Sociological tools in the study of knowledge and practice in mathematics teacher education

Abstract

In this paper, we put Basil Bernstein’s theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is our focus, the particular example provides a compelling story at the heart of which is the problem of integration of knowledge(s) within a pedagogic practice. Here, a constructivist pedagogy is at work, but differentially with respect to teaching/learning mathematics and teaching/learning mathematics teaching. The example illuminates mathematics and teaching, and their co-constitution in a particular pedagogic context.

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Notes

  1. 1.

    As Graven (2002) explains, “in educational terms, Bernstein’s use of the terms ‘transmitter’ and ‘acquirer’ may seem pejorative. However, he uses them throughout various pedagogic models and they are merely sociological labels for descriptive purposes. They should therefore not be interpreted to imply transmission pedagogies”. (Ch. 2, p. 28).

  2. 2.

    Elsewhere (Adler & Davis, 2006), we discuss how the internal grammar of these fields varies considerably from very strong (e.g. instances of ‘pure mathematics’) to very weak (e.g. instances of teaching as grounded in ‘experience’), and the impact of these on their integration in mathematics teacher education practice.

  3. 3.

    Note that the process does not include the normal checking of a solution against the original problem which would be typical of this kind of problem, and would generally be expected. However within this context the meaning is contingently fixed.

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Acknowledgments

This paper forms part of the Quantum research project on Mathematics for Teaching, directed by Jill Adler, at the University of the Witwatersrand. This material is based upon work supported by the National Research Foundation under Grant number FA2006031800003.

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Any opinion, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Research Foundation.

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Correspondence to Jill Adler.

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The study reported here was part of a PhD taken at the University of the Witwatersrand

Appendix 1

Appendix 1

Eight forms of pedagogic interaction used to analyse a particular evaluative event:

  • whole class discussions: where there is interaction amongst students and the lecturer which focuses on a specific idea/example etc, where varied input is welcomed from all parties, and ideas are developed;

  • small group discussions/work: where students sit in small groups and discuss ideas/examples amongst themselves; where students work together on a problem;

  • individual work: where students sit on their own and independently work on a problem/reproduction;

  • lecturer exposition: lecture/expository teaching, where the lecturer presents ideas, examples, and so on, explaining ideas and showing procedures or methods that would lead to reproductions of the legitimate text;

  • lecturer question and answer: lecturer-controlled questioning and answer sessions, where the lecturer elicits answers to specific questions in order to evaluate specific texts;

  • student presentations: where students address the whole class and present a specific piece of work, e.g. writing a solution on the board and explaining it to all;

  • lecturer questions: where the lecturer interacts with students on an individual or small group or whole group basis, asking questions, not to elicit answers, but to get them to consider possibilities/evaluate their own thinking and promote discussion

  • student questioning: nontrivial student questioning, where students independently ask probing questions of the lecturer, without the questions being elicited by the lecturer—these are not simple questions for purposes of clarification

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Parker, D., Adler, J. Sociological tools in the study of knowledge and practice in mathematics teacher education. Educ Stud Math 87, 203–219 (2014). https://doi.org/10.1007/s10649-012-9421-y

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Keywords

  • Mathematics teacher education
  • Pedagogic device
  • Knowledge and practice
  • Evaluative judgement