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Presentation 6A3. Assessing and Tracing the Development of Basotho Elementary Students' Probabilistic Thinking

Mokaeane V. Polaki (South Africa)


Presentation Abstract

I will report on two studies that involved the assessment and development of Basotho (people of Lesotho, Southern Africa) elementary students' probabilistic thinking. As an extension of framework research on probabilistic thinking by Jones and his colleagues (Jones et al., 1997), we generated and validated a framework that described and predicted the probabilistic thinking of Basotho students' in grades 1, 3, 5, 7 and 8 across five constructs: sample space, probability of an event, probability comparisons, conditional probability, and independence (Polaki, Lefoka,& Jones, 2000). The framework described students' probabilistic thinking in terms of four developmental levels that were found to be consistent with the thinking levels in Case's (1996) more general cognitive model, and in essence, demonstrated that Case's model was applicable to probabilistic thinking in addition to the three knowledge domains previously examined by Case: quantitative thinking, spatial thinking, and narrative thinking.

As a follow- up to this study (Polaki et al., 2000), I designed and implemented two versions of a teaching experiment that traced the development of Basotho elementary (grades 4 and 5) students' growth in probabilistic thinking (Polaki, 2000). The first version focused on small-sample experiments and analysis of sample space composition. The second version incorporated small-and large-sample experimentation (simulations) in addition to analyses of sample space symmetry. Grounded in Cobb's (1999) developmental research cycle, the main objectives of each version were to (a) to identify and trace the evolution of mathematical practices associated with growth in thinking about sample space and probability of an event, (b) identify key episodes that were associated with students' growth in probabilistic thinking, and (c) evaluate the effectiveness of each version of the teaching experiment. Analyses of the data revealed existence of the following thinking patterns: (a) a sample space misconception (Jones et al., 1999) that was highly resistant to instruction, (b) a weak and often unstable part-part schema that was minimally effective in enabling target students to identify complete sample space and to order probabilities for 1-dimensional experiments, and (c) a stronger and more stable part-part schema that enabled target students to reason with greater consistency when listing the complete set of outcomes and when ordering probabilities for 1-dimensional experiments. Additionally, as evidenced by changes in thinking levels, each version of the teaching experiment had a substantial impact on the target students' probabilistic thinking.

Case, R. (1996). Reconceptualizing the nature of children's' conceptual structures and their development in middle childhood. Monographs of the Society for Research in Child Development, 61, (1-2, Serial N0. 246), 1-26.

Cobb, P. (1999). Individual and collective mathematical development: The case of statistical analysis. Mathematical Thinking and Learning, 1 (1), 5-43.

Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics, 32, 101-125.

Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Using students' probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30, 487-519.

Polaki M. V. (2000). Using instruction to trace the development of Basotho elementary students' probabilistic thinking. Unpublished doctoral dissertation, Illinois State University, Normal.

Polaki, M. V., Lefoka, P. J., & Jones, G. A (2000). Developing a cognitive framework for describing and predicting Basotho students' probabilistic thinking. BOLESWA Educational Research Journal, 17, 1-20.


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