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Versatile thinking and the learning of statistical concepts

Graham, Alan T.; Pfannkuch, Maxine and Thomas, Michael O. J. (2009). Versatile thinking and the learning of statistical concepts. ZDM (The International Journal of Mathematics Education), 41(5) pp. 681–695.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s11858-009-0210-8
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Abstract

Statistics was for a long time a domain where calculation dominated to the detriment of statistical thinking. In recent years, the latter concept has come much more to the fore, and is now being both researched and promoted in school and tertiary courses. In this study, we consider the application of the concept of flexible or versatile thinking to statistical inference, as a key attribute of statistical thinking. Whilst this versatility comprises process/object, visuo/analytic and representational versatility, we concentrate here on the last aspect, which includes the ability to work within a representation system (or semiotic register) and to transform seamlessly between the systems for given concepts, as well as to engage in procedural and conceptual interactions with specific representations. To exemplify the theoretical ideas, we consider two examples based on the concepts of relative comparison and sampling variability as cases where representational versatility may be crucial to understanding. We outline the qualitative thinking involved in representations of relative density and sample and population distributions, including mathematical models and their precursor, diagrammatic forms.

Item Type: Journal Article
Copyright Holders: 2009 FIZ Karlsruhe
ISSN: 1863-9704
Keywords: representation; register; statistical thinking; flexibility; versatility; conceptual interactions
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Interdisciplinary Research Centre: Centre for Research in Education and Educational Technology (CREET)
Item ID: 22338
Depositing User: Alan Graham
Date Deposited: 15 Jul 2010 10:24
Last Modified: 26 Mar 2014 10:53
URI: http://oro.open.ac.uk/id/eprint/22338
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