USING TECHNOLOGY TO SUPPORT DIAGRAMMATIC REASONING ABOUT CENTER AND VARIATION

We conducted two design experiments aimed at engaging sixth graders (11 years old) in statistical reasoning about center and variation. We examine in particular students’ informal notion of a “modal clump.” Using Peirce’s concept of diagrammatic reasoning, we analyze the interplay of 1) making plots with TinkerPlots – a computer data analysis tool, 2) experimenting with those plots, and 3) developing a language to talk about features of the data sets as represented in the plots by reflecting on judgments. More generally, we draw on Brandom’s recent work in philosophy to argue that an “inferential” view should be privileged over a “referential” view of teaching and learning statistics. PRIVILEGING INFERENCE OVER REFERENCE The central thesis of this paper is that the meanings of statistical concepts such as mean and variation should be understood in their role in a reasoning practice and that this epistemological view has implications for the pedagogy of statistics. We start with an important point established in Brandom’s (2000) philosophy: the inextricable connection between reference and inference. The gist of Brandom’s argument is that there can be no reference (e.g., to a concept or a data set) without inference (a reasoning process). Brandom takes issue with the Cartesian paradigm of representationalism that has prioritized reference over inference in the order of semantic explanation. His major work, Making it Explicit (1994), makes a powerful case for the reversal of this order—for the prioritization of inference over reference. It is never straightforward to formulate educational consequences from philosophical