# The participating third grade teacher took part in a

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The participating third grade teacher took part in a professional development workshop on the process of statistical investigation and the development of curriculum merging this perspective with elementary curriculum topics in Summer 2000. The participating teacher in this study was a best case scenario in that the teacher had considerable prior experience with statistics through a local implementation of Quantitative Literacy and the American Statistical Association’s project competitions. The object of our investigation was the teacher’s knowledge about data and distribution in the context of teaching during the school year following the summer workshop. An open-ended, hands off approach was used to observe teaching practice. All subsequent interventions regarding statistical content were made after a teaching episode in response to teacher questions. The statistical investigation units were planned in advance and video-taped by researchers in the elementary classroom. Five artifacts on classroom teaching with supporting video were shared to illustrate the contextual features influencing statistical reasoning in the context of applied statistical investigations into topics across the third grade curriculum. We found our group’s discussion and interaction with our data extremely valuable. Three main ideas were raised in the discussion of our data that point to the need to focus on pedagogical content knowledge in teaching statistical investigation. The first idea focused on the relationship between questions posed, data collected and the purpose of the investigation. The pressing question was: “when should the teacher and children consider the investigation question in the process of reasoning with data?” One perspective presented is that one ought to consider the question in the planning phase of an investigation, then with the question in mind proceed to think through the data collection process. Another perspective argued that one should simply gather data without a pre-planned purpose in mind and then ask what is the data telling me now? The second idea centred on the role of central tendency and variability, in making interpretations, inferences and predictions based on data. We repeatedly saw the teacher and children interpret data based on frequency of occurrence, in terms of which group had more and which had less. There was little/no evidence of the teacher or children using variability in their interpretations, inferences or prediction. Considering the interplay of central tendency, variability, interpretation and prediction, and the underlying story from the data raises interesting questions about the nature of learning opportunities offered and possibly missed. In regards to these first two ideas, it was pointed out during discussion that when teachers do not know or understand the content sufficiently well, they fall back to a comfortable position in terms of what they do know. In the case of teaching and

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