Pre-service teachers’ difficulties in reasoning about sampling variability

Past studies have documented some pre-service teachers’ (PSTs) difficulties in reasoning about sampling variability. This study adds to the body of literature by investigating the ideas that PSTs employ in reasoning about sampling variability, and by conjecturing what is behind the difficulties especially during the contextuality episodes. This issue was studied in the context of a content course on statistics and probability for elementary and middle grade PSTs at a Midwestern American university. An analysis of a PST’s video and screen records of a task-based interview was guided by techniques of knowledge analysis (diSessa et al., 2016), and focused on two clear contextuality episodes that have caused disequilibrium in the PST’s knowledge system. The analysis described at a moment-by-moment level the cognitive dynamics of the transitions that occurred in the PST’s knowledge system and highlighted some of the difficulties that arise from the activation of less-productive knowledge elements over others. The significance of this study is in its use for the techniques of knowledge analysis from the field of cognitive science to provide a fine-grained description of PSTs’ difficulties in reasoning about sampling variability that went beyond the traditional description of these difficulties as misconceptions.