Discourse, Cognition, and Chaotic Systems: An Examination of Students' Argument About Density

This article examines an extended argument about density among a small, multi-graded, middle school class of 10 studeWnts. The argument is examined from several perspectives with the primary focus on (a) the argument as an example of a chaotic and complex system, (b) the emerging development of understandings, and (c) the underlying cognitive structures affecting the students' understandings. Student talk during the class sessions were audio and videotape recorded. Each group of 3 or 4 students was individually audio recorded. A single video recorder was used to capture excerpts of each group's dialogue, as well as intergroup dialogue. The argument began after students predicted which of an assortment of different objects would or would not float. The specific case of a block of ebony initiated the argument and acted as the initial attractor, which developed into 2 opposing assertions: 1 side proposing that the pressure on a larger volume of water affects the density and the other side proposing that the molecules of water cannot be compressed. Extensive conceptual development occurred as the argument progressed with a variety of bifurcation points leading to new but related conceptual themes and higher levels of complexity. Several underlying structures, which have been referred to as interpretive frameworks (Bloom, 1992a) and p-prims (diSessa, 1993), played a central role in the development of both understandings and the argument itself. Such interpretive frameworks included (a) uniformity of molecular size and weight across different substances, (b) directionality of pressure, (c) external forces (e.g., gravity) affect pressure, (d) pressure affects density, and (e) surface area affects action of external forces on pressure.