MODELLING PROBLEMS OF STATISTICAL REASONING

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Published: Jul 13, 2017
DOI: https://doi.org/10.12681/enedim.14179
Keywords:
Modelling Dynamic Statistics Software Model Eliciting Activities Inferential Statistics Informal Statistical Inference
Έφη Παπαριστοδήμου (Efi Paparistodimou)
Παιδαγωγικό Ινστιτούτο Κύπρου
Μαρία Μελετίου - Μαυροθέρη (Maria Meletiou- Mavrotheri)
Ευρωπαϊκό Πανεπιστήμιο Κύπρου
Ana Serrado Bayes
La Salle-Buen Consejo
Abstract

The transition from descriptive to inferential statistics is a known area of difficulties for students. This article shares the experiences from a teaching experiment in a graduate-level quantitative research methods course, which adopted a non-conventional approach to teaching statistics that put models and modelling at the core of the curriculum. Findings indicate that the informal approach to statistical inference adopted in the course, which focused on modelling and simulation using the dynamic statistics software Tinkerplots2 as an investigation tool, promoted powerful ways of thinking statistically, while at the same time also developing students’ appreciation for the practical value of statistics. The affordances offered by the technological tool for building data models and for experimenting with these models to make sense of the situation at hand, were instrumental in supporting student understanding of both informal and formal inferential statistics.

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References
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. 16-42). Dordrecht: Kluwer.
Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman, & B. Chance (Eds.), Working Cooperatively in Statistics Education: Proceedings of the Seventh International Conference of Teaching Statistics (ICOTS-7), Salvador, Brazil.
Biehler, R., & Prömmel, A. (2010). Developing students' computer-supported simulation and modelling competencies by means of carefully designed working environments. In C. Reading (Ed.), Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS-8), Ljubljana, Slovenia. Voorburg, The Netherlands: International Statistical Institute.
delMas, R. C., 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.
Eichler, A., & Vogel, M. (2014). Three approaches for modelling situations with randomness. In E. J. Chernoff, & B.
Sriraman (Eds.), Probabilistic thinking (pp. 75-100). Dordrecht: Springer.
Erickson, T. (2006). Using simulation to learn about inference. In Rossman, A. & Chance, B. (Eds.), Working Cooperatively in Statistics Education: Proceedings of the Seventh International Conference of Teaching Statistics (ICOTS-7), Salvador, Brazil. Voorburg, The Netherlands: International Statistical Institute.
Erickson, T. (2013). Designing games for understanding in a data analysis environment. Technology Innovations in Statistics Education, 7(2).
Finzer, W. (2001). fathom dynamic statistics (v1.0) [Current version is 2.1]. Emeryville, CA: Key Curriculum Press.
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
Garfield, J., & Ahlgren, A. (1998). Difficulties in learning basic concepts in probability and statistics: implications for research. Journal for Research in Mathematics Education, 19, 44-63.
Garfield, J., & Ben-Zvi, D. (2008). Developing students' statistical reasoning: connecting research and teaching practice. New York: Springer.
Garfield, J., delMas, R., & Zieffler, A. (2010). Developing tertiary-level students’ statistical thinking through the use of model-eliciting activities. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society. Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS8, July, 2010), Ljubljana, Slovenia. Voorburg, The Netherlands: International Statistical Institute. Online: www.stat.auckland.ac.nz/~iase/publications.php
Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinking in an introductory, tertiary - level statistics course. ZDM – The International Journal on Mathematics Education, 44 (7), 883 – 898.
Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of students’ informal inferential reasoning. Mathematical Thinking and Learning, 13, 87–108.
Graham, A. (2006). Developing thinking in statistics. London: Paul Chapman Publishing.
Konold, C, Harradine, A. & Kazak, S. (2007). Understanding distribution by modelling them, International Journal for Computers and Mathematical Learning, 12, 217-230.
Konold, C., & Lehrer, R. (2008). Technology and mathematics education: An essay in honor of Jim Kaput. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 49–72). New York, NY: Routledge.
Konold, C., & Miller, C. D. (2005). TinkerPlots: dynamic data exploration (v1.0) [Current version is 2.1]. Emeryville, CA: Key Curriculum Press.
Konold, C., & Miller, C. (2011). TinkerPlots (Version v2.0) [Computer software]. Emeryville, CA: Key Curriculum Press.
Lee, H. (2013). Quantitative reasoning in digital world: laying the pebbles for future research frontiers. In R.L. Mayes & L.L. Hatfield (Eds.), Quantitative reasoning in mathematics and science education: Papers from an international STEM research symposium, WISDOM e Mongraph # 3 (pp. 65-82). Laramie, Wyoming: University of Wyoming College of Education.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum.
Meletiou-Mavrotheris, M., and Paparistodemou, E. (2015). Developing young learners’ reasoning about samples and sampling in the context of informal inferences. Educational Studies in Mathematics, 88(3), 385-404.
Murtonen, M., & Lehtinen, E. (2003). Difficulties experienced by education and sociology students in quantititative methods courses. Studies in Higher Education, 28 (2), 171-185.
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Enhancing reasoning about statistical inference in 8 year-old students. Statistics Education Research Journal, 7 (2), 83–106.
Paparistodemou, E., Noss, R., & Pratt, D. (2008). The interplay between fairness and randomness in a spatial computer game. International Journal of Computers for Mathematical Learning, 13(2), 89–110.
Pratt, D. (2011). Re-connecting probability and reasoning about data in secondary school teaching. In Proceedings of the 58th World Statistics Conference of the International Statistical Institute (pp. 880-899), Dublin Ireland.
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 of Teaching Statistics (ICOTS-7), Salvador, Brazil.
Serrado, B., Meletiou-Mavrotheris, M., and Paparistodemou, E. (2017). A study on statistical technological and pedagogical content knowledge on an innovative course on quantitative research methods. In G. Aldon, F. Hitt, L. Bazzini, and U. Gellert (Eds.), Mathematics and technology (pp. 467-494). Springer.
Στυλιανού, Δ., & Μελετίου-Μαυροθέρη, Μ. (2003). Δυναμικά λογισμικά: νέεσ προοπτικέσ για τη χρήση τεχνολογίασ στη διδασκαλία των μαθηματικών. Σύγχρονη Εκπαίδευση, 132, 27-37.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67 (3), 223-265.
Zieffler, A., delMas, R., & Garfield, J. (2014). The symbiotic, mutualistic relationship between modelling and simulation in developing students’ statistical reasoning about inference and uncertainty. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute. Online: www.iase-web.org.
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