Sponsored by the National Science Foundation

Principal Investigator: Paul Cobb

Co-Principal Investigator: Kay McClain

Collaborators: Koeno Gravemeijer of The Freudenthal Institute, The Netherlands & Vanderbilt University; Cliff Konold, University of Massachusetts; Janet Bowers of San Diego State University

Graduate Students: Lynn Hodge, Maggie McGatha, Beth Petty, Carla Richards, Michelle Stephan, and Andrew Wilson

This is a one-year planning project for an envisioned larger project that will focus on statistics at the middle school level ( grades seven and eight). As currently envisioned, the overall intent of the larger project will be to:

1. Develop prototypical instructional sequences that incorporate computer-based mini-tools designed to support both exploratory data analysis and the development of big ideas in statistics.

 

2. Develop partnerships with middle school teachers and administrators to develop exemplary action-research sites at a total of ten schools in Nashville and Boston.

The specific goals of the planning project are to:

 

1. Investigate the feasibility of the approach to instructional design that we plan to pursue in the larger project by developing and investigating an instructional sequence that incorporates a customized mini-tool prototyped in Java.

2. Develop a research team capable of carrying out the larger project.

In the larger project, we will develop a series of computer-based mini-tools as integral components of prototypical instructional sequences. In line with Ball and Cohen's (1996) recent analysis of the role of instructional materials in the reform process, these mini-tools and the associated instructional sequences will be designed to support teachers' as well as students' learning. In addition, we will attend to the social context of both the students' and teachers' learning (i.e., classroom and school contexts), issues of equity
(i.e., culturally specific norms of communication), and the teacher's role in proactively supporting students' mathematical learning. However, for the purposes of this proposal for a planning grant, we restrict our focus to students' learning as it relates to exploratory data analysis and the development of big ideas in statistics.

Our decision to focus on statistics in middle school reflects the increasingly central role of statistical reasoning in both work-related activities and in informed citizenship (de Lange et al., 1991; National Council of Teachers of Mathematics, 1989, 1991). Several reviews ( e.g., Garfield, 1988; Shaughnessy, 1992) reveal that statistics typically receives, at best, limited attention at the middle school level and that instruction usually focuses on computational and procedural aspects (e.g., calculating means) at the expense of conceptual understanding ( e.g., developing notions of representativeness when comparing data sets). Further, exploratory data analysis in which data is created and interrogated in order to answer realistic questions or to make decisions is rarely the focus of attention. Instead, statistics is experienced by most students as an activity that involves remembering what they are supposed to do with the numbers of given data sets.

In addition to these important pragmatic considerations, our review of the literature indicates that further research is needed on students' statistical reasoning in innovative instructional settings. Numerous non-interventionist psychological studies of statistical reasoning have been conducted. However, these are inadequate for our purposes as instructional designers in that they typically document the generally undesirable beliefs and understandings that students develop in the context of traditional instruction. Thus while the findings of these studies provide a powerful rational for reforming statistics instruction, they do not provide positive guidance for those of us who want to investigate not what is but what can be. The relevant research base is therefore extremely thin. We have in fact only been able to identify seven investigations that document the process of students' learning as they conduct exploratory data analyses in technology-intensive instructional environments at any grade level, K-12 (Biehler, 1993; deLange et al., 1991; Hancock, Kaput, & Goldsmith, 1992; Jacobs & Lajoie, 1994; Konold, Pollatsek, Well, & Gagnon, 1996; Lehrer & Romberg, 1996; Metz, 1995). As a consequence, our understanding of both how students' might develop expertise in exploratory data analysis and how we can design tools and activities to support its development is relatively limited. The planning project and the main project will both contribute to this needed research base.

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