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Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education pp 323–333Cite as

Developing Teachers’ Statistical Thinking

Part of the New ICMI Study Series book series (NISS,volume 14)

Abstract

In this chapter learning experiences that teachers need in order to develop their ability to think and reason statistically are described. It is argued that teacher courses should be designed around five major themes: developing understanding of key statistical concepts; developing the ability to explore and learn from data; developing statistical argumentation; using formative assessment; and learning to understand students’ reasoning.

Keywords

  • Formative Assessment
  • Pedagogical Content Knowledge
  • Statistical Reasoning
  • Enquiry Cycle
  • Statistical Argumentation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • Abelson, R. (1995). Statistics as principled argument. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Andriessen, J. (2006). Arguing to learn. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 443–459). New York: Cambridge University Press.

    Google Scholar 

  • 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 (pp. 147–168). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5), 389–407.

    CrossRef  Google Scholar 

  • Batanero, C., Burrill, G., Reading, C., & Rossman, A. (Eds.). (2008). Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey, Mexico: International Commission on Mathematical Instruction and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications

  • Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Bahia, Brazil: International Statistical Institute and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications

  • Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35–65.

    CrossRef  Google Scholar 

  • Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning and thinking. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Canada, D. (2008). Variability in a sampling context: Enhancing elementary preservice teachers’ conceptions. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Cobb, G. (2007). One possible frame for thinking about experiential learning. International Statistical Review, 75(3), 336–347.

    CrossRef  Google Scholar 

  • Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of develo­ping statistical literacy, reasoning, and thinking (pp. 375–396). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • De Oliveira, A., Paranaiba, P., Kataoka, V., de Souza, A., Fernandes, F., & de Oliveira, M. (2008). Statistics teaching for prospective teachers of mathematics: Reflections and perspectives. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Driver, R., Newton, P., & Osborne, J. (2000). Establishing the norms of scientific argumentation in classrooms. Science & Education, 84, 287–312.

    CrossRef  Google Scholar 

  • Engel, J., Sedlmeier, P., & Worn, C. (2008). Modeling scatterplot data and the signal-noise metaphor: Towards statistical literacy for pre-service teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-k-12 curriculum framework. Alexandria, VA: American Statistical Association. Online: www.amstat.org/Education/gaise/

  • Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Dordrecht, The Netherlands: Springer.

    Google Scholar 

  • Garfield, J., & Ben-Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a Statistical Reasoning Learning Environment. Teaching Statistics, 31(3), 72–77.

    CrossRef  Google Scholar 

  • Godino, J. D., Batanero, C., Roa, R., & Wilhelmi, M. (2008). Assessing and developing peda­gogical content and statistical knowledge of primary school teachers through project work. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Groth, R., & Bergner, J. (2005). Pre-service elementary school teachers’ metaphors for the concept of statistical sample. Statistics Education Research Journal, 4(2), 27–42.

    CrossRef  Google Scholar 

  • Key Curriculum Press. (2006). Fathom dynamic data™ software. Emeryville, CA: Key Curriculum Press.

    Google Scholar 

  • Kirschner, P. A., Buckingham Shum, S. J., & Carr, C. S. (Eds.). (2003). Visualizing argumentation: Software tools for collaborative and educational sense-making. London: Springer.

    Google Scholar 

  • Konold, C., & Higgins, T. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 193–214). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic data explorations. Emeryville, CA: Key Curriculum Press.

    Google Scholar 

  • 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.

    CrossRef  Google Scholar 

  • Lehrer, R., & Romberg, T. (1996). Exploring children’s data modelling. Cognition and Instruction, 14(1), 69–108.

    CrossRef  Google Scholar 

  • Ministry of Education. (2007). The New Zealand curriculum. Wellington, New Zealand: Learning Media Limited.

    Google Scholar 

  • Mokros, J., & Russell, S. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20–39.

    CrossRef  Google Scholar 

  • Moore, D. (1990). Uncertainty. In L. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.

    Google Scholar 

  • Moore, D. (2007). The basic practice of statistics (4th ed.). New York: W.H. Freeman.

    Google Scholar 

  • Moritz, J. (2004). Reasoning about covariation. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 227–256). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Pratt, D., & Ainley, J. (2008). Introducing the special issue on informal inferential reasoning. Statistics Education Research Journal, 7(2), 3–4. Online: www.stat.auckland.ac.nz/serj/

    CrossRef  Google Scholar 

  • Rubin, A., & Hammerman, J. (2006). Understanding data through new software representations. In G. Burrill (Ed.), Thinking and reasoning with data and chance: 2006 NCTM yearbook (pp. 241–256). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Sanchez, E., & Blancarte, A. (2008). Statistical thinking as a fundamental topic in training the teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Sanchez, E., & Garcia, J. (2008). Acquisition of notions of statistical variation by in-service teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Shaughnessy, M. (2007). Research on statistics learning and reasoning. In F. Lester (Ed.), Second handbook of research on the teaching and learning of mathematics (Vol. 2, pp. 957–1009). Charlotte, NC: Information Age Publishers and National Council of Teachers of Mathematics.

    Google Scholar 

  • Shaughnessy, M., & Pfannkuch, M. (2002). How faithful is Old Faithful? Statistical thinking: A story of variation and prediction. Mathematics Teacher, 95(4), 252–259.

    CrossRef  Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.

    CrossRef  Google Scholar 

  • Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Wild, C. J. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26. Online: www.stat.auckland.ac.nz/serj/

    CrossRef  Google Scholar 

  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223–265.

    CrossRef  Google Scholar 

  • Wild, C. J., Pfannkuch, M., Regan, M., & Horton, N. (2011). Towards more accessible conceptions of statistical inference. Journal of the Royal Statistical Society. Series A, 174(2), 247–295.

    CrossRef  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics, The University of Auckland, 92019, Auckland, 1142, New Zealand

    Maxine Pfannkuch

  2. Faculty of Education, The University of Haifa, Mount Carmel, Haifa, 31905, Israel

    Dani Ben-Zvi

Authors
  1. Maxine Pfannkuch
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  2. Dani Ben-Zvi
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Corresponding author

Correspondence to Maxine Pfannkuch .

Editor information

Editors and Affiliations

  1. Fac. Ciencias de la Educación, Universidad de Granada, Granada, 18071, Spain

    Carmen Batanero

  2. Dept. Counseling,, Educational Psychology &, Michigan State University, Erickson Hall 240, East Lansing, 48824, Michigan, USA

    Gail Burrill

  3. SiMERR National Centre, University of New England, Armidale, 2350, New South Wales, Australia

    Chris Reading

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Pfannkuch, M., Ben-Zvi, D. (2011). Developing Teachers’ Statistical Thinking. In: Batanero, C., Burrill, G., Reading, C. (eds) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education. New ICMI Study Series, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1131-0_31

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