From inference processes to situations of misunderstanding

In this paper, we describe inferences on a school task, which are reconstructed by the mean of two perspectives from argumentation theory: The pragma-dialectical model and Grize’s natural logic. Both analyses focus on the same item of mathematics, issued from a PISA survey, in order to discuss their specific contribution in elucidating the actual reasoning involved in both the student's answer and the evaluator’s expectations. The mismatch between these two points of view allow us to discuss the potentiality of a situation of misunderstanding. Investigating how specific tasks in particular contexts are interpreted provides a contribution to methodological approaches treating thinking processes as situated and socially negotiated from a diversity of points of views, as for example Inhelder’s (1962) microgenetic approach. In order to extend such analysis to interpretations of discourse, an interdisciplinary approach combining argumentation theory and socio-cognitive psychology is needed. Here, we observed for instance that students may provide the expected answers and still interpret the question or problem differently from the task’s designers (or “teacher”). The meaning of language and other signs, such as graphs or mathematical symbols, cannot be taken for granted when several interlocutors are involved. This issue chiefly concerns argumentation theory, since it raises the question of the integration of specific contexts and points of view in the analysis of argumentation. Therefore, argumentation should be analysed also as a process, and not only as a product; For more detail on this distinction, see for instance Grize (1996) and Kuhn & Udell (2003, 2007).