Activity Theory in Mathematics Education
KeywordsVygotsky Leont’ev Dialectics Consciousness Personality Change
Activity theory is the result of an attempt to construct a psychology that draws on and concretely implements epistemological principles of materialist dialectics as K. Marx presented them (Leont’ev 1978; Vygotsky 1997). Like Marx’s Das Kapital, activity theory is intended to explain change, learning, and development as an immanent feature of a system rather than in terms of externally produced cause-effect relations.
History of Activity Theory
L. S. Vygotsky generally is recognized as the founding father of activity theory because he introduced the idea of tool-mediated activity as a way of overcoming on-going psychological ideas consistent with stimulus–response or disembodied thinking approaches to cognition. Responding to the crisis of psychology, he explicitly stated the need for developing a Marxist psychology. Expanding on Vygotsky’s work, A. N. Leont’ev articulated what is now known as second-generation cultural-historical activity theory in his Activity, Consciousness, and Personality (Leont’ev 1978), in which the first two chapters are devoted to establish the Marxist foundation of the theory. The third-generation activity theory was formulated in two different lineages. The Helsinki version originally established by Y. Engeström (1987) focuses on the structural-systemic aspects of activity, whereas the Berlin version, developed by K. Holzkamp (1993) and his colleagues, is a subject-oriented psychology that focuses on the person and consciousness. Fourth-generation cultural-historical activity theory builds on both third-generation versions and also includes emotions (affect) and ethics as irreducible fundamental moments of human activity (Roth and Lee 2007).
Scenario 1: Connor and his peers in a second-grade mathematics class sort objects into groups, which become constitutive of geometrical relations within and between the objects.
Scenario 2: Erica, a fish culturist, talks about the production of coho salmon smolt to be released into the river to increase natural stocks; she monitors and controls the production process using a spreadsheet-based database and mathematical functions such as graphs, histograms, and mathematical functions (e.g., to calculate amount of food).
Structure of Activity
Central to activity theory is the transformation of the object into a product, which initially only consists ideally. The intended transformation is the motive of activity. Activity theorists therefore speak of the object/motive; this makes thematic the in-order-to nature of all human activity. By definition, this category includes both material (the materials started with) and ideal dimensions (e.g., the envisioned product). For Erica, the intended outcome is clear. She wants to end the work cycle with a healthy brood of about one million coho salmon, with an average weight per specimen of about 20 g. In contrast, the second-grade students do not know the intended outcome of their task; and they are not likely aware of the ultimate motive of schooling (Roth and Radford 2011). As a result, they have to engage in the activity constituting task without knowing its object/motive. With respect to the task, they can become conscious of the reasons for doing what they do – that is, they can become aware of the goal – only when they have completed their task. It is when they realize the grouping in Fig. 2 that they can come to understand why the teacher, for example, asked Connor to rethink his actions when he placed one of the squares with the rectangles rather than with the other squares.
Subjectification and Personality
Cultural-historical activity theory allows us to understand two developmental processes. On the one hand, when a person participates in an activity, such as Connor in schooling or Erica in producing young coho salmon, they undergo subjectification. This concept names the process by means the person, together with everything else that makes the activity system, undergoes change. This change can be noted as the emergence of new capacities for actions of a body together with new forms of talk, neither of which has been identifiable previously. Together, these changes in objects, bodies, and forms of talk reconfigure the field of experience. Thus, for example, as Erica uses the spreadsheet to track and model the coho salmon population, she becomes more proficient with spreadsheets, mathematical models, calculating feed needs, graphs, histograms, and calculations. With these changes, her entire field of experience is reconfigured. Most importantly, activity theory does not allow us to speak of her development independent of everything else at her worksite; her transformation also means transformation of the entire field.
For Erica, working in the hatchery is only part of her everyday life, just as for Connor going to school is only part of his everyday life. Both participate in many other activities: as family members, shoppers, participants in leisure activities, or as members in urban traffic systems. That is, in the course of their everyday lives, both contribute to realizing other object/motives other than producing a population of young coho salmon and doing schooling. Leont’ev introduced the category personality to integrate all these object/motives that an individual takes on when participating in the correlated activities. Thus, personality is understood as a network of societal object/motives. That is, personality is made up of an ensemble of collective object/motives. However, each network is highly individual. Personality, therefore, is utterly singular while being entirely constituted by societal/collective moments.
A Holistic Psychology
Cultural-historical activity theory is a holistic approach to psychology. It does not reduce the individual to its thoughts (mental constructions). It in fact integrates body and mind, on the one hand, and individual and collective, on the other hand (Vygotsky 1989). It focuses on change as inherent in life and society and, therefore, inherent in individual life and understanding. That is, everything we do has to be understood in terms of this intersection of dimensions, which manifest themselves in mutually excluding ways: mind versus body, individual versus society, and the natural world versus the social world. The developments at the different timescales also are irreducible and therefore mutually constitute each other. The moment-to-moment changes – e.g., the transformation of a collection of objects in the second-grade mathematics classroom or the entering of fish size and weight into the database – are related to the development of system and people (i.e., subjectification) over time, and because people and systems are part of society, the cultural-historical changes of the human life form.
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