Every rose has its thorn: secondary teachers’ reasoning about statistical models
Tóm tắt
Statistical modeling is a core component of statistical thinking and has been identified by several countries as a curricular goal for secondary education. However, many secondary teachers have minimal preparation for teaching this topic. The goal of this research study is to learn about teachers’ perceptions of the role statistical models play in statistical inference and how these perceived purposes affect their reasoning about statistical models and inference. Problem-solving interviews were conducted with four in-service teachers who had recently taught a modeling and simulation-based introductory statistics course. Teachers’ responses suggest they may not see modeling variation as the primary purpose of statistical modeling and instead substitute two other purposes: making a decision and replicating the data collection process. Suggestions for how to build on teachers’ transitional conceptions and refocus attention on modeling variation are discussed.
Tài liệu tham khảo
Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1–2), 5–26.
Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 15–37). New York: Springer.
Behrens, J. T. (1997). Toward a theory and practice of using interactive graphics in statistics education. In J. B. Garfield & G. Burril (Eds.), Research on the role of technology in teaching and learning statistics: Proceedings of the 1996 International Association for Statistics Education (IASE) roundtable (pp. 111–122). Voorburg: International Statistical Institute.
Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42–63. https://www.stat.auckland.ac.nz/~iase/serj/SERJ3(2)_BenZvi.pdf.
Biehler, R., Frischemeier, D., & Podworny, S. (2015). Preservice teachers’ reasoning about uncertainty in the context of randomization tests. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: learning and teaching informal inferential reasoning (pp. 129–162). Minneapolis: Catalyst Press.
Biehler, R., Frischemeier, D., & Podworny, S. (2017). Elementary preservice teachers’ reasoning about modeling a “family factory” with TinkerPlots—a pilot study. Statistics Education Research Journal, 16(2), 244–286.
Biembengut, M. S., & Hein, N. (2010). Mathematical modeling: Implications for teaching. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 481–490). New York: Springer.
Brown, E. N., & Kass, R. E. (2009). What is statistics? The American Statistician, 63(2), 105–110.
Burgess, T. A. (2002). Investigating the ‘data sense’ of pre-service teachers. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics. Cape Town: International Statistical Institute.
Conference Board of the Mathematical Sciences (2012). The mathematical education of teachers II (MET-II), Providence: American Mathematical Society. http://www.cbmsweb.org/archive/MET2/met2.pdf. Accessed 27 July 2016.
Creswell, J. W. (2007). Qualitative inquiry and research design (2nd edn.). Thousand Oaks: SAGE Publications.
Creswell, J. W. (2009). Research design: qualitative, quantitative, and mixed methods approaches. Los Angeles: Sage Publications, Inc.
Davison, A. C. (2003). Statistical models (Vol. 11). Cambridge: Cambridge University Press.
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.
Derry, S. J., Levin, J. R., Osana, H. P., Jones, M. S., & Peterson, M. (2000). Fostering students’ statistical and scientific thinking: Lessons learned from an innovative college course. American Educational Research Journal, 37(3), 747–773.
Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. L. Galbraith, H. W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. New York: Springer.
Franklin, C. A., Bargagliotti, A. E., Case, C. A., Kader, G. D., Scheaffer, R. L., & Spangler, D. A. (2015). The statistical education of teachers (SET). Alexandria: American Statistical Association. http://www.amstat.org/asa/files/pdfs/EDU-SET.pdf.
Fry, E. B. (2017). Introductory statistics students’ conceptual understanding of study design and conclusions. (Doctoral dissertation, University of Minnesota). Available at http://iase-web.org/Publications.php.
Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics revisited: a current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–396.
Garfield, J., & Ben-Zvi, D. (2008). Preparing school teachers to develop students’ statistical reasoning. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), 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: ICMI & IASE. https://www.stat.auckland.ac.nz/~iase/publications/rt08/T4P6_Garfield.pdf.
Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM – The International Journal on Mathematics Education, 44(7), 883–898.
Garfunkel, S., & Montgomery, M. (2016). Guidelines for assessment and instruction in mathematical modeling education (GAIMME) report. Boston: Consortium for Mathematics & Its Applications (COMAP)/Society for Industrial and Applied Mathematics (SIAM).
Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38(5), 427–437.
Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8, 37–63.
Hammerman, J. K., & Rubin, A. (2004). Strategies for managing statistical complexity with new software tools. Statistics Education Research Journal, 3(2), 17–41. http://iase-web.org/documents/SERJ/SERJ3(2)_Hammerman_Rubin.pdf.
Heaton, R. M., & Mickelson, W. T. (2002). The learning and teaching of statistical investigation in teaching and teacher education. Journal of Mathematics Teacher Education, 5(1), 35–59.
Konold, C., & Miller, C. (2011). TinkerPlots 2.0. Emeryville: Key Curriculum Press. Available from http://www.tinkerplots.com.
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.
Lee, H., & Hollebrands, K. (2008). Preparing to teach mathematics with technology: an integrated approach to developing technological pedagogical content knowledge. Contemporary Issues in Technology and Teacher Education, 8(4), 326–341. http://www.citejournal.org/vol8/iss4/mathematics/article1.cfm.
Lee, H. S., & Mojica, G. F. (2008). Examining how teachers’ practices support statistical investigations. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 Conference and IASE 2008 Round Table Conference, Monterrey: ICMI & IASE.
Liu, Y., & Thompson, P. W. (2009). Mathematics teachers’ understandings of proto-hypothesis testing. Pedagogies, 4(2), 126–138.
Madden, S. R. (2011). Statistically, technologically, and contextually provocative tasks: supporting teachers’ informal inferential reasoning. Mathematical Thinking and Learning, 13(1–2), 109–131.
Makar, K., & Confrey, J. (2004). Secondary teachers’ reasoning about comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 353–373). Dordrecht: Kluwer Academic Publishers.
Mickelson, W. T., & Heaton, R. M. (2004). Primary teachers’ statistical reasoning about data. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 327–352). Dordrecht: Kluwer Academic Publishers.
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: a methods sourcebook (3rd edn.). Thousand Oaks: Sage Publications.
Ministry of Education. (2007). The New Zealand curriculum. Wellington: Learning Media. http://nzcurriculum.tki.org.nz. Accessed 27 July 2016.
Moore, D. S. (1990). Uncertainty. In L. S. Steen (Ed.), On the shoulders of giants: new approaches to numeracy (pp. 95–137). Washington: National Academy Press.
National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core state standards for mathematics. http://www.corestandards.org/. Accessed 27 July 2016.
Noll, J., Clement, K., Dolor, J., & Petersen, M. (2017). Students’ use of narrative when constructing statistical models in TinkerPlots™. In S. Budgett & M. Pfannkuch (Eds.), Proceedings of SRTL-10: Innovations in statistical modelling to connect data, chance and context (pp. 50–60). Auckland: University of Auckland.
Noll, J., & Kirin, D. (2015). Students’ emerging statistical models using TinkerPlots™. In R. Biehler, D. Frischemeier, & S. Podworney (Eds.), Proceedings of Ninth International Research Forum on Statistical Reasoning, Thinking and Literacy (SRTL-9) (pp. 24–36). Paderborn: University of Paderborn.
Noll, J., & Kirin, D. (2016). Student approaches to constructing statistical models using TinkerPlots. Technology Innovations in Statistics Education, 9(1). http://escholarship.org/uc/item/05b643r9.
Noll, J., & Kirin, D. (2017). TinkerPlots™ model construction approaches for comparing two groups: Student perspectives. Statistics Education Research Journal, 16(2), 213–243.
Pawitan, Y. (2013). In all likelihood: Statistical modelling and inference using likelihood. Oxford: Oxford University Press.
Peters, S. A., Watkins, J. D., & Bennett, V. M. (2014). Middle and high school teachers’ transformative learning of center. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics, Flagstaff, Arizona, USA. Voorburg: International Statistical Institute. http://iase-web.org/icots/9/proceedings/pdfs/ICOTS9_C151_PETERS.pdf.
Pfannkuch, M. (2006). Comparing box plot distributions: A teacher’s reasoning. Statistics Education Research Journal, 5(2), 27–45. http://iase-web.org/documents/SERJ/SERJ5(2)_Pfannkuch.pdf.
Pfannkuch, M., Budgett, S., & Arnold, P. (2015). Experiment-to-causation inference: understanding causality in a probabilistic setting. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: learning and teaching informal inferential reasoning (pp. 95–127). Minneapolis: Catalyst Press.
Reading, C., & Reid, J. (2006). An emerging hierarchy of reasoning about distribution: From a variation perspective. Statistics Education Research Journal, 5(2), 46–68. https://www.stat.auckland.ac.nz/~iase/serj/SERJ5(2)_Reading_Reid.pdf.
Roback, P., Chance, B., Legler, J., & Moore, T. (2006). Applying Japanese lesson study principles to an upper-level undergraduate statistics course. Journal of Statistics Education, 14(2).
Rossman, A. J., St. Laurent, R., & Tabor, J. (2015). Advanced placement statistics: expanding the scope of statistics education. The American Statistician, 69(2), 121–126.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–23.
Simon, J. L. (1994). What some puzzling problems teach about the theory of simulation and the use of resampling. The American Statistician, 48(4), 290–293.
Smith, J., DiSessa, A., & Roschelle, J. (1993). Misconceptions reconceived: a constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115–163. http://www.jstor.org/stable/1466679.
Watson, J. M., Kelly, B., Callingham, R., & Shaughnessy, M. (2003). The measurement of school students’ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1–29.
Watson, J. M., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31, 44–70.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.
Zapata-Cardona, L. (2015). Exploring Teachers’ Ideas of Uncertainty. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: learning and teaching informal inferential reasoning (pp. 95–127). Minneapolis: Catalyst Press.
Zieffler, A., Garfield, J., delMas, R., & Gould, R. (2005). Studying the development of college students’ informal reasoning about statistical inference. Paper presented at the Fifth International Research Forum on Statistical Reasoning, Thinking and Literacy, Warwick, England.
Zieffler, A., & Huberty, M. D. (2015). A catalyst for change in the high school math curriculum. Chance, 28(3), 44–49. https://doi.org/10.1080/09332480.2015.1099365.