visión de la didáctica francesa desde el enfoque ontosemiótico de la cognición e instrucción matemática. Revista Latinoamerica de Investigación en Matemática Educativa, 9(1), 117–150.Google Scholar
  24. Hjelmslev, L. (1943). Prolegómenos a una teoría del lenguaje. Madrid: Gredos, 1971.Google Scholar
  25. Lakatos, I. (1983). La metodología de los programas de investigación científica. Madrid: Alianza.Google Scholar
  26. Peirce, Ch. S. (1965). Obra lógico-semiótica. Madrid: Taurus, 1987Google Scholar
  27. Radford, L. (2006). The anthropology of meaning. Educational Studies in Mathematicas, 61(1–2), 39–65.CrossRefGoogle Scholar
  28. Sáenz-Ludlow, A., & Presmeg, N. (2006). Semiotic perspectives on learning mathematics and communicating mathematically. Educational Studies in Mathematics, 61(1–2), 1–10.CrossRefGoogle Scholar
  29. Saussure, F. (1915). Curso de lingüística general. Madrid: Alianza, 1991.Google Scholar
  30. Sfard, A. (2000). Symbolizing mathematical reality into being—Or how mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K. McCain (Eds.), Symbolizing and Communicating in Mathematics Classroom (pp. 37– 97). London: LEA.Google Scholar
  31. Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In A. J. Bishop, et al. (Eds.), International Handbook of Mathematics Education (pp. 827–876). Dordrecht: KluwerGoogle Scholar
  32. Steiner, H. G. (1985). Theory of mathematics education (TME): an introduction. For the Learning of Mathematics, 5(2), 11–17.Google Scholar
  33. Steiner, H. G. (1990). Needed cooperation between science education and mathematics education. Zentralblatt für Didaktik der Mathematik, 6, 194–197.Google Scholar
  34. Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactiques des Mathématiques, 10(2,3), 133–170.Google Scholar
  35. Vygotski, L. S. (1934). El desarrollo de los procesos psicológicos superiores, 2ª edición. Barcelona: Crítica-Grijalbo, 1989.Google Scholar
  36. Wittgenstein, L. (1953). Investigaciones filosóficas. Barcelona: Crítica.Google Scholar

Copyright information

© FIZ Karlsruhe 2007

Authors and Affiliations

  • Juan D. Godino
    • 1
    Email author
  • Carmen Batanero
    • 1
  • Vicenç Font
    • 2
  1. 1.Departamento de Didáctica de la MatemáticaUniversidad de GranadaGranadaSpain
  2. 2.Departament de Didàctica de les Ciències Experimentals i la MatemàticaUniversitat de BarcelonaBarcelonaSpain

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