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Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course

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Abstract

While models are an important concept in statistics, few introductory statistics courses at the tertiary level put models at the core of the curriculum. This paper reports on a radically different approach to teaching statistics at the tertiary level, one that uses models and simulation as the organizing theme of the course. The focus on modeling and simulation—along with inference—was facilitated by having students use TinkerPlots™ software for all modeling and analysis. Results from a 3-month teaching experiment suggest that a course focused on modeling and simulation through randomization and resampling methods in which students learn to think using a powerful and conceptual modeling tool can foster ways of thinking statistically. Furthermore, such an approach seems to help students develop experiences with and appreciation for the science and practice of statistics.

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References

  • Antonioli, C., & Reveley, M. A. (2005). Randomised controlled trial of animal facilitated therapy with dolphins in the treatment of depression. British Medical Journal, 331(7527), 1231–1234.

    Article  Google Scholar 

  • Biehler, R., & Prömmel, A. (2010). developing students’ computer-supported simulation and modelling competencies by means of carefully designed working environments. Paper presented at the ICOTS 8, Ljubljana, Slovenia.

  • Box, G. E. P., & Draper, N. R. (1987). Empirical model-building and response surfaces. New York: Wiley.

    Google Scholar 

  • Cobb, G. W. (2005). The introductory statistics course: A saber tooth curriculum? After dinner talk given at the United States Conference on Teaching Statistics.

  • Cobb, G. W. (2007). The introductory statistics course: a ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1). Retrieved September 28, 2010, http://escholarship.org/uc/item/6hb3k0nz#page-1.

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

    Article  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. 375–395). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • delMas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28–58. http://www.stat.auckland.ac.nz/~iase/serj/SERJ6(2)_delMas.pdf.

  • delMas, R., Zieffler, A. & Garfield, J. (2012). Tertiary students’ reasoning about samples and sampling variation in the context of a modeling and simulation approach to inference. Educational Studies in Mathematics (in review).

  • Diefes-Dux, H.A., Imbrie, P.K., & Moore, T.J. (2005). First-year engineering themed seminar—A mechanism for conveying the interdisciplinary nature of engineering. Paper presented at the 2005 American Society for Engineering Education National Conference, Portland, OR.

  • Doerr, H., & English, L. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.

    Article  Google Scholar 

  • Efron, B. (1981). Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics, 9, 139–172.

    Article  Google Scholar 

  • Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.

    Google Scholar 

  • Finzer, W. (2012). Fathom ® Dynamic Data™ (v. 2L) [computer software]. Emeryville, CA: Key Curriculum Press.

  • Garfield, J. & Ben-Zvi, D. (2008). Developing Students’ Statistical Reasoning: Connecting Research and Teaching Practice. Berlin: Springer.

  • Harper, S.R. & Edwards, M. T. (2011) A new recipe: No more cookbook lessons. Mathematics Teacher 105(3), 180–188.

    Google Scholar 

  • Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12, 217–230.

    Article  Google Scholar 

  • Konold, C. & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1), Article 1.

    Google Scholar 

  • Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., et al. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13, 68–86.

    Article  Google Scholar 

  • Konold, C., & Miller, C. (2011). TinkerPlots™ Version 2 [computer software]. Emeryville, CA: Key Curriculum Press.

    Google Scholar 

  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought—revealing activities for students and teachers. In A. E. Kelley & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 591–646). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Maxara, C., & Biehler, R. (2006). Students’ probabilistic simulation and modeling competence after a computer-intensive elementary course in statistics and probability (Electronic Version). In: Proceedings of the 7th International Conference on Teaching Statistics (ICoTS 7). http://www.stat.auckland.ac.nz/~iase/publications/17/7C1_MAXA.pdf.

  • Maxara, C., & Biehler, R. (2007). Constructing stochastic simulations with a computer tool—students’ competencies and difficulties (Electronic Version). In: Proceedings of CERME 5. http://www.erme.unito.it/CERME5b/WG5.pdf#page=79.

  • Moore, T. J., Diefes-Dux, H. A., & Imbrie, P. K. (2006). The quality of solutions to open-ended problem solving activities and its relation to first-year student team effectiveness. Chicago, IL: Paper presented at the American Society for Engineering Education Annual Conference.

    Google Scholar 

  • Moore, T.J., Diefes-Dux, H.A., & Imbrie, P.K. (2007). How team effectiveness impacts the quality of solutions to open-ended problems. In: Distributed journal proceedings from the International Conference on Research in Engineering Education 2007 special issue of the Journal of Engineering Education.

  • Saldanha, L. A., & Thompson, P. W. (2003). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51, 257–270.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1998). Making mathematics and making pasta: From cookbook procedures to really cooking. In J. G. Greeno & S. V. Goldman (Eds.), Thinking practices in mathematics and science learning (pp. 299–319). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Schwartz, D. L., Sears, D., & Chang, J. (2007). Reconsidering prior knowledge. In M. C. Lovett & P. Shah (Eds.), Thinking with Data (pp. 319–344). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

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

    Article  Google Scholar 

  • Zawojewski, J.,K., Bowman, K., & Diefes-Dux, H.A. (Eds.). (2011). Mathematical modeling in engineering education: Designing experiences for all students. Rotterdam, The Netherlands: Sense Publishers.

  • Zieffler, A., Garfield, J., delMas, R., Isaak, R., Ziegler, L., & Le, L. (2011). How do tertiary students reason about samples and sampling in the context of a modeling and simulation approach to informal inference? Paper presented at the Seventh International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-7). Texel Island, The Netherlands.

  • Zieffler, A., Harring, J., & Long, J. (2011b). Comparing groups: Randomization and bootstrap methods using R. New York: Wiley.

    Book  Google Scholar 

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Acknowledgments

The authors gratefully acknowledge the support of the National Science Foundation for the CATALST project. (Collaborative Research: The CATALST Project, Change Agents for Teaching and Learning Statistics, DUE-0814433). They also appreciate the contributions of their CATALST collaborators Beth Chance, George Cobb, John Holcomb and Allan Rossman. The advice given by Cliff Konold, Richard Lesh, Tamara Moore, and Rob Gould was extremely valuable. The work and dedication of graduate students Rebekah Isaak, Laura Le and Laura Ziegler, and of Dr. Herle McGowan at North Carolina State University, was a major contribution to this project. Lastly, the authors thank Anelise Sabbag for her copy-editing on this paper.

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Correspondence to Joan Garfield.

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Garfield, J., delMas, R. & Zieffler, A. Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM Mathematics Education 44, 883–898 (2012). https://doi.org/10.1007/s11858-012-0447-5

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