The role of simulation in secondary students' reasoning about probability distributions
Bruce, Mary H.
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Technological advancements have added a new dimension to the teaching and learning of mathematics. Research has praised the use of simulations as a technological tool in probability instruction. Using a social constructivist perspective, this study addressed secondary students' reasoning about probability distributions using simulations. A probabilistic thinking framework developed by Jones, Langrall, Thornton, and Mogill (1999) and the GAISE curriculum framework endorsed by the American Statistical Association (2007) were used to trace the evolution of secondary students' probabilistic reasoning in this study. Four classes of Advanced Placement Statistics students were randomly assigned to two groups, a control group using a formulaic, textbook-oriented approach to learning about probability distributions and a simulation group using physical and technological simulations to supplement their learning. Students were subjectively designated as low- and high-level students based on course histories and performance in the class. A mixed-methods design included a pre-, post-, and retention test for quantitative sources of data and written feedback, student interviews, and observation notes for qualitative sources of data. Results from the quantitative analysis did not show significant group differences on the posttest but did show significant group differences on the retention test. Performance level differences were significant on the posttest but not on the retention test, and the interaction of group and level was significant for the posttest scores but not for the retention scores. Low-level students in the simulation group appeared to benefit more from the simulations than the high-level students. Qualitative results revealed that students in the simulation group reasoned differently about probability distributions than students in the control group. The simulations initiated new representational structures to aid the students in their conceptual understanding. Interviews, written feedback, and observations indicated a connected understanding of such critical concepts as randomness, variation, central tendency, distribution, and the law of large numbers. Although the study reinforced the persistence of various probabilistic misconceptions, the results fuel an optimism that simulations can possibly lead to conceptual change in students' understanding of probabilistic concepts. The results indicate that using such exploratory instructional designs in the teaching of probability and probability distributions can lead to the achievement of an equilibrium among students in the classroom.