Advertisement

Educational Studies in Mathematics

, Volume 77, Issue 2–3, pp 149–156 | Cite as

Signifying and meaning-making in mathematical thinking, teaching, and learning

  • Luis RadfordEmail author
  • Gert Schubring
  • Falk Seeger
Article

Not meaning, not consciousness lies behind life, but life lies behind consciousness.

Leont’ev (2009, p. 96)

Introduction

In the last decades, concepts of learning have changed dramatically. The classical concept of learning as the simple reproduction of given conceptual contents has yielded space to a modern concept that emphasizes the creative and critical involvement of the students. Some recent theoretical accounts add a symmetrical stance and claim that, in highly social and cultural organized institutional settings, such as the school, learning cannot be abstracted from teaching. Teaching entails not only a critical stance toward the teachers’ own teaching but also a fundamental and creative involvement in the students’ act of learning. In those accounts, teaching and learning appear as two sides of the same coin: They are considered as part of a same process, connected by interrelated processes of signifying and meaning-making—that is to say, processes of communication and mutual...

Keywords

Meaning-making Mathematical thinking Teaching Learning 

References

  1. Brier, S. (2008). Cybersemiotics. Toronto, ON, Canada: Toronto University Press.Google Scholar
  2. Damasio, A. (1999). The feeling of what happens. San Diego, CA: Harcourt.Google Scholar
  3. Damasio, A. (2005). Descarte’s error. Emotion, reason, and the human brain. New York: Penguin Books.Google Scholar
  4. Foucault, M. (1969). L’archéologie du savoir [Archeology of knowledge]. Paris, France: Éditions Gallimard.Google Scholar
  5. Ilyenkov, E. (1977).The concept of the ideal. In R. Daglish (Tr.), Philosophy in the USSR: Problems of dialectical materialism (pp. 71–99). Moscow, Russia: Progress.Google Scholar
  6. Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  7. Leontyev [or Leont’ev], A. N. (2009). Activity and consciousness. Pacifica, CA: MIA. Retrieved August 29, 2009, from http://www.marxists.org/archive/leontev/works/activity-consciousness.pdf.
  8. Lévi-Strauss, C. (1958). Anthropologiestructurale [Structural anthropology]. Paris, France: Plon.Google Scholar
  9. Lévi-Strauss, C. (1962). La penséesauvage [The savage mind]. Paris, France: Plon.Google Scholar
  10. Malinowski, B. (1923). The problem of meaning in primitive languages, supplement 1. In C. K. Ogden & I. A. Richards (Eds.), The meaning of meaning (pp. 296–336). New York: Harcourt, Brace, & Co.Google Scholar
  11. Marková, I. (2003). Dialogicality and social representations. Cambridge, MA: Cambridge University Press.Google Scholar
  12. Merleau-Ponty, M. (1945). Phénomenologie de la perception [Phenomenology of perception]. Paris, France: Gallimard.Google Scholar
  13. Miguel, A., Vilela, D., & Lanner de Moura, R. (2010). Desconstruindo a matemática escolar sob umaperspectivapós-metafísica de educação [Deconstructing school mathematics from a post-metaphysical perspective on education]. Zetetiké, 18, 129–205.Google Scholar
  14. Peirce, C. S. (1931–1958). Collected papers (Vol. I–VIII). Cambridge, MA: Harvard University Press.Google Scholar
  15. Piaget, J. (1970). Genetic epistemology. New York: Norton.Google Scholar
  16. Piaget, J. (1971). Structuralism. New York: Harper & Row.Google Scholar
  17. Radford, L. (2006). Semiótica y educaciónmatemática [Semiotics and mathematics education]. Revista Latinoamericana de Investigación en MatemáticaEducativa, Special Issue: Semiótica, cultura y pensamientomatemático [Semiotics, culture, and mathematical thinking], 7–21.Google Scholar
  18. Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126.CrossRefGoogle Scholar
  19. Radford, L. (2011). La evolución de paradigmas y perspectivas en la investigación. El caso de la didáctica de lasmatemáticas [The evolution of paradigms and perspectives in research. The case of mathematics education]. In J. Vallès, D. Álvarez, & R. Rickenmann (Eds.), L’ctivitat docent intervenció, innovació, investigació [Teacher’s activity: Intervention, innovation, research]. Girona, Spain: Documenta Universitaria.Google Scholar
  20. Radford, L., Schubring, G., & Seeger, F. (2008). Semiotics in mathematics education: Epistemology, history, classroom, and culture. Rotterdam, The Netherlands: Sense.Google Scholar
  21. Saussure, F. (1916). Cours de linguistiquegénérale [Lectures on general linguistics]. Paris, France: Payot.Google Scholar
  22. Sheets-Johnstone, M. (2009). The corporeal turn. Exeter, UK: Imprint-academic.com.Google Scholar
  23. Stawarska, B. (2009). Between you and I. Dialogical phenomenology. Athens, OH: Ohio University Press.Google Scholar
  24. Vološinov, V. N. (1973). Marxism and the philosophy of language. Cambridge, MA: Harvard University Press.Google Scholar
  25. Vygotsky, L. S. (1962). Thought and language. Cambridge, MA: MIT.CrossRefGoogle Scholar
  26. Vygotsky, L. S. (1987). Thinking and speech. In R. W. Rieber & A. S. Carton (Eds.), Collected works (Vol. 1). New York: Plenum.Google Scholar
  27. Wittgenstein, L. (1953). Philosophical investigations. Oxford, UK: Blackwell.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Universite LaurentienneSudburyCanada
  2. 2.Institut für Didaktik der MathematikFakultät für Mathematik, Universität BielefeldBielefeldGermany
  3. 3.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

Personalised recommendations