A FRAMEWORK FOR THINKING ABOUT INFORMAL STATISTICAL INFERENCE
DOI:
https://doi.org/10.52041/serj.v8i1.457Keywords:
Statisitcs education research, Informal inferential reasoning, Statistical inquiry, Ill-structured problems, Teacher professional developmentAbstract
Informal inferential reasoning has shown some promise in developing students’ deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference – generalizations ‘beyond the data,’ probabilistic language, and data as evidence. The authors use primary school classroom episodes and excerpts of interviews with the teachers to illustrate the framework and reiterate the importance of embedding statistical learning within the context of statistical inquiry. Implications for the teaching of more powerful statistical concepts at the primary school level are discussed.
First published May 2009 at Statistics Education Research Journal: Archives
References
Abelson, R. (1995). Statistics as principled argument. Hillsdale, NJ: Lawrence Erlbaum Associates.
Ainley, J., & Pratt, D. (Eds.) (2007). Reasoning about Informal Inferential Statistical Reasoning: A collection of current research studies. Proceedings of the Fifth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-5), University of Warwick, UK.
Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht, the Netherlands: CD Beta Press.
Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distribution. In D. Ben- Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking. Dordrecht, the Netherlands: Kluwer Academic Publisher.
Ben-Zvi, D. (2006). Using Tinkerplots to scaffold students’ 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 ]
Ben-Zvi, D., & Sharett-Amir, Y. (2005). How do primary school students begin to reason about distributions? In K. Makar (Ed.), Reasoning about distributions: A collection of recent research studies. Proceedings of the Fourth International Research Forum for Statistical Reasoning, Thinking and Literacy (SRTL-4), University of Auckland (New Zealand). Brisbane: University of Queensland.
Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5-43.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13. Curriculum Corporation (2006). National Statements of Learning in Mathematics. Melbourne: Author.
Dewey, J. (1910/1997). How we think. Mineola, NY: Dover.
Erickson, T. (2006). Using simulation to learn about inference. 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/17/7G2_ERIC.pdf]
Finzer, W. (2001). Fathom! (Version 1.16) [Computer Software]. Emeryville, CA: KCP Technologies.
Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158.
Gardner, H., & Hudson, I. (1999). University students’ ability to apply statistical procedures. Journal of Statistics Education, 7(1). [Online: www.amstat.org/publications/jse/secure/v7n1/gardner.cfm]
Gideon, J. (Ed.) (1996). Teach-Stat activities: Statistics investigations for grades 3-6. Parsippany, NJ: Dale Seymour Publications.
Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry into data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337-364.
Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2003). Data seen through different lenses. Unpublished manuscript.
Konold, C., & Miller, C. (2005). Tinkerplots (v. 1.0). Emeryville, CA: Key Curriculum Press.
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.
Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A., Wing, R., et al. (2002). Students’ use of modal clumps to summarize data. In B. Phillips (Ed.), Developing a statistically literate society: Proceedings of the Sixth International Conference on Teaching Statistics, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute. [Online: http://www.stat.auckland.ac.nz/~iase/publications/1/8b2_kono.pdf]
Magnani, L. (2001). Abduction, reason, and science: Processes of discovery and explanation. New York: Kluwer Academic Publisher.
Makar, K., & Confrey, J. (2004). Secondary teachers’ reasoning about comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 353-373). Dordrecht, the Netherlands: Kluwer Academic Publisher.
Makar, K., & Confrey, J. (2005). “Variation-talk”: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27-54. [Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ4(1)_Makar_Confrey.pdf]
Makar, K., & Confrey, J. (2007). Moving the context of modeling to the forefront. In W. Blum, P. Galbraith, H-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 485-490). New York: Springer.
Makar, K., & McPhee, D. (in press). Young children’s explorations of average in an inquiry classroom. Paper to be presented at the 32nd annual conference of the Mathematics Education Research Group of Australasia, Massey University, Wellington NZ, 5-9 July 2009.
Marshall, J., Makar, K., & Kazak, S. (2002). Young urban students’ conceptions of data uses, representation, and analysis. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the Twenty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA24), Athens GA (USA), Vol. 3, pp. 1293-1304. Columbus, OH: ERIC Clearinghouse, Mathematics and Environment Education.
Mokros, J., & Russell, S. J. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20-39. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
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]
Pfannkuch, M., Budgett, S., & Parsonage, R. (2004, July). Comparison of data plots: Building a pedagogical framework. Paper presented at the Tenth Meeting of the International Congress on Mathematics Education, Copenhagen, Denmark. ]
Pratt, D., & Ainley, J. (Eds.) (2008). Introducing the special issue on informal inference.
Statistics Education Research Journal, 7(2), 3-4. [Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ7(2)_Pratt_Ainley.pdf]
Queensland Studies Authority (2006). Essential learnings and standards (Year 3, 5, 7, and 9. Spring Hill QLD: Author.
Reichardt, C. S., & Gollob, H. F. (1997). When confidence intervals should be used instead of statistical significance tests, and vice versa. In L. L. Harlow. S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (Vol. I, pp. 259-284). Mahwah, NJ: Lawrence Erlbaum Associates.
Rossman, A. (2008). Reasoning about informal statistical inference: One statistician’s view. Statistics Education Research Journal, 7(2), 5-19. [Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ7(2)_Rossman.pdf]
Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualization software. 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/17/2D3_RUBI.pdf]
Sorto, M. A. (2006). Identifying content knowledge for teaching statistics. 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/C130.pdf]
Tukey, J. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265.
Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40-58. [Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ7(2)_Zieffler.pdf]
