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

## 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.

## Keywords

Mathematics teaching Teaching as activity Activity theory Expanded meditational triangle Macroanalysis Microanalysis Teaching triad## References

- Abboud-Blanchard, M., Cazes, C., & Vandebrouck, F. (2007). Teachers’ activity in exercises-based lessons: Some case studies. In D. Pitta- Pantazi, & G. Philippou (Eds.),
*Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education*(pp. 1827–1836). Cyprus: University of Cyprus.Google Scholar - Bartolini Bussi, M. G. (1998). Verbal interaction in the mathematics classroom: A Vygotskian analysis. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.),
*Language and communication in the mathematics classroom*(pp. 65–84). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Boaler, J., & Wiliam, D. (2001). ‘We’ve still got to learn!’ Student’s perspectives on ability grouping and mathematical achievement. In P. Gates (Ed.),
*Issues in mathematics teaching*(pp. 77–92). London: Routledge.Google Scholar - Chazan, D. (2000).
*Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom*. New York: Teacher’s College Press.Google Scholar - Christiansen, B., & Walther, G. (1986). Task and activity. In B. Christiansen, B. Howson, & M. Otte (Eds.),
*Perspectives on mathematics education*(pp. 243–307). Dordrecht: Reidel.Google Scholar - Cobb, P., Yackel, E., & Wood, T. (1992). Interaction and learning in mathematics classroom situations.
*Educational Studies in Mathematics*,*23*, 99–122. doi: 10.1007/BF00302315.CrossRefGoogle Scholar - Cole, M., & Engeström, Y. (1993). A cultural-historical approach to distributed cognition. In G. Salomon (Ed.),
*Distributed cognition: Psychological and educational considerations*(pp. 1–46). New York: Cambridge University Press.Google Scholar - Daniels, H. (2001).
*Vygotsky and pedagogy*. London: Routledge Falmer.Google Scholar - Engeström, Y. (1998). Reorganising the motivational sphere of classroom culture: An activity-theoretical analysis of planning in a teacher team. In F. Seeger, J. Voigt, & U. Waschescio (Eds.),
*The Culture of the Mathematics Classroom*(pp. 76–103). Cambridge: Cambridge University Press.Google Scholar - Engeström, Y., & Cole, M. (1997). Situated cognition in search of an agenda. In J. A. Whitson, & D. Kirshner (Eds.),
*Situated cognition. Social, semiotic, and psychological perspectives*(pp. 301–309). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Jaworski, B. (1994).
*Investigating mathematics teaching: A constructivist enquiry*. London: Falmer.Google Scholar - Jaworski, B. (1998). Mathematics teacher research: Process, practice and the development of teaching.
*Journal of Mathematics Teacher Education*,*1*, 3–31. doi: 10.1023/A:1009903013682.CrossRefGoogle Scholar - Jaworski, B., & Goodchild, S. (2006). Inquiry community in an activity theory frame. In J. Navotná, H. Moraová, M. Krátká, & N. Stehliková (Eds.),
*Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education*(Vol. 3, pp. 353–360). Prague: Charles University.Google Scholar - Kieran, C., Forman, E., & Sfard, A. (2001). Bridging the individual and the social: Discursive approaches to research in mathematics education.
*Educational Studies in Mathematics*,*46*, 1–3. doi: 10.1023/A:1014276102421.CrossRefGoogle Scholar - Leont’ev, A. N. (1979). The problem of activity in psychology. In J. V. Wertsch (Ed.),
*The concept of activity in soviet psychology*(pp. 37–71). New York: M. E. Sharpe.Google Scholar - Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm.
*Journal for Research in Mathematics Education*,*27*, 133–150. doi: 10.2307/749597.CrossRefGoogle Scholar - Lerman, S. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics.
*Educational Studies in Mathematics*,*46*, 87–113. doi: 10.1023/A:1014031004832.CrossRefGoogle Scholar - Lerman, S., Xu, G., & Tsatsaroni, A. (2002). Developing theories of mathematics education research: The ESM story.
*Educational Studies in Mathematics*,*51*, 23–40. doi: 10.1023/A:1022412318413.CrossRefGoogle Scholar - Mellin Olsen, S. (1987).
*The politics of mathematics education*. Dordrecht: D. Reidel.Google Scholar - Potari, D., & Jaworski, B. (2002). Tacking complexity in mathematics teaching development: Using the teaching triad as a tool for reflection and analysis.
*Journal of Mathematics Teacher Education*,*5*, 351–380. doi: 10.1023/A:1021214604230.CrossRefGoogle Scholar - Seeger, F., Voigt, J., & Waschescio, U. (1998).
*The culture of the mathematics classroom*. Cambridge: Cambridge University Press.Google Scholar - Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers.
*Journal of Mathematics Teacher Education*,*1*, 157–189. doi: 10.1023/A:1009984621792.CrossRefGoogle Scholar - Valero-Dueñas, P. X. (2002).
*Reform, democracy and mathematics education: Towards a socio-political frame for understanding change in the organisation of secondary school mathematics*. Unpublished PhD thesis. The Danish University of Education, Denmark.Google Scholar - Van Oers, B. (2001). Educational forms of initiation in mathematical culture.
*Educational Studies in Mathematics*,*46*, 59–85. doi: 10.1023/A:1014031507535.CrossRefGoogle Scholar - Voigt, J. (1996). Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.),
*Theories of mathematical learning*(pp. 21–50). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Wertsch, J. V., & Lee, B. (1984). The multiple levels of analysis in a theory of action.
*Human Development*,*27*, 193–196.Google Scholar - Wertsch, J. V., del Rio, P., & Alvarez, A. (1995). Sociocultural studies: History, action and mediation. In J. V. Wertsch, P. del Rio, & A. Alvarez (Eds.),
*Sociocultural studies of the mind*(pp. 1–34). Cambridge: Cambridge University Press.Google Scholar