# Having established some meaning for analysis and

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Having established some meaning for analysis and interpretation, we looked at videotapes of individual students (Grades 1 through 6) as they engaged in tasks involving analysis and interpretation. These structured interviews revealed four hierarchical levels of statistical reasoning: idiosyncratic, transitional, quantitative and analytical. Students who exhibit idiosyncratic reasoning consistently focus on ideas that are unrelated to the given data and frequently focus on their own personal data banks. Students characterized as transitional have begun to recognize the importance of quantitative thinking and generally provide relevant but limited responses to tasks. Students who exhibit quantitative reasoning can analyze and interpret data from more than one perspective; however they do not make connections between different aspects of the data. Consequently, they do not detect inconsistencies in their reasoning. Students characterized as analytical interpret data from different perspectives and are able to make connections between different aspects of the data. We also examined Grade 2 students’ analysis and interpretation of data during a teaching experiment. Our analysis revealed that these children were able to read between the data and beyond the data under certain conditions. Context plays a key role, and by providing opportunities for children to describe and investigate themes like a butterfly garden for an extended period, the teacher was able to build up a stronger contextual background for tasks involving analysis and interpretation. Children had difficulty focusing on subsets of data and this, in turn, affected their ability to make comparisons between two subsets of data. When looking at two subsets, we found that children focused on individual data values like the mode rather than examining the data subsets as a whole. REFERENCE Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education , 18, 382-393 . GRAHAM A. JONES Mathematics Department Illinois State University Normal, IL 61790-4520 USA
43 13. METHODS FOR ASSESSING AND RESEARCHING STUDENT REASONING ABOUT SAMPLING DISTRIBUTIONS MARK EARLEY Bowling Green State University, USA The main objective of this session was to present a discussion of how we as statistics education researchers could capture statistical reasoning. What does it look like? What should be assessed? How can we assess it? Why are we assessing it? All of these questions were addressed during the session. What follows is a basic outline of our discussion. The general outcome of the session, as I anticipated, was not any new specific knowledge, but rather a set of ideas that we as researchers should consider when investigating statistical reasoning in any context.

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