Commenced in January 2007
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Informal Inferential Reasoning Using a Modelling Approach within a Computer-Based Simulation

Authors: Theodosia Prodromou


The article investigates how 14- to 15- year-olds build informal conceptions of inferential statistics as they engage in a modelling process and build their own computer simulations with dynamic statistical software. This study proposes four primary phases of informal inferential reasoning for the students in the statistical modeling and simulation process. Findings show shifts in the conceptual structures across the four phases and point to the potential of all of these phases for fostering the development of students- robust knowledge of the logic of inference when using computer based simulations to model and investigate statistical questions.

Keywords: Inferential reasoning, learning, modelling, statistical inference, simulation.

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[1] Aberson, C. L., Berger, D. E., Healy, M. R., & Romero, V. L. (2003). Evaluation of an interactive tutorial for teaching hypothesis testing concepts. Teaching of Psychology, 30, 76-79.
[2] Bakker, A., Kent, P., Derry, J., Noss, R., & Hoyles, C. (2008). Statistical inference at work: Statistical process control as an example. Statistics Education Research Journal, 7(2), 131-146. iase/serj/SERJ7(2)_Bakker.pdf. Accessed 10 January 2013.
[3] Batanero, C. (2005). Statistics education as a field for research and practice. In Proceedings of the 10th international commission for mathematical instruction. Copenhagen, Denmark: International Commission for Mathematical Instruction.
[4] Batanero, C., Tauber, L. M., & S´anchez, V. (2004). Students’ reasoning about the normal distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 257–276). Dordrecht, The Netherlands: Kluwer Academic Publishers.
[5] Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers misunderstand intervals and standard errors bars. Psychological Methods, 10, 389-396.
[6] Chance, B., delMas, R., & Garfield, J. (2004). Reasoning about sampling distributions. In D. Ben-Zvi and J. Garfield (Eds.), The Challenge of Developing Statistical Literacy, Reasoning, and Thinking (pp. 295-323). Dordrecht, The Netherlands: Kluwer Academic Publishers.
[7] Cobb, G. W. (2007). The introductory statistics course: a ptolemaic curriculum? Technology innovations in statistics Education, 1 (1).
[8] Garfield, J., delMas, B., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM−The International Journal on Mathematics Education, 44(3), 883-898. doi:10.1007/s11858-012-0447-5
[9] Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Berlin: Springer.
[10] Kirk, R. E. (2001). Promoting good statistical practices: Some suggestions. Educational and Psychological Measurement, 61 (2), 213−218.
[11] Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259-289.
[12] Lipson, K. (2002). The role of computer based technology in developing understanding of the concept of sampling distribution. In Proceedings of the sixth international conference on teaching statistics. Voorburg, The Netherlands: International Statistical Institute.
[13] Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105. iase/ serj/SERJ8(1)_Makar_Rubin.pdf. Accessed 10 January 2013.
[14] Pfannkuch, M. (2005). Probability and statistical inference: How can teachers enable learners to make the connection? In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 267-297). Dorcdrecht, The Netherlands: Kluwer Academic Publishers.
[15] Prodromou, T. (2012). Developing a modeling approach to probability using computer-based simulations. Proceedings of the 12th International Congress on Mathematical Education, Topic Study Group 11, pp. 2394-2403. COEX, Seoul, Korea: ICME. /upload /UpFile2/TSG/0978.pdf. Accessed 10 January 2013.
[16] Robson, C. (1993). Real world research. Oxford, England: Blackwell.
[17] Saldanha, L., & Thompson, P. (2003). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51, 257-270.
[18] TinkerPlots: Dynamic data exploration (Version 2.0)
[Computer software]. Emeryville: CA: Key Curriculum Press.
[19] Watson, J. M., & Moritz, J. B. (2000). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behaviour, 19, 109-136.
[20] Wilensky, U. (1997). What is normal anyway? Therapy for epistemological anxiety. Educational Studies in Mathematics, 33(2), 171–202.