Local and global thinking
in
statistical inference
dave pratt
d.pratt@ioe.ac.uk
peter johnston-wilder
p.j.johnston-wilder@warwick.ac.uk
JANET AINLEY
janet.ainley@le.ac.uk
JOHN MASON
Centre for Mathematics Education, Open University
j.h.mason@open.ac.uk
ABSTRACT
In this reflective paper, we explore students’ local and global thinking about informal statistical inference through our observations of 10- to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes in the frequency or relative frequency as the sample size grew larger. They generally failed to recognise that larger samples provided stability in the aggregated proportions, not apparent when the data were viewed from a local perspective. We draw on Mason’s theory of the Structure of Attention to illuminate our observations, and attempt to reconcile differing notions of local and global thinking.
Keywords: Statistics
education research, Task design,
Informal statistical inference, Sample size, Local and global meanings or
perspectives, Structure of Attention
__________________________
Statistics
Education Research Journal, 7(2), 107-129, http://www.stat.auckland.ac.nz/serj
Ó International
Association for Statistical Education (IASE/ISI), May, 2008
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Dave Pratt
Institute of Education
University of London
20 Bedford Way
London
WC1H 0AL