Local and global thinking in statistics inference
Pratt, D. (Dave), Johnston‐Wilder, Peter, Ainley, Janet and Mason, John. (2008) Local and global thinking in statistics inference. Statistics Education Research Journal, Vol.7 (No.2). pp. 107-129. ISSN 1570-1824Full text not available from this repository.
Official URL: http://www.stat.auckland.ac.nz/~iase/publications....
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.
|Item Type:||Journal Article|
|Subjects:||L Education > LB Theory and practice of education
Q Science > QA Mathematics
|Divisions:||Faculty of Social Sciences > Institute of Education|
|Library of Congress Subject Headings (LCSH):||Mathematical statistics -- Study and teaching (Elementary), Probabilities -- Study and teaching (Elementary), Inference|
|Journal or Publication Title:||Statistics Education Research Journal|
|Publisher:||International Association for Statistical Education|
|Page Range:||pp. 107-129|
|Access rights to Published version:||Restricted or Subscription Access|
|References:||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 129 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). [Online: http://www.keypress.com/x5715.xml]|
Actions (login required)