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The SimCalc Vision and Contributions pp 403–418Cite as

You Can Lead a Horse to Water…: Issues in Deepening Learning Through Deepening Teaching

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Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Teaching “well” is seen here not as an engineering problem in which specific practices are located and demonstrated to “work,” but rather as a human endeavor calling upon the whole of the human psyche: behavior, cognition, affect and attention. The construct of different forms of attention as different ways of attending to something is used to analyze data from the chapter by Bishop, in order to shed light on what can happen when students are expected to explain, elaborate, and evaluate for themselves. Other constructs used include metaphor and metonymy, reflection and “taking a reflexive stance” as vital to learning effectively, the ways in which teachers, students and mathematics each mediate in interactions between the other two to form six modes of interaction, and a four-fold structure of activity based on motivational and resource axes.

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References

  • Bachelard, G. (1980). La formation de l’esprit scientifique. Paris: J. Vrin. (Original work published in 1938.)

    Google Scholar 

  • Bennett, J. (1966). The dramatic universe. London: Routledge.

    Google Scholar 

  • Brentano, F. (1988). Philosophical investigations on space, time and the continuum (trans: B. Smith). Beckenham: Croom Helm. (Original work published in 1940.)

    Google Scholar 

  • Brousseau, G. (1984). The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics. In H. Steiner (Ed.), Theory of mathematics education (pp. 110–119). Bielefeld: Institut fur Didaktik der Mathematik der Universitat.

    Google Scholar 

  • Brousseau, G. (1997) Theory of didactical situations in mathematics: didactiques des mathématiques, 1970–1990 (trans: N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield). Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Christiansen, B., & Walther, G. (1986). Task and activity. In B. Christiansen, G. Howson, & M. Otte (Eds.), Perspectives in mathematics education (pp. 243–307). Dordrecht, The Netherlands: Reidel.

    Chapter  Google Scholar 

  • Cornu, B. (1991). Limits. In D. O. Tall (Ed.), Advanced mathematical thinking (pp. 153–166). Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Dainton, B. (2010). Temporal consciousness. In E. Zalta (Ed.), The Stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/fall2010/entries/consciousness-temporal.

    Google Scholar 

  • Davis, B. (1996). Teaching mathematics: towards a sound alternative. New York: Ablex.

    Google Scholar 

  • Davis, J., & Mason, J. (1988). Cognitive and metacognitive shifts. In A. Borbás (Ed.), Proceedings of 12th annual conference of the international group for the psychology of mathematics education (Vol. 2, pp. 487–494). Vezprém, Hungary: PME.

    Google Scholar 

  • diSessa, A. (1993). Many faces of a computational medium: teaching the mathematics of motion. In B. Jaworski (Ed.), Proceedings of the technology in mathematics teaching conference (pp. 23–38). Birmingham: University of Birmingham.

    Google Scholar 

  • Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht, The Netherlands: Freudenthal Institute.

    Google Scholar 

  • Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: a proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116–140.

    Article  Google Scholar 

  • Griffin, P. (1989). Teaching takes place in time, learning takes place over time. Mathematics Teaching, 126(1), 12–13.

    Google Scholar 

  • Hegel, G. (1975). Georg Willhelm Hegel: lectures on the philosophy of world history—an introduction (trans: H. Nisbet). Cambridge: Cambridge University Press. (Original work published in 1840.)

    Google Scholar 

  • Jakobson, R. (1951). Fundamentals of language (2nd ed.). Den Hague: Mouton de Gruyter.

    Google Scholar 

  • James, W. (1950). Principles of psychology. New York: Dover Publications. (Original work published in 1890.).

    Google Scholar 

  • Laborde, C. (1989). Audacity and reason: French research in mathematics education. For the Learning of Mathematics, 9(3), 31–36.

    Google Scholar 

  • Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press.

    Google Scholar 

  • Love, E., & Mason, J. (1992). Teaching mathematics: action and awareness. Milton Keynes: Open University.

    Google Scholar 

  • Marton, F., Hounsell, D., & Entwistle, N. (Eds.) (1997). The experience of learning (2nd ed.). Edinburgh: Scottish Academic.

    Google Scholar 

  • Mason, J. (1979). Which medium, which message. Visual Education, (Feb), 29–33.

    Google Scholar 

  • Mason, J. (1982). Attention. For the Learning of Mathematics, 2(3), 21–23.

    Google Scholar 

  • Mason, J. (1989). Mathematical abstraction seen as a delicate shift of attention. For the Learning of Mathematics, 9(2), 2–8.

    Google Scholar 

  • Mason, J. (1994). Researching from the inside in mathematics education: locating an I-You relationship. In J. Ponte & J. Matos (Eds.), Proceedings of 18th annual conference of the international group for the psychology of mathematics education (Vol. 1, pp. 176–194). Lisbon, Portugal: PME.

    Google Scholar 

  • Mason, J. (1998). Enabling teachers to be real teachers: necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267.

    Article  Google Scholar 

  • Mason, J. (2002). Mathematics teaching practice: a guide for university and college lecturers. Chichester: Horwood.

    Google Scholar 

  • Mason, J. (2007). Hyper-learning from hyper-teaching: what might the future hold for learning mathematics from and with electronic screens? Interactive Educational Multimedia, 14, 19–39.

    Google Scholar 

  • Mason, J., & Johnston-Wilder, S. (2004a). Designing and using mathematical tasks. Milton Keynes: Open University.

    Google Scholar 

  • Mason, J., & Johnston-Wilder, S. (2004b). Fundamental constructs in mathematics education. London: Routledge.

    Google Scholar 

  • McNair, K. (1978a). Capturing inflight decisions: thoughts while teaching. Educational Research Quarterly, 3(4), 26–42.

    Google Scholar 

  • McNair, K. (1978b). Thought and action: a frozen section. Educational Research Quarterly, 3(4), 16–25.

    Google Scholar 

  • Piaget, J. (2001). Studies in reflecting abstraction (trans: R. Campbell). Hove: Psychology Press. (Original work published in 1977.)

    Google Scholar 

  • Schön, D. (1983). The reflective practitioner: how professionals think in action. New York: Basic Books.

    Google Scholar 

  • Schorr, R., & Goldin, G. (2008). Students’ expression of affect in an inner-city SimCalc classroom. Educational Studies in Mathematics, 68(2), 131–148.

    Article  Google Scholar 

  • Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.

    Article  Google Scholar 

  • Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics, 14(1), 44–55.

    Google Scholar 

  • Sierpinska, A. (1994). Understanding in mathematics. London: Falmer Press.

    Book  Google Scholar 

  • Simon, M., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: an elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.

    Article  Google Scholar 

  • Stein, M., Remillard, J., & Smith, M. (2007). How curriculum influences student learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–370). Charlotte: Information Age.

    Google Scholar 

  • St. Maurice, H. (1991). A guide to commonplaces: on the use of loci in educator’s discourse. Journal of Curriculum Studies, 2-3(1), 41–54.

    Article  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(2), 151–169.

    Article  Google Scholar 

  • Treffers, A. (1987). Three dimensions, a model of goal and theory description in mathematics education. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Treffers, A., & Goffree, F. (1985). Rational analysis of realistic mathematics education: The Wiskobas program. In L. Streefland (Ed.), Proceedings of 9th annual conference of the international group for the psychology of mathematics education (Vol. 2, pp. 97–121). Utrecht, The Netherlands: PME

    Google Scholar 

  • Watson, A., & Mason, J. (1998). Questions and prompts for mathematical thinking. Derby: Association of Teachers of Mathematics (ATM).

    Google Scholar 

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Authors and Affiliations

  1. Department of Education, University of Oxford, Oxford, OX2 6PY, UK

    John Mason

  2. Department of Mathematics, Statistics and Computing, The Open University, Milton Keynes, Buckinghamshire, MK7 6AA, UK

    John Mason

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  1. John Mason
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Correspondence to John Mason .

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Editors and Affiliations

  1. University of Massachusetts, Mill Road 200, Fairhaven, 02719, Massachusetts, USA

    Stephen J. Hegedus

  2. Center for Technology in Learning, SRI International, Ravenswood Avenue 333BN-376, Menlo Park, 94025, California, USA

    Jeremy Roschelle

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Mason, J. (2013). You Can Lead a Horse to Water…: Issues in Deepening Learning Through Deepening Teaching. In: Hegedus, S., Roschelle, J. (eds) The SimCalc Vision and Contributions. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5696-0_22

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