Learning entropy among peers through the lens of coordination class theory

Coordination class theory has proven to be a useful theoretical framework for describing processes of conceptual change in certain physical and mathematical concepts. Its development throughout different studies has allowed us to understand numerous mechanisms of conceptual learning by individual subjects. There have been attempts to implement this theory to collective-learning environments. Although there are valuable contributions in this sense, there are still details at the fine-grain level to be unveiled in relation to how conceptual change proceeds within small groups. For this purpose, the development of a coordination class is analyzed in the case of an interview with two students addressing a problem-solving task about entropy, focusing on the role that interactions between participants play in the evolution of the entropy concept. A microcomplementary analysis is proposed by bringing in elements from a sociocultural approach of learning. Thus, we were able to identify different forms of codevelopment of a coordination class. Students exhibiting central as well as peripheral participation benefit from each other during the conceptual learning process of the small group, constituting a “virtuous” interaction for learning.

Figure 1

Schematic representation of theoretical elements that constitute a coordination class.

Figure 2

Problem given to students.

Figure 3

Development of the entropy class during segment 1. $F$’s contributions in blue frames, $D$’s contributions in red frames, where $S_{\mathrm{gas}}$ stands for the entropy of the gas and ΔS the entropy variation.

Figure 4

Students’ intervention types during segment 1.

Figure 5

Students’ sketch during segment 2.

Figure 6

Diagram of the projection development during segment 2. In blue, $F$’s contributions.

Figure 7

Students interventions during the whole segment 2.

Figure 8

Articulation diagram during the third segment. Purple highlight is used for contributions or changes proposed by both students.

Figure 9

Types of interventions during segment 3.

Figure 10

Class development during segment 4. Purple highlight is used for contributions or changes proposed by both students.

Figure 11

Type of interventions during segment 4.