AN INFERENTIALISM-BASED FRAMEWORK FOR CAPTURING STATISTICAL CONCEPT FORMATION OVER TIME
DOI:
https://doi.org/10.52041/serj.v24i1.714Keywords:
Inferentialism, statistical modelling, middle school students, theoretical framework, statistical concept formationAbstract
Statistics education researchers have been challenged to consider the theory of inferentialism in understanding concept formation in students. A critique of inferentialism is that no comprehensive method has been formulated to use the theory in practice. In this paper an inferentialism-based framework is presented that appears to be capable of explicating the development of statistical concepts during learning. By following six 11-year-olds’ learning over several statistical modelling cycles using TinkerPlots, the framework was used to capture their interrogative cycles of noticing and wondering, giving and asking for reasons, and sanctioning and censuring, as well as oscillations between concretising language about actions and conceptualising language towards concept formation. Five teaching episodes occurring near the beginning of a 12-week learning sequence are used to illustrate how the framework might be able to capture student concept formation over time.
References
Arnold, P., & Pfannkuch, M. (2024). Engaging novice statisticians in statistical communications. Mathematics Education Research Journal, 36(Suppl 1), 147–173. https://doi.org/10.1007/s13394-022-00442-w
Bakker, A., Ben–Zvi, D., & Makar, K., (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference. Mathematics Education Research Journal, 29(4), 455–470. https://doi.org/10.1007/s13394-016-0187-x
Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1–2), 5–26. https://doi.org/10.1080/10986065.2011.538293
Bakker, A., & Hußmann, S. (2017). Inferentialism in mathematics education: Introduction to a special issue. Mathematics Education Research Journal, 29(4), 395–401. https://doi.org/10.1007/s13394-017-0224-4
Baroody, A. J., Cibulskis, M., Lai, M., & Li, X. (2004). Comments on the use of learning trajectories in curriculum development and research. Mathematical Thinking and Learning, 6(2), 227–260. https://doi.org/10.1207/s15327833mtl0602_8
Brandom, R. (2000). Articulating reasons: An introduction to inferentialism. Harvard University Press. https://doi.org/10.4159/9780674028739
Charmaz, K. (2014). Constructing grounded theory. SAGE.
Chernoff, E., & Zazkis, R. (2011). From personal to conventional probabilities: From sample set to sample space. Educational Studies in Mathematics, 77(1), 15–33. https://doi.org/10.1007/s10649-010-9288-8
Derry, J. (2017). An introduction to inferentialism in mathematics education. Mathematics Education Research Journal, 29(4), 403–418. https://doi.org/10.1007/s13394-017-0193-7
Dvir, M., & Ben-Zvi, D. (2018). The role of model comparison in young learners’ reasoning with statistical models and modeling. ZDM–Mathematics Education, 50(7), 1183–1196. https://doi.org/10.1007/s11858-018-0987-4
Fergusson, A., & Pfannkuch, M. (2022). Introducing high school teachers to predictive modelling and APIs using code-driven tools. Statistics Education Research Journal, 21(2), Article 8. https://doi.org/10.52041/serj.v21i2.49
Heusdens, W., Baartman, L., & De Bruijn, E. (2019). Know your onions: An exploration of how students develop vocational knowledge during professional performance. Scandinavian Journal of Educational Research, 63(6), 839–852. https://doi.org/10.1080/00313831.2018.1452291
Heusdens, W., Bakker, A., Baartman, L., & De Bruijn, E. (2016). Contextualising vocational knowledge: A theoretical framework and illustrations from culinary education. Vocations and Learning, 9(2), 151–165. https://doi.org/10.1007/s12186-015-9145-0
Kaplan J., & Peters, S. (2023). Publishing in SERJ: Processes and suggestions [Webinar]. International Association for Statistical Education. https://www.youtube.com/watch?v=rhMig3ZhZBU
Konold, C., & Harradine, A. (2014). Contexts for highlighting signal and noise. In T. Wassong, D. Frischemeier, P. Fischer, R. Hochmuth, & P. Bender (Eds.), Mit Werkzeugen Mathematik und Stochastik lernen: Using tools for learning mathematics and statistics (pp. 237–250). Springer. https://doi.org/10.1007/978-3-658-03104-6_18
Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1), 1–37. https://doi.org/10.5070/T521000032
Konold, C., & Miller, C. (2011). TinkerPlots: Dynamic data exploration (Version 2.3) [Computer software]. Learn Troop.
Lehrer, R. (2015). Developing practices of model–based informal inference. In Proceedings of the Ninth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL9, July 2015) (pp. 76–86). University of Paderborn.
Lehrer, R., & English, L. (2018). Introducing children to modeling variability. In D. Ben–Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 229–260). Springer. https://doi.org/10.1007/978-3-319-66195-7_7
Lesh, R., & Doerr, H. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Lawrence Erlbaum Associates.
Noll, J., Clement, K., Dolor, J., Kirin, D., & Petersen, M. (2018). Students’ use of narrative when constructing statistical models in TinkerPlots. ZDM–Mathematics Education, 50(7), 1267–1280. https://doi.org/10.1007/s11858-018-0981-x
Noorloos, R., Taylor, S., Bakker, A., & Derry, J. (2017). Inferentialism as an alternative to socio–constructivism in mathematics education. Mathematics Education Research Journal, 29(4), 437–453. https://doi.org/10.1007/s13394-017-0189-3
Nilsson, P. (2020). Students’ informal hypothesis testing in a probability context with concrete random generators. Statistics Education Research Journal, 19(3), 53–73. https://doi.org/10.52041/serj.v19i3.56
Nilsson, P., Schindler, M., & Bakker, A. (2018). The nature and use of theories in statistics education. In D. Ben–Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 359–386). Springer. https://doi.org/10.1007/978-3-319-66195-7_11
Patel, A. (2022). Statistical modelling: An enquiry into novice students’ co-creation of reasoning and practice. [Unpublished doctoral dissertation]. The University of Auckland. https://hdl.handle.net/2292/58778
Patel, A., & Pfannkuch, M. (2018). Developing a statistical modeling framework to characterize year 7 students' reasoning. ZDM–Mathematics Education, 50(7), 1197–1212. https://doi.org/10.1007/s11858-018-0960-2
Patel, A., & Pfannkuch, M. (2022). A framework for capturing the development of statistical concepts. In S. Peters, L. Zapata-Cardona, F. Bonafini, & A. Fan (Eds.), Bridging the gap: Empowering and educating today’s learners in statistics. Proceedings of the Eleventh International Conference on Teaching Statistics (ICOTS11, September 2022), Rosario, Argentina. International Association for Statistical Education. https://doi.org/10.52041/iase.icots11.T2A1
Pratt, D. (2011). Re–connecting probability and reasoning from data in secondary school teaching. In Proceedings of the 58th International Statistical Institute World Statistical Congress, Dublin, (pp. 890–899). International Statistical Institute.
Radford, L. (2017). On inferentialism. Mathematics Education Research Journal, 29(4), 493–508. https://doi.org/10.1007/s13394-017-0225-3
Radford, L. (2018). On theories in mathematics education and their conceptual differences. In B. Sirakov, P. de Souza, & M. Viana (Eds.), Proceedings of the International Congress of Mathematicians, (Vol 4. pp. 4055–4074). World Scientific Publishing. https://doi.org/10.1142/9789813272880_0211
Shaughnessy, J. (1997). Missed opportunities in research on the teaching and learning of data and chance. In F. Biddulph & K. Carr (Eds.), People in mathematics education. Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 6–22). Mathematics Education Research Group of Australasia.
Taylor, S., Noorloos, R., & Bakker, A. (2017). Mastering as an inferentialist alternative to the acquisition and participation metaphors for learning. Journal of Philosophy of Education, 51(4), 769–784.
Van Oers, B. (1998). From context to contextualizing. Learning and Instruction, 8(6), 473–488. https://doi.org/10.1016/S0959-4752(98)00031-0
von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. The Falmer Press
