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Bridging the macro- and micro-divide: using an activity theory model to capture sociocultural complexity in mathematics teaching and its development

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Abstract

This paper is methodologically based, addressing the study of mathematics teaching by linking micro- and macro-perspectives. Considering teaching as activity, it uses Activity Theory and, in particular, the Expanded Mediational Triangle (EMT) to consider the role of the broader social frame in which classroom teaching is situated. Theoretical and methodological approaches are illustrated through episodes from a study of the mathematics teaching and learning in a Year-10 class in a UK secondary school where students were considered as “lower achievers” in their year group. We show how a number of questions about mathematics teaching and learning emerging from microanalysis were investigated by the use of the EMT. This framework provided a way to address complexity in the activity of teaching and its development based on recognition of central social factors in mathematics teaching–learning.

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Notes

  1. We follow Bartolini Bussi (1998) in using “teaching–learning” as a unifying concept in addressing activity in classroom situations.

  2. “Ability grouping in mathematics is deeply embedded into school practices and British traditions” (Boaler & William, 2001, p. 80).

  3. Working turn by turn on a transcript of interaction, triangulating with interview and other data, and relating to the teaching triad (Potari & Jaworski, 2002).

  4. There is growing literature relating to the concept and nature of homework, especially for low achieving pupils (see, for example, Chazan 2000). However, a deeper analysis relating to the homework issue is beyond the scope of this paper.

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Authors and Affiliations

  1. Mathematics Education Centre, Loughborough University, Loughborough, LE11 3TU, UK

    Barbara Jaworski

  2. University of Athens, Athens, Greece

    Despina Potari

Authors
  1. Barbara Jaworski
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  2. Despina Potari
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Correspondence to Barbara Jaworski.

Appendix: One set of cards for the task on averages given in Sam’s lesson

Appendix: One set of cards for the task on averages given in Sam’s lesson

Card 1: The sum of the numbers divided by the number of numbers.

Card 2: The middle number after the numbers have been arranged in order of size.

Card 3: One item or number that represents the whole group.

Card 4: The most popular item or the item that occurs the most often.

Card 5: The…of 2, 4, 1, 3, 4, 1, 5 is 4 because the highest number is 5 and the lowest is 1.

Card 6: The…is 5 − 1 = 4.

Card 7: The difference between the highest and lowest number.

Card 8: The…of 2, 0, 1, 3, 4, 1, 5 is 1 because there are more 1’s than any other item.

Card 9: The…of 1, 4, 3, 0, 1, 2, 1, 4 is (1+…+4) ÷8 = 16 ÷ 8 = 2.

Card 10: The…of 2, 0, 1, 3, 4, 1, 5 is found from 0, 1, 1, 2, 3, 4, 5. 2 is the…because it’s in the middle.

Card 11: The…of 2, 0, 1, 3, 4, 1, 5, 3 is found from 0, 1, 1, 2, 3, 3, 4, 5. Numbers 2 and 3 are both in the middle so the… is 2 1/2.

The above set of cards emphasized the definition of the statistical terms (cards 1, 2, 3, 4, 7), and the process through examples of calculating the specific averages (cards 5, 6, 8, 9, 10, 11). The students had to build meaning of the statistical terms by linking the verbal symbol, the definition and the example.

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Jaworski, B., Potari, D. Bridging the macro- and micro-divide: using an activity theory model to capture sociocultural complexity in mathematics teaching and its development. Educ Stud Math 72, 219–236 (2009). https://doi.org/10.1007/s10649-009-9190-4

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