Abstract
This paper investigates the construction of systems of competence in two middle school mathematics classrooms. Drawing on analyses of discourse from videotaped classroom sessions, this paper documents the ways that agency and accountability were distributed in the classrooms through interactions between the teachers and students as they worked on mathematical content. In doing so, we problematize the assumption that competencies are simply attributes of individuals that can be externally defined. Instead, we propose a concept of individual competence as an attribute of a person's participation in an activity system such as a classroom. In this perspective, what counts as “competent” gets constructed in particular classrooms, and can therefore look very different from setting to setting. The implications of the ways that competence can be defined are discussed in terms of future research and equitable learning outcomes.
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Notes
This move simultaneously serves to reinforce the relative power difference between teacher and students by indexing the teacher's position relative to the student as the person who is responsible for determining the flow of activity and the direction of the discussion (Lemke 1990). Although students can also utter the same words, the meaning of such an utterance is slightly different as it does not (usually) promise the same kinds of potential outcomes (namely, good grades). In some rare classrooms this structure can be disrupted, but it is difficult to imagine a complete reversal of these positions.
A person's agency in a brief episode of interaction is, in part, whether he or she initiates an idea, agrees with, elaborates on, questions, or disagrees with what someone else initiated, or refrains from responding. It also depends on whether her or his action is accepted, elaborated, questioned, challenged, or ignored.
Here, we are talking about characteristic ways of engaging in the classroom, at the level of what Cobb and his colleagues (Cobb and Yackel, 1998; Forman 1996; Yackel and Cobb, 1996) call social norms. Learning, as we and others conceive of it, can be seen through individual students' changes in participation with respect to particular content (c.f. Lave and Wenger 1991). Thus, although often students have characteristic ways of participating in the classroom activity system (c.f. Gresalfi 2004), their participation may change, particularly with respect to their engagement with particular ideas. These processes are intermingled, as students' participation with the social norms of the classroom (i.e. tendency to justify ideas or not) shapes the ways that she might engage with particular mathematical ideas, and vice versa.
However, whether the inference of competence is justified by a positive evaluation of performance depends on the way in which the participants attribute causality for the valuable contribution. For example, that inference can be qualified or negated if there is evidence of a different causal attribution (e.g., “That was a lucky guess”).
It is important to note here that although we have focused on how competence is constructed at the level of the classroom, this does not mean that all student behaviors in the classroom are likely to be positioned in exactly the same way. Although this was not the focus of our analysis, it is likely that individual experiences, such as students' histories in the classroom, their sensitivities to particular kinds of opportunities to participate, or even membership in particular racial, ethnic, or gender groups, could shape the likelihood of particular students being reified as competent (or not; c.f. Jungwirth 1991).
Of particular concern is an issue raised by Stein et al. (2000), and others, who note that it is far too common for teachers, in their attempt to make their expectations clear to their students, to limit the cognitive demand of tasks. In such cases, students end up following a set of prescribed rules or steps, rather than engaging in a task that involves meaning-making.
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This research was supported by a grant from the U.S. National Science Foundation. We are grateful that this project afforded collaboration with Frank Davis, Mary Maxwell West, and Robert Moses.
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Gresalfi, M., Martin, T., Hand, V. et al. Constructing competence: an analysis of student participation in the activity systems of mathematics classrooms. Educ Stud Math 70, 49–70 (2009). https://doi.org/10.1007/s10649-008-9141-5
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DOI: https://doi.org/10.1007/s10649-008-9141-5