Abstract
This chapter explores connections between theories of tacit knowing and theories of situated learning and communities of practice aiming at a better understanding of school mathematics as a socio-cultural practice. By contrasting both school and other socio-cultural mathematical contexts, we discuss the usefulness of a perspective from which the identification and circulation of tacit knowing within school mathematics practice is a central concern. Empirical data are presented to illustrate our ideas.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Araújo, C. R., Andrade, F., Hazin, I., Da Rocha Falcão, J. T., Nascimento, J. C., & Lins Lessa, M. M. (2003). Affective aspects on mathematics conceptualization: From dichotomies to an integrated approach. In N. Pateman, B. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 269-276). Honolulu, USA: PME.
Bishop, A. J. (2006). Values and mathematics education - a developing research field. Plenary lecture at culture and affect. Faculdade de Educação, Universidade Federal de Minas Gerais, Brazil.
Brito Lima, A. P., & Da Rocha Falcão, J. T. (1997). Early development of algebraic representation among 6-13 year-old children: The importance of didactic contract. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 201-208). Helsinki, Finland: PME.
Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37(2), 121-143.
Burton, L. (2002). Recognizing commonalities and reconciling differences in mathematics education. Educational Studies in Mathematics, 50(2), 157-175.
Clot, Y., D., F., Fernandez, G., & Scheller, L. (2001). Les entretiens en auto-confrontation croisée: Une méthode en clinique de l’activité. Education permanente, 146, 17-27.
Da Rocha Falcão, J. T. (2005). Conceptualisation en acte, conceptualisation explicite: Quels apports théoriques à offrir à la didactique des mathématiques et des sciences? Actes du Colloque Les processus de conceptualisation en debat-hommage a Gérard Vergnaud. Paris: Association pour la Recherche sur le Développement des Compétences.
Ernest, P. (1998a). Social constructivism as a philosophy of mathematics. Albany, NY: SUNY.
Ernest, P. (1998b). Mathematical knowledge and context. In A. Watson (Ed.), Situated cognition and the learning of mathematics (pp. 13-29). Oxford: Centre for Mathematics Education, University of Oxford.
Frade, C. (2003). Polanyi’s social construction of personal knowledge and the theories of situatedlearning.Philosophy Of Mathematics Education Journal,17 ( http://www.people.ex.ac.uk/PErnest/).
Frade, C. (2005). The tacit-explicit nature of students’ knowledge: A case study on area measurement. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 321). Melbourne, Australia: PME.
Frade, C., & Borges, O. (2002). Tacit knowledge in curricular goals in mathematics. Proceedings of the 2nd International Conference on the Teaching of Mathematics (p. 128). Crete, Greece: John Wiley & Sons.
Frade, C., & Borges, O. (2006). The tacit-explicit dimension of the learning of mathematics: An investigation report. International Journal of Science and Mathematics Education, 4, 293-317.
Frade, C., Winbourne, P., & Braga, S. M. (2006). Aline’s and Julia’s stories: Reconceptualizing transfer from a situated point of view. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 97-103). Prague, Czech Republic: PME.
Grigorenko, E., Meier, E., Lipka, J., Mohatt, G., Yanez, E., & Sternberg, R. (2001). The relationship between academic and practical intelligence: A case study of the tacit knowledge of native American yup’ik people in Alaska. ERIC: Educational Resources Information Center.
Latour, B., & Woolgar, S. (1979). Laboratory life: The social construction of scientific facts. Los Angeles, Londres: Sage.
Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press.
Leontiev, A. N. (1994). Uma contribuição à teoria do desenvolvimento da psique infantil. In L. S. Vygotsky, A. R. Luria & A. N. Leontiev (Eds.), Linguagem, desenvolvimento e aprendizagem (pp. 103-117). São Paulo: Ícone/EDUSP.
Lerman, S. (2001). Getting used to mathematics: Alternative ways of speaking about becoming mathematical. Ways of Knowing, 1(1), 47-52.
Lins Lessa, M. M., & Da Rocha Falcão, J. T. (2005). Pensamento e linguagem: Uma discussão no campo da psicologia da educação matemática. Psicologia, reflexão e crítica, 18 (3), 315-322.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.
Piaget, J. (1974). Réussir et comprendre. Paris: Presses Universitaires de France.
Polanyi, M. (1962). Personal knowledge. London: Routledge & Kegan Paul.
Polanyi, M. (1969). Knowing and being (M. Grene, Ed.). Chicago: Chicago University Press.
Ponte, J. P., & Matos, J. F. (1991). Cognitive processes and social interactions in mathematical investigations. In J. P. Ponte, J. F. Matos, J. M. Matos & D. Fernandes (Eds.), Mathematical problem solving: Research in the context of practice (pp. 239-254). Berlim: Springer-Verlag.
Romberg, T. A. (1992). Problematic features of the school mathematics curriculum. In P. W. Jackson (Ed.), Handbook for research on curriculum(pp.749-788). New York: MacMillan.
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.
Tirosh, D. (Ed.). (1994). Implicit and explicit knowledge: An educational approach. Norwood, NJ: Ablex Publishing Co.
Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10(23), 133-170.
Vergnaud, G. (1997). The nature of mathematical concepts. In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 5-28). London: Psychology Press.
Vergnaud, G. (2000). Que peut apporter l’analyse de l’activité à la formation des enseignants et des formateurs? Carrefours de l’éducation, 10, 49-63.
Vygotsky, L. S. (1986). Thought and language (A. Kozulin, Trans. Revised ed.). Cambridge: MIT Press.
Watson, A. (Ed.). (1998). Situated cognition and the learning of mathematics. Oxford: Centre for Mathematics Education, University of Oxford.
Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge: Cambridge University Press.
Wigner, E. P; Hodgkin, R.A.. (1997). “Michael Polanyi” in Biographical Memoirs of Fellows of the Royal Society, (Vol. 23, pp. 413-438). London: The Royal Society.
Winbourne, P. (2002). Looking for learning in practice: How can this inform teaching. Ways of Knowing, 2(2), 3-18.
Winbourne, P., & Watson, A. (1998). Learning mathematics in local communities of practice. In A. Watson (Ed.), Situated cognition in the learning of mathematics. Oxford: Centre for Mathematics Education Research, University of Oxford.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Frade, C., da Rocha Falcão, J. (2008). Exploring Connections Between Tacit Knowing And Situated Learning Perspectives In The Context Of Mathematics Education. In: Watson, A., Winbourne, P. (eds) New Directions for Situated Cognition in Mathematics Education. Mathematics Education Library, vol 45. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71579-7_10
Download citation
DOI: https://doi.org/10.1007/978-0-387-71579-7_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-71577-3
Online ISBN: 978-0-387-71579-7
eBook Packages: Humanities, Social Sciences and LawEducation (R0)