Scientific Program > Topic 8 > Session 8B >
Presentation 8B1. Supporting Teachers' Understanding of Statistical Data Analysis: Learning Trajectories as Tools for Change

Presenter
Kay McClain (USA) kay.mcclain@vanderbilt.edu

 

Presentation Abstract

The purpose of this paper is to provide an analysis that documents the change in a cohort of middle-school teachers' understandings as they engaged in activities aimed at improving their teaching of statistical data analysis. The goal is to account for changes in the teachers' perceptions of what it means to teach statistical data analysis effectively and how they develop an understanding of the complexities involved. In a process similar to Simon's (1997) Mathematics Teaching Cycle, the goal is to develop a conjectured learning route for the teachers, engage the teachers in activities designed to support that learning, and conduct ongoing analysis of this process in order to test and refine the initial conjecture. The image that emerges is one of a generative activity during which decisions about appropriate next steps are based on ongoing analysis of the data. The iterative process can then provide the means of supporting the teachers' developing understandings of the content that they teach. In addition, it provides a continuous improvement model to guide the collaborative work. The research then involves analyzing this process to determine its effectiveness in supporting change, thereby testing and refining the initial conjecture.

The learning trajectory for the teachers that are the focus of analysis is grounded in prior research efforts conducted with cohorts of middle-school students (ages twelve and thirteen) (cf. Cobb, 1999; Cobb, McClain, & Gravemeijer, in press; McClain, Cobb, & Gravemeijer, 2000; McClain & Cobb, in press). The initial activities with the cohort are derived from the instructional materials that were tested and refined in the course of two twelve-week classroom teaching experiments (cf. Cobb, 2000; Steffe & Thompson, 2000). As part of the process of designing the instructional sequences to be used in the classroom teaching experiments, the research team1 attempted to identify the "big ideas" in statistics. Our goal was to develop coherent sequences that would tie together the separate, loosely related topics that typically characterize American middle-school statistics curricula. The notion that emerged as central from our synthesis of the literature was that of distribution. We therefore wanted students to come to view data sets as entities that are distributed within a space of values (Hancock, in press; Konold, Pollatsek, Well, & Gagnon, in press; Wilensky, 1997). In the case of univariate data sets, for example, this enabled us to treat measures of center, spreadout-ness, skewness, and relative frequency as characteristics of the way the data are distributed. In addition, it allowed us to view various conventional graphs such as histograms and box-and-whiskers plots as different ways of structuring distributions. Our instructional goal was therefore to support students' gradual development of a single, multi-faceted notion, that of distribution, rather than a collection of topics to be taught as separate components of a curriculum unit. As a result, the work with teachers is guided by the same premise in order to ground the teachers' activity in the context of exploring the mathematics that underlies the concepts they will teach.

The activities of the cohort build from the conjectured learning trajectory and include monthly work sessions and summer seminars focused on 1) an in-depth exploration of statistical data analysis, and 2) development of modified lesson sequences to address statistical data analysis. In a process that combines features of the Japanese lesson study (cf. Lewis, 2000; Stigler and Hiebert, 1999) and the Work Circle (cf. Confrey, Bell, & Carrejo, 2001; Gomez, Fishman, & Pea, 1998) the teachers use the exploration, development and refinement of lesson sequences as situations for exploring students' diverse ways of reasoning and how they would account for them in their teaching, planning and assessing. An ongoing part of this process is to test and revise the conjectures about the learning route for teachers and the means of supporting it. The primary focus of analysis will therefore be on documenting changes in the teachers' understandings and how that relates to their day-to-day activity.

References

Cobb, P. (1999). Individual and collective mathematical learning: The case of statistical data analysis. Mathematical Thinking and Learning, 5-44.

Cobb, P. (2000). Conducting classroom teaching experiments in collaboration with teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education, 307-334. Mahwah, NJ: Lawrence Erlbaum Associates.

Confrey, J. Bell, K., & Carrejo, D. (2001). Systemic crossfire: What implementation research reveals about urban reform in mathematics. Paper presented at the annual meeting of the American Educational Research Association, Seattle, WA.

Gomez, L., Fishman, B., & Pea, R. (1998). Exploring rapid achievement gains in North Carolina and Texas. Washington, D.C.: National Education Goals Panel.

Hancock, C. (in press). The medium and the curriculum: Reflection on transparent tools and tacit mathematics. In A. diSessa, C. Hoyles, R. Noss & L. Edwards (Eds.), Computers and exploratory learning. Heidelberg, Germany: Springer Verlag.

Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (in press). "Students analyzing data: Research of critical barriers." Journal of Research in Mathematics Education.

Lewis, C. (2000). Lesson study: The core of Japanese professional development. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.

McClain, K., Cobb, P., & Gravemeijer, K. (2000). Supporting students' ways of reasoning about data. In M. Burke & F. Curcio (Eds.), Learning mathematics for a new century, 174-187. Reston, VA: National Council of Teachers of Mathematics.

McClain, K., & Cobb, P. (in press). Supporting students' ability to reason about data. Educational Studies in Mathematics.

Simon, M. (1997). Developing new models of mathematics teaching. In E. Fennema and B.S. Nelson (Eds.), Mathematics teachers in transition, 55-86.

Simon, M. A. (2000). Research on mathematics teacher development: The teacher development experiment. In A. Kelly & R. Lesh (Eds.). Research design in mathematics and science education. Hillsdale, NJ: LEA.

Steffe, L. & Thompson, P.W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. Kelly (Eds.), Research design in mathematics and science education, 267-307. Hillsdale, NJ: Erlbaum.

Stigler, J.W., & Hiebert, J. (1999). The teaching gap. New York: Free Press.

Wilensky, U. (1997.) What is normal anyway? Therapy for epistemological anxiety. Educational studies on Mathematics, 33, 171-202.

 

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