Scientific Program > Topic 6 > Session 6B >
Presentation 6B3. A Framework on Middle school Students' Statistical Thinking

Cynthia W. Langrall (USA)
Edward S. Mooney (USA)


Presentation Abstract
Professional education organizations for mathematics, science, social studies, and geography recommend that students, as early as middle school (grades 6 - 8), have experience collecting, organizing, representing, and interpreting data. However, research on middle school students' statistical thinking is sparse. A cohesive picture of middle school students' statistical thinking is needed to better inform curriculum developers and classroom teachers. Mooney (2001) developed and validated a framework for describing middle school students' thinking across four processes: describing data, organizing and reducing data, representing data, and analyzing and interpreting data. The validation process supported the claim that students progress through four levels of thinking within each statistical process. These levels of thinking are consistent with the cognitive levels postulated in the Biggs & Collis (1991) general developmental model.

We used a similar validation process to focus on three sub-processes of statistical thinking that were not adequately represented in Mooney's (2001) Middle School Students' Statistical Thinking (M3ST) Framework. These sub-processes are: (a) students' use of multiplicative reasoning in analyzing data, (b) categorizing and grouping data, and (c) representing data to make comparisons between two data sets. These three sub-processes are considered important to the overall development of students' statistical thinking (Cobb, 1999; Curcio, 1987; NCTM, 2000). Thus, addressing these gaps in the M3ST Framework is especially important if the framework is to be used by teachers and curriculum developers to inform statistics instruction.

Students in grades six through eight at a Midwestern U.S. school formed the population for this study. Twelve students, four from each grade level, were selected for case-study analysis based on levels of performance in mathematics: one high, two middle, and one low. Based on the M3ST framework and drawing from the research literature (e.g., Berg & Phillips, 1994; Cobb, 1999; Wainer, 1992) an interview protocol was developed to assess the middle school students' understanding of the three sub-processes. The protocol comprised four tasks; each with a series of questions designed to assess students' thinking across the four levels of the M3ST Framework. Questions were designed so students could respond orally or by generating tables or data displays. A double-coding procedure (Miles & Huberman,1994) was used to analyze the interview data. We independently coded students' responses, including student-generated work, according to descriptors in M3ST Framework and descriptors generated during data analysis that characterized student responses that were not present in the framework. For each sub-process, we analyzed the data to discern key thinking patterns exhibited by the students at each level. These patterns were incorporated into the M3ST framework as descriptors for each of the four levels of statistical thinking.

In this paper, we will report on the validation process and will present the Refined M3ST Framework. This study was the first of three in an extended research program that includes a nationwide validation of the Refined M3ST Framework, and a professional development program using the refined framework with middle school teachers to guide instruction in statistics.

Berg, C. A., & Phillips, D. G. (1994). An investigation of the relationship between logical thinking structures and the ability to construct and interpret line graphs. Journal of Research in Science Teaching, 31, 323-344.

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

Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18, 382-393.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data. Thousand Oaks, CA: Sage Publications.

Mooney (2001). Development of a middle school statistical thinking framework. Submitted for publication, Mathematical Thinking and Learning.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

Resnick, L. (1983). Toward a cognitive theory of instruction. In S. G. Paris, G. M. Olson, & H. W. Stevenson (Eds.), Learning and motivation in the classroom (pp. 5-38). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.

Wainer, H. (1992). Understanding graphs and tables. Educational Researcher, 21 (1), 14-23.


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