Abstract
The analysis reported in this article is grounded in the practice of classroom-based developmental or transformational research and focuses on the distributed views of intelligence developed by Pea (1993) and by Hutchins (1995). The general areas of agreement with this theoretical perspective include both the nondualist orientation and the critical role attributed to tool use. Against this background, I focus on two aspects of the distributed view that I and my colleagues have found necessary to modify for our purposes. The first concerns the legitimacy of taking the individual as the unit of analysis, and here I argue that the distributed view implicitly accepts key tenets of mainstream American psychology’s characterization of the individual even as it explicitly rejects it. The second modification concerns distributed intelligence’s characterization of tool use. Drawing on a distinction made by Dewey, I argue that it is more useful for the purposes of instructional design to focus on activity that involves using the tool as an instrument, rather than focusing on the tool itself.
Mind, Culture, and Activity, 5 (1998), 187–204.
Copyright © 1998, Regents of the University of California on behalf of the Laboratory of Comparative Human Cognition
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Notes
- 1.
I repeatedly use the first-person plural to acknowledge the collaborative nature of our research. From 1986 until 1991, these colleagues were Ema Yackel and Terry Wood, and from 1991 until the present they are Ema Yackel, Koeno Gravemeijer, Janet Bowers, Kay McClain, and Joy Whitenack.
- 2.
These provisional sequences provide an initial orientation for the teaching experiment. Adaptations and modifications are made on a daily basis throughout the experiment so that the actual sequences realized in the classroom typically differ significantly from those envisioned at the outset.
- 3.
Coming to reason with groups of beads rather than counting beads one by one is itself a developmental achievement for young children. We supported the development of these ways of reasoning in the teaching experiment by designing an instructional sequence called Patterning and Partitioning. This sequence was enacted in the classroom immediately before the arithmetic rack was introduced.
- 4.
Psychological analyses almost universally report a developmental progression of increasingly sophisticated counting methods (e.g., counting all and counting on) followed by thinking strategies. The purview of these analyses is, of course, restricted to students who participate in currently institutionalized classroom practices.
- 5.
Although atypical in the United States, this approach of monitoring students’ activity to plan for the subsequent whole-class discussion is routine in Japan (Stigler, Fernandez, & Yoshida, 1996).
- 6.
Judgments of mathematical significance are made with respect to current conjectures about the classroom community’s learning trajectory and the means of supporting it. In other words, although goals and conjectures continue to evolve throughout the experiment, one has in mind an envisioned learning trajectory at any particular point in the experiment. The currently anticipated learning trajectory both provides a sense of direction and constitutes the broader setting in which judgments of mathematical significance are made. In particular, an issue is judged to be mathematically significant if it contributes to the realization of the currently envisioned learning trajectory. Our observations of the subsequent whole-class discussion can, however, lead us to revise this judgment and to modify the conjectured learning trajectory. As a consequence, the actual learning trajectory realized in the classroom is enacted jointly by the students, the teacher, and the researchers. To paraphrase Varela, Thompson, and Rosch (1991), it is much like a path that exists only as it is laid down by walking, even though we have a sense of where we are going and how we might get there at each moment.
- 7.
This is particularly the case with Hutchins (1995), whose book is directed primarily toward cognitive scientists.
- 8.
Some years ago, we described this relation as dialectical. However, German colleagues noted that, in their country, the use of the term dialectical is often viewed as indicating a commitment to the philosophy of dialectical materialism. To avoid such confusions, we prefer to speak of reflexive rather than dialectical relations.
- 9.
It is important to stress that the issue at hand is not that of coordinating two sets of separate processes—one psychological and the other communal. Instead, we coordinate different ways of interpreting and describing classroom activity.
- 10.
As stated at the outset, the interests that motivate this discussion are those of instructional design and reform at the classroom level. It should however be acknowledged that mathematical knowing is social through and through in a second sense. In particular, generally accepted beliefs about what counts as normal in development and as more and less sophisticated are themselves social constructions that are reflexively verified in practice (Cobb & Yackel, 1996; Walkerdine, 1988).
- 11.
In doing so, we took a psychological perspective and focused on individual students’ qualitatively distinct ways of participating in classroom mathematical practices. In contrast, we adopted a social perspective when we planned the instructional sequence and envisioned the evolution of taken-as-shared, communal ways of reasoning with the arithmetic rack.
- 12.
Strictly speaking, this focus on experience is redundant: The world acted in is the world experienced. I have used the term experience to differentiate the world-acted-in from what an observer might take to be the environment that can be analyzed independently of activity in propositional terms.
- 13.
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Acknowledgments
The analysis reported in this article was supported by the National Science Foundation under Grant RED-9353587 and by the Office of Educational Research and Improvement under Grant R305A60007. The opinions expressed do not necessarily reflect the views of either the Foundation or of OERI.
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Cobb, P. (2010). Learning from Distributed Theories of Intelligence. In: Sfard, A., Gravemeijer, K., Yackel, E. (eds) A Journey in Mathematics Education Research. Mathematics Education Library, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9729-3_7
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