Torquetum

 

Black et al use concepts from cultural historical activity theory (CHAT) to develop a theory of identity which is associated with shifting hierarchies of motives within the individual. A student’s evolving sense of self and relationship with mathematics affects their mathematical identity and hence their level of engagement with mathematical studies. Black et al explore two key aspects, namely “how [students] perceive doing mathematics fits with ‘other’ motives – particularly, their understanding of themselves in relation to future aspirations” and “how a connection between future aspirations and ‘mathematical identity’ shifts or changes over time as students progress [through their studies]” (p. 56).

 

In CHAT there is a notion of leading activity (credited to Leont’ev). CHAT “views identity as emerging from engagement in joint object-oriented and socio-culturally mediated ‘activity’” (p. 56). The theory (as I understand it) is that we, throughout our lives, encounter a wide variety and great number of activities. We are a unique product of these “constellations” of activities and experience a variety of motives associated with these activities. These motives and associated “subjectivities” form a hierarchy. Each activity and associated motive forms part of an identity, where we each draw upon a hierarchical collection of identities. Some activities are more significant in one’s development than others, specifically any activity which brings about a change in motive as to why one is carrying out the activity is called a leading activity. Black et al, here adding to existing CHAT concepts, suggest calling the identity invoked by the leading activity and associated motives, a leading identity. A leading activity shapes “psychic processes to the extent that development is essentially dependent on such activities” (p. 57).

 

By understanding (naming? locating? identifying?) a student’s leading identity it may inform the teacher of the student’s understanding of self and his/her trajectory. The authors cite Leont’ev in saying “activities become leading when new motives are generated so that the original motive of actions is surpassed by a new motive, and hence, a new activity” (p. 57). The notion of leading activity can form a useful methodological tool for understanding periods of transition.

 

This approach to identity differs from others in two major respects

1. While the authors acknowledge multiple simultaneous identities as do other scholars, the notion of leading identity indicates an identity which is more significant that others in that it suggests changes in a hierarchy of motives and associated developmental change.

2. Framing developmental change and notions of identity through CHAT allows access to theories of social psychology and socio-situated processes.

 

Motives are derived from aspirations. In order to bring about a change in motive towards studying mathematics and development of a leading identity related to enjoyment of mathematics, there needs to be an aspiration to study mathematics for more than the “exchange value” of good grades. There needs to be an understanding of the long-term “use value” (and labour power) of mathematics and it is the challenge of the instructor and course designer to come up with and design activities which will become leading activities.

 

“[I]t is important that teachers, colleges and policymakers recognise the varied motives students have for studying mathematics. By seeking to understand the particular motive or identity which may be leading for the student at a given point in time, there is much to be gained in terms of offering tailored support and appropriate ways of teaching and learning mathematics. Therefore, we suggest a move away from strategies which focus on maximising the exchange value of grades” (p. 71).

 

Boaler, J. (2002) Exploring the nature of mathematical activity; using theory, research and ‘working hypotheses’ to broaden conceptions of mathematics knowing, Educational Studies in Mathematics, 51, 1-2, 3 – 21.

Boaler, J., Greeno, J. (2000) Identity, agency and knowing in mathematical worlds, in J. Boaler (Ed.) Multiple Perspectives on Mathematics Teaching and Learning (pp. 45 – 82). Westport: Ablex.

Solomon, Y. (2007) Not belonging? What makes a functional learner identity in the undergraduate mathematics community of practice? Studies in Higher Education, 32, 1, 79 – 96.

Williams, J. (2008) Towards a theory of value in education. Paper presented at the Society for Research in Higher Education Conference, Liverpool, December.

William, J., Davis, P., Black, L. (2007) Sociocultural and Cultural Historical Activity Theory perspectives on subjectivities and learning in schools and other educational contexts. International Journal of Educational Research, 46, 1-2, 1 – 7.