Abstract
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.
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Notes
All names are pseudonyms.
I use “normative reasoning” to indicate reasoning that is statistically accurate and/or appropriate for the context and “non-normative reasoning” to indicate reasoning that is either statistically inaccurate or not applicable to the context at hand.
In this analysis, I refer to myself in the transcription as “O” or “I.” The transcription conventions used are the following: (a) “[…]” for a break in the speech, typically including a pause, when restart or new direction; (b) “[ Italic]” for interpretive and informal commentary, including references to particular displays; (c) pictures of the sampling outcomes or the screens are embedded in the text; and (d) no deletions have been made from the transcript segments provided.
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Abu-Ghalyoun, O. Pre-service teachers’ difficulties in reasoning about sampling variability. Educ Stud Math 108, 553–577 (2021). https://doi.org/10.1007/s10649-021-10067-8
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DOI: https://doi.org/10.1007/s10649-021-10067-8