Local and global thinking in

statistical inference


dave pratt

Institute of Education, University of London



peter johnston-wilder

Institute of Education, University of Warwick




School of Education, University of Leicester




Centre for Mathematics Education, Open University






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






Ben-Zvi, D., & Sharett-Amir, Y. (2005). How do primary school students begin to reason about distributions? In K. Makar (Ed.), Reasoning about Distribution: A collection of studies. Proceedings of the Fourth International Research Forum on Statistical Reasoning, Thinking and Literacy (SRTL-4). [CDROM, with video segments]. Brisbane, Australia: University of Queensland.

Ben-Zvi, D. (2006). Using Tinkerplots to scaffold informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. Voorburg, The Netherlands: International Statistical Institute.

   [Online: http://www.stat.auckland.ac.nz/~iase/publications/17/2D1_BENZ.pdf]
Camtasia Studio (Version 6.0) [Computer software]. Okemos, MI: Techsmith Corporation. 

[Online: http://www.techsmith.com/camtasia.asp]

Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.

Johnston-Wilder, P. (2006). Learners’ shifting perceptions of randomness. Unpublished doctoral dissertation, Open University, UK.

Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59-98.

Konold, C. (1995). Confessions of a coin flipper and would-be instructor. The American Statistician, 49(2), 203-209.

Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 589-593.

Makar, K., & Rubin, A. (2007, August). Beyond the bar graph: Teaching informal statistical inference in primary school. Paper presented at the Fifth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-5), University of Warwick, UK.

Mason, J., & Johnston-Wilder, S. (2004). Fundamental constructs in mathematics education. London: RoutledgeFalmer.

Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. London: Kluwer Academic Publishers.

Pfannkuch, M. (2006). Informal inferential reasoning. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. Voorburg, The Netherlands: International Statistical Institute.

   [Online: http://www.stat.auckland.ac.nz/~iase/publications/17/6A2_PFAN.pdf]

Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31(5), 602-625.

Pratt, D. & Noss, R. (2002). the micro-evolution of mathematical knowledge: The case of randomness. Journal of the Learning Sciences, 11(4), 453-488.

Prodromou, T. (2007). Making connections between the two perspectives on distribution. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the Fifth Conference of the European Society for Research in Mathematics Education (pp. 801-810). Larnaca, Cyprus: University of Cyprus.

Prodromou, T. (2008). Connecting thinking about distribution. Unpublished Doctoral Dissertation, University of Warwick, UK

Prodromou, T., & Pratt, D. (2006). The role of causality in the coordination of two perspectives on distribution within a virtual simulation. Statistics Education Research Journal, 5(2), 69-88.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ5(2)_Prod_Pratt.pdf]

Smith, J. P., diSessa, A. A., & Rochelle, J. (1993). Misconceptions reconceived - A constructivist analysis of knowledge in transition. Journal of Learning Sciences, 3(2), 115-163.

Konold, C., & Miller, C. (2001). Tinkerplots (version 0.23) [Data Analysis Software] University of Massachusetts, Amherst (USA).



Dave Pratt

Institute of Education
University of London
20 Bedford Way