Peer interaction and problem solving: One example of a logical-discursive analysis of a process of joint decision making

Abstract

This article proposes a qualitative analysis of a dialogue between two children solving the Tower of Hanoi problem. We know that in some circumstances, two heads are better than one. The question is how interactional constraints are likely to provide cognitive benefits? To carry out such an analysis, we use Interlocutory Logic, which is a formal system constructed to express the logical and phenomenological properties of natural conversation. More particularly, we showed how this logical analysis of the interlocution can formalise the socio-cognitive conflict that appears to be an essential ‘‘ingredient'' of cognitive development from the socio-constructivist perspective.

Keywords:

• Peer interaction
• Problem solving
• Conversation
• Interlocutory logic

Acknowledgments

This article comes from work carried out within a workshop co-ordinated by Sorsana and Trognon at the University of Nancy 2 (during 2002, 2003 and 2004) and entitled “Analytic methodological constraints of the cognitive production of a conversation”. This workshop was subsidized by the Scientific Counsel of the University of Nancy 2 as well as by the “Psychology of interaction – GRC” laboratory (EA 1129) of the same university.

We would like to thank Ciarán O'Keeffe and Maryse Noté for their help with the translation into English.

Notes

¹A very accessible presentation of these methods can be found in Vernant (2001).

²A “sequent” is a pair (note Γ⊢F) where: Γ is a finite set of formulas. Γ represents the hypotheses that one can use. This set is also called the sequent context; - F is a formula. It is the formula that one wants to demonstrate. This formula is said to be the conclusion of the “sequent” (David, Nour, & Raffalli, 2003, p. 24).

³Even in his recent publications (e.g., 1996) Carlson does not refer to the logic theory of sequents. We think nevertheless that his theory calls for this extension.

⁴This is the cognitive environment of A defined by Sperber and Wilson (1995).

⁵p v q, or ∼p, so q.

⁶Interlocutory logic integrates general semantics (Searle & Vanderveken, 1985; Vanderveken, 1990) as one of its most fundamental components.

⁷f₂, f₃, f₄ are not given simultaneously in the discourse. They result from a process of sharing the inter-comprehension, which transforms the “meaning of the locutor” into the “interlocutors' meaning” (Clark, 1996, 1999), according to a process described in Trognon (2003), Trognon and Brassac (1992), and Trognon and Saint Dizier (1999). The formula that describes, in interlocutory logic, the different levels (from the utterance to the direct act, from the direct act to the indirect act, from the indirect act to the conversational move) of the interpretative genesis of the sign-for-interlocutors is borrowed from Jones (1983). For more detail see Trognon and Batt (2007b), Trognon, Batt, and Laux (2006a).

⁸“Quantified modal first-order predicate logic” was amended, as suggested by Hintikka, in order to adapt it to the “natural logic of the discourse”. The connectors of interlocutory logic are the connectors of Hintikka's semantic games (Hintikka & Kulas, 1983). But presentation of this complication is unnecessary in the present study.

⁹For Richard (1988), planning, in the strictest sense of the word, occurs: either “when the actions necessary to satisfy the instructions can be calculated by action calculation rules but when their execution must be delayed because other constraints must be taken into account to determine the actions' sequential layout”; or “when the situation and the knowledge about the actions is such that other action calculation rules are required to satisfy the task demands” (p. 35). He describes different forms of planning.

¹⁰Through the use of a sociometric questionnaire, aimed at children, and a standardized interview with the teachers, we selected pairs of children that appreciated each other (which we called “affinity” pairs in reference to the work of Maisonneuve, 1966) and pairs of children that did not appreciate each other (called “no-affinity” pairs).

¹¹In game theories (and in particular dialogue game theory), this factor would play a important role (cf. Bromberg & Trognon, 2000, 2004; Hintikka, 1962, 1976, 1984).

¹²The authors hold at the disposal of readers a recursive data-processing model of the children's enacted reasoning.