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School Practices With The Mathematical Notion Of Tangent Line

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Part of the book series: Mathematics Education Library ((MELI,volume 45))

Abstract

We seek to understand the process of learning mathematical notions as forms of practice in the classrooms of two different technical school courses. More specifically, we investigate students’ and teachers’ experiences and use of the mathematical concept of tangent line in these different contexts. We use empirical data collected through non-participant observation, analysis of students’ written responses to a questionnaire, and semi-structured interviews with groups of six students from each course observed. We take a situated perspective of learning which enables us to see these classroom activities as genuinely mathematical, though distinct. Through our analysis, we describe aspects of what we see as the common direction of learning mathematics in the two vocational course lessons; this is found to be closer to ‘being mathematical’ in work settings than in school mathematics classrooms.

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References

  • Adler, J. (1998). Lights and limits: Recontextualising Lave and Wenger to theorise knowledge of teaching and of learning school mathematics. In A. Watson (Ed.), Situated cognition and the learning of mathematics (pp. 161-177). Oxford: University of Oxford, Centre for Mathematics Education Research.

    Google Scholar 

  • Lave, J. (1996). Teaching, as learning, in practice. Mind, Culture and Activity, 3(3), 149-164.

    Article  Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning. Legitimate peripheral participation. Cambridge: Cambridge University Press.

    Google Scholar 

  • Magajna, Z. (1998). Formal and informal mathematical methods in working settings. In A. Watson (Ed.), Situated cognition and the learning of mathematics (pp. 59-70). Oxford: Centre for Mathematics Education.

    Google Scholar 

  • Magajna, Z., & Monaghan, J. (2003). Advanced mathematical thinking in a technological workplace. Educational Studies in Mathematics, 52(2), 101-122.

    Article  Google Scholar 

  • Moreira, V. G. (2004). Comunidades de prática da matemática no ensino médio técnico. Unpublished Master Dissertation. Faculty of Education. Universidade Federal de Minas Gerais, Brazil.

    Google Scholar 

  • Moreira, V. G., & Pinto, M. M. F. (2004). Technical school students’ conceptions of tangent lines. In Proceedings of 28 conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 33-40). Haifa, Israel: PME..

    Google Scholar 

  • Moreira, V. G., Sampaio, V., Cardoso, R., Almeida, A., Prado, H., Zumpano, A., & Pinto, M. M. F. (2001). Investigando a Transição da Matemática da Escola Elementar para a da Universidade. Poster Presentation. Scientific Week, Universidade Federal de Minas Gerais, Brazil.

    Google Scholar 

  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(1), 151-169.

    Article  Google Scholar 

  • Vinner, S. (1991). The role of definition in teaching and learning mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer.

    Google Scholar 

  • Winbourne, P., & Watson, A. (1998). Participating in learning mathematics through shared local practices in classrooms. In A. Watson (Ed.), Situated cognition and the learning of mathematics (pp. 93-104). Oxford: Centre for Mathematics Education Research, University of Oxford.

    Google Scholar 

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Pinto, M., Moreira, V. (2008). School Practices With The Mathematical Notion Of Tangent Line. 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_12

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