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Presentation 6A2. Assessing and Fostering Children's Statistical Thinking

Graham A. Jones (USA)
Cynthia W. Langrall (USA)
Carol A. Thornton (USA)
Edward S. Mooney (USA)


Presentation Abstract

Our presentation will be based on a suite of studies involving children's statistical thinking in the elementary grades. In our seminal study (Jones et al., 2000a), we generated and validated a Framework that described and predicted children's statistical thinking in Grades 1 through 5 on four processes: describing data, organizing and reducing data, representing data, and analyzing and interpreting data. This study showed that students' statistical thinking could be characterized according to four level of thinking that were consistent with a more general neo-Piagetian model of cognitive development (Biggs & Collis, 1991). A follow-up study (Nisbet, Jones, Langrall & Thornton, 2000) elaborated children's thinking in organizing and representing both categorical and numerical data.
We will also report on two teaching experiments (Jones et al., 2000b; Wares, Jones, Langrall, and Thornton, 2000) that used our Framework as a means of informing instruction. One of these teaching experiments was conducted with a Grade 2 class (n = 19) and the other with two Grade 1 classes (n1 = 20 and n2 = 19). Both of the teaching experiments were situated in the theoretical underpinnings of Cobb's work (1999) and involved the development and implementation of learning trajectories (Simon, 1995) as a means of analyzing children's statistical thinking during instruction. Our analyzes revealed that: experiences with the data context reduced children's idiosyncratic descriptions, data values of zero were problematic, the children possessed intuitive knowledge of center and spread, and making predictions was difficult for these children.

Biggs, J. B. & Collis, K. F. (1991). Multimodal learning and intelligent behavior. In H. Rowe (Ed.), Intelligence: Reconceptualization and measurement (pp. 57-76). Hillsdale, NJ: Erlbaum.

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

Jones, G. A., Thornton,C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000a). A framework for characterizing children's statistical thinking. Mathematical Thinking and Learning, 2, 269-307.

Jones, G. A., Langrall, C. W., Thornton, C. A., Mooney, E. S., Wares, A., Perry, B., Putt, J., & Nisbet, S. (2000b). Using students' statistical thinking to inform instruction. Journal of Mathematical Behavior, submitted.

Nisbet, S., Jones, G. A., Langrall, C. W., & Thornton, C. W. (2000). Children's representation of data. Manuscript in preparation.

Simon, M. A. (1995). Restructuring mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114-145.

Wares, A., Jones, G. A., Langrall, C. W., & Thornton, C. A. (2000). Statistical thinking among children: An instructional case study. Proceedings of 22nd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tuscon, Arizona: PME.


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