Critical thinking as an approach to coordinating personal, experimental and theoretical notions of chance
DOI:
https://doi.org/10.52041/iase24.602Abstract
To foster secondary students’ probabilistic thinking, the coordination of personal, experimental, and theoretical notions of chance is necessary but rather challenging. Whereas critical thinking is effective in terms of self-awareness and self-regulation of learning, it also has the potential as an approach to overcome the challenge of coordinating the three notions. This study aimed to propose a framework for task design and analysis based on an enactivist view of cognition and a reformulated learning model, Judgment-Enactment-Reflection integrated with critical thinking. Tasks were designed according to the framework and implemented in two Grade-9 classes. Results indicated that the personal, experimental, and theoretical notions of chance could be coordinated to develop the subjectivist, frequentist and classical perspectives of probability with critical thinking as an approach.References
Barab, S., & Squire, K. (2004). Design-based research: Putting a stake in the ground. Journal of the Learning Sciences, 13(1), 1–14. https://doi.org/10.1207/s15327809jls1301_1
Batanero, C. (2020). Probability teaching and learning. In S. Lerman (Ed.), Encyclopedia of mathematics education, (pp. 682-686). Springer. https://reurl.cc/26KkDr
Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G.A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 15-37). Springer. https://doi.org/10.1007/0-387-24530-8_2
Ben-Zvi, D., & Friedlander, A. (1997). Statistical thinking in a technological environment. In J. B. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics: Proceedings of the 1996 IASE Round Table Conference (pp. 45–55). IASE. https://reurl.cc/G5n2QG
Borasi, R. (1994). Capitalizing on errors as "Springboards for Inquiry": a teaching experiment. Journal for Research in Mathematics Education, 25(2), 166-208. https://doi.org/10.5951/ jresematheduc.25.2.0166
Borovcnik, M., & Kapadia, R. (2014). A historical and philosophical perspective on probability In E. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives, (pp, 7-34). Springer. https://doi.org/10.1007/978-94-007-7155-0_2
Chernoff, E. J., & Zazkis, R. (2011). From personal to conventional probabilities: from sample set to sample space. Educational Studies in Mathematics, 77, 15-33. https://doi.org/10.1007/s10649- 010-9288-8
Chinn, C. A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: A theoretical framework and implications for science instruction. Review of Educational Research, 63(1), 1-49. https://doi.org/10.3102/00346543063001001
Dellantonio, S., & Pastore, L. (2021). Ignorance, misconceptions and critical thinking. Synthese, 198(8), 7473-7501. https://doi.org/10.1007/s11229-019-02529-7
Fenwick, T. J. (2001). Experiential learning: A theoretical critique from five perspectives (Information Series No. 385). Columbus: ERIC Clearinghouse on Adult, Career and Vocational Education, The Ohio State University. https://eric.ed.gov/?id=ED454418
Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. In G.A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). Springer. https://reurl.cc/nqmjod
Hartman, H. J. (2001). Metacognition in science teaching and learning. In H.J Hartman (Ed.), Metacognition in learning and instruction: Theory, research and practice (pp. 173-201). Springer. https://reurl.cc/geRjzQ
Jolley, D., Davis, M., Lavender, A. P., & Roberts, L. (2022). An online critical thinking course reduces misconceptions in the knowledge of personal trainers. Studies in Continuing Education, 44(1), 39-54. https://doi.org/10.1080/0158037X.2020.1738373
Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., ... & Kazak, S. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13(1-2), 68-86. https://doi.org/10.1080/10986065.2011. 538299
Kowalski, P., & Taylor, A. K. (2004). Ability and critical thinking as predictors of change in students’ psychological misconceptions. Journal of Instructional Psychology, 31(4), 297-303. https://reurl. cc/p9ajMZ
Maturana, H. R., & Varela, F. J. (1987). The tree of knowledge: The biological roots of human understanding. New Science Library/Shambhala Publications. https://reurl.cc/74KQnk
Park, J., & Kim, D. W. (2023). Facilitating factors and obstacles in the coordination of theoretical probability and relative frequency estimates of probability. Educational Studies in Mathematics, 114(3), 439-460. https://doi.org/10.1007/s10649-023-10253-w
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council on Teaching Mathematics (pp. 465-494). MacMillan Publishing Co. https://reurl. cc/ZZ45XM
Simionescu-Panait, A. (2020). Are Constructivism and Enactivism two opposite philosophies on learning mathematics?. Revista Pesquisa Qualitativa, 8(18), 419-430. https://doi.org/10.33361/ RPQ.2020.v.8.n.18.338
Varela, F. J., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. MIT press. https://reurl.cc/ZZ4ka6
