Solving problems to learn concepts, how does it happen? A case for buoyancy

Problem solving is a preferred activity teachers choose to help students learn concepts. At the same time, successful problem solving is widely regarded as a very good indicator of conceptual learning. Many studies have provided evidence that problem solving often improves students’ chances of learning concepts. Still, the question remains relatively unexplored as to how this activity is useful to promote concept learning. In this study we explore this question in the setting of three university students solving a problem on hydrostatics, in which the concept of buoyancy is involved. We use coordination class theory to study how these students progress on their conceptual understanding. We were able to describe how this progress is related to contextual traits, as well as to students’ particular epistemic stances. Finally, we discuss some implications for research and for teaching.

Figure 1

The problem posed to students. Adapted from Leonard et al. 19].

Figure 2

Schematic representation of theoretical elements that constitute a coordination class.

Figure 3

Schematic diagrams of the three projections reported in ${\mathbf{S}}_{\mathbf{1}}$. (a) No buoyancy on sunk cube, (b) nonzero buoyancy for sunk sphere, and (c) nonzero buoyancy for either sunk body.

Figure 4

Schematic diagram of the projection described in ${\mathbf{S}}_{\mathbf{2}}$.

Figure 5

Analogy proposed by students. The case C’, in which the force “supporting” the metal cube is smaller than in case A.

Figure 6

Schematic diagram of the projection described in ${\mathbf{S}}_{\mathbf{3}}$.

Figure 7

Model proposed by the students from a “microscopic” point of view. ($P_1$ and $P_2$ are pressures, $P$ is weight, $N$ is normal force, and $E$ stands for buoyancy).

Figure 8

Schematic diagram of projection described in ${\mathbf{S}}_{\mathbf{4}}$.