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On inferentialism

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Abstract

This article is a critical commentary on inferentialism in mathematics education. In the first part, I comment on some of the major shortcomings that inferentialists see in the theoretical underpinnings of representationalist, empiricist, and socioconstructivist mathematics education theories. I discuss in particular the criticism that inferentialism makes of the social dimension as conceptualized by socioconstructivism and the question related to the objectivity of knowledge. In the second part, I discuss some of the theoretical foundations of inferentialism in mathematics education and try to answer the question of whether or not inferentialism overcomes the individual-social divide. In the third part, I speculate on what I think inferentialism accomplishes and what I think it does not.

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References

  • Bachelard, G. (1986). La formation de l'esprit scientifique (The formation of the scientific spirit). Paris: Vrin.

    Google Scholar 

  • Bakker, A., Ben-Zvi D., & Makar, K. (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference. Mathematics Education Research Journal. This Special Issue.

  • Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13, 5–26.

    Article  Google Scholar 

  • Bikner-Ahsbahs, A., & Prediger, S. (2006). Diversity of theories in mathematics education—how can we deal with it? Zentralblatt Für Didaktik Der Mathematik, 38(1), 52–57.

    Article  Google Scholar 

  • Bikner-Ahsbahs, A., & Prediger, S. (2014). Networking of theories as a research practice in mathematics education. In Cham, Switzerland: Springer.

    Google Scholar 

  • Bishop, L. (1985). The social psychology of mathematics education. In L. Streefland (Ed.), Proceedings of the 9th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 1–13). Noordwijkerhout: PME.

    Google Scholar 

  • Brandom, R. (1994). Making it explicit. Reasoning, representing, and discursive commitment. Cambridge: Harvard University Press.

    Google Scholar 

  • Brandom, R. (2000). Articulating reasons. An introduction to inferentialism. Cambridge: Harvard University Press.

    Google Scholar 

  • Bransen, J. (2002). Normativity as the key to objectivity: an exploration of Robert Brandom’s articulating reasons. Inquiry, 45(3), 373–392.

    Article  Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.

    Google Scholar 

  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175–190.

    Article  Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education,23(1), 2-33.

    Article  Google Scholar 

  • D’Ambrosio, U. (2006). Ethnomathematics. Rotterdam: Sense Publishers.

    Google Scholar 

  • D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44–48.

    Google Scholar 

  • Darling, J., & Nordenbo, S. (2002). Progressivism. In N. Blake, P. Smeyers, R. Smith, & P. Standish (Eds.), The philosophy of education (pp. 288–308). Oxford: Blackwell.

    Google Scholar 

  • Davydov, V. (1962). An experiment in introducing elements of algebra in elementary school. Russian Education and Society, 5(1), 27–37.

    Article  Google Scholar 

  • Davydov, V. (1991). Psychological abilities of primary school children in learning mathematics. Soviet studies in mathematics education, vol. 6. Reston, Virginia: NCTM.

  • Derry, J. (2017). An introduction to inferentialism in mathematics education. Mathematics Education Research Journal. This Special Issue.

  • Detienne, M. (1996). The masters of truth in archaic Greece. New York: Zone Books.

    Google Scholar 

  • Holmes, L. (1991). The Kremlin and the schoolhouse: reforming education in Soviet Russia, 1917–1931. Bloomington and Indianapolis: Indiana University Press.

    Google Scholar 

  • Kidron, I., Bikner-Ahsbahs, A., Monaghan, J., Author, L., & Sensevy, G. (2012). CERME7 Working Group 16: different theoretical perspectives and approaches in research in mathematics education. Research in Mathematics Education, 14(2), 213–214.

    Article  Google Scholar 

  • Kuzniak, A., Tanguay, D., & Elia, I. (2016). Mathematical working spaces in schooling: an introduction. ZDM Mathematics Education, 48, 721–737.

    Article  Google Scholar 

  • Labaree, D. (2005). Progressivism, schools and schools of education: an American romance. Paedagogica Historica, 41(1–2), 275–288.

    Article  Google Scholar 

  • Lerman, S. (1996). Intersubjectivity in mathematics learning: a challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133–150.

    Article  Google Scholar 

  • Lyotard, J. (1979). La condition postmoderne [The postmodern condition]. Paris: Les éditions de minuit.

    Google Scholar 

  • Mackrell, K., & Pratt, D. (2017). Constructionism and the space of reasons. Mathematics Education Research Journal. This Special Issue.

  • MacBeth, D. (n.d.). Inference, meaning, and truth in Brandom, Sellars, and Frege. Dowloaded from: http://www.pitt.edu/~brandom/mie/downloads/XI%20MacBeth.doc

  • Neill, A. (1992). Summerhill school. New York: St. Martin’s Griffin (Original work published 1960).

    Google Scholar 

  • Noorloos, R., Taylor, A., Bakker, S., & Derry, J. (2017). Inferentialism as an alternative to socioconstructivism in mathematics education. Mathematics Education Research Journal. This Special Issue.

  • Presmeg, N., Author, L., Roth, M., & Kadunz, G. (2017). Signs of signification: semiotics in mathematics education research. Cham: Springer. (in press)

  • Radford, L. (2016a). The epistemic, the cognitive, the human: a commentary on the mathematical working space approach. ZDM Mathematics Education, 48, 925–933.

    Article  Google Scholar 

  • Radford, L. (2016b). The theory of objectification and its place among sociocultural research in mathematics education. International Journal for Research in Mathematics Education—RIPEM, 6(2), 187–206.

    Google Scholar 

  • Radford, L., Arzarello, F., Edwards, L., & Sabena, C. (2017). The multimodal material mind: Embodiment in mathematics education. In J. Cai (Ed.), First compendium for research in mathematics education (pp. 700-721). Reston, VA: NCTM.

  • Röhrs, H., & Lenhart, V. (1995). Progressive education across the continents. Frankfurt and Main: Peter Lang.

    Google Scholar 

  • Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal. This Special Issue.

  • Sfard, A. (1999). Doing research in mathematics education in time of paradigm wars. In O. Zaslavsky (Ed.), Proceedings of the 23rd conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 75–92). Haifa: PME.

    Google Scholar 

  • Sheets-Johnstone, M. (2009). The corporeal turn. Exeter, Devon, United Kingdom: imprintacademic.com.

  • Steffe, L. P., & Gale, J. (1995). Constructivism in education. Hillsdale. New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Szabó, A. (1978). The beginnings of Greek mathematics. Dordrecht: D. Reidel.

    Book  Google Scholar 

  • Tzekaki, M., Kaldrimidou, M., & Sakonidis, H. (Eds.). (2009). Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education. Thessaloniki: PME.

    Google Scholar 

  • Voller, K. (2012). On Robert Brandom’s conceptual realism. Downloaded from http://www.steelsunshine.com/philosophy-papers/Kevin-R-Voller-On-Robert-Brandoms-Conceptual-Realism.pdf .

  • von Glasersfeld, E. (1995). Radical constructivism: a way of knowing and learning. London: The Falmer Press.

  • Williams, J. & Brandom, R. (2013). Inferential man: an interview with Robert Brandom. Symplokē, 21(1–2),367–391.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Ecole des Sciences de l’Education, Université Laurentienne, Sudbury, Ontario, P3E 2C6, Canada

    Luis Radford

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  1. Luis Radford
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Radford, L. On inferentialism. Math Ed Res J 29, 493–508 (2017). https://doi.org/10.1007/s13394-017-0225-3

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  • DOI: https://doi.org/10.1007/s13394-017-0225-3

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