Professional and Student Visions of Statistics

• In Event: Representing and Supporting the Development of Epistemic Practices in Classroom Communities

Abstract

Students often view statistics as procedures that are routinely applied to a batch of data (Zawojewski & Shaughnessy, 2000). However, from a disciplinary perspective, statistics measure characteristics of a distribution to answer a question. To support the development of such a perspective, we engage students in designing measures of distribution where the context of data generation is within their grasp, such as a collection of measurements of a person’s arm-span. These data-generating contexts have the advantage of providing salient interpretation of a distribution as being composed of signal (e.g., true value of the measure) and noise (e.g., the error of measure), with statistics of center and variability as indicators of each. We ask students to first invent measures of center and precision, and then to share them during an activity structure that we term measure reviews (Lehrer & Kim, 2009). These measure reviews provide an apt forum for student critique of particular measures. Students’ critiques provide a window to their conceptions and valuations of statistics.

To investigate the nature of the approximation to professional practice emerging during these episodes of invention and critique, we compared what students noticed and said about one student-generated measure of variability with what professionals noticed and said about the same measure. We proceeded by creating transcriptions of video records of 12 measure reviews generated in four sixth-grade classrooms and selected a prototypical episode for consideration by two professionals, one a mathematician and the other a quantitative methodologist. The professionals saw the record of the initial presentation by a student of his measure, but did not view the ensuing critique by other students.

We found that both students and professionals invoked figured worlds (Holland, Lachicotte, Skinner & Cain, 1998) during their critiques of the measure. Common to both figured worlds were imagined transformations of the distribution in which the measure was initially constituted. These transformations suggested common ground between student and professional practice, including analysis of the behavior of the statistic as a measure (e.g., how did the value of the measure correspond to differences in distributions?), generalization (e.g., how did the measure behave in alternative distributions?), and clarity of method (e.g., was the measure communicated in a way that allowed meaningful joint regard?). Other aspects of figured worlds were not mentioned by students but were salient to professionals. For example, the mathematician invoked realms not envisioned by students in which the value of any particular statistic was viewed in relation to a system of statistical models. Additionally, the methodologist invoked the need for normalization so that differences in sample sizes could be accommodated. These comparisons suggest the forms of approximation to professional practice that appeared to be within the grasp of students while suggesting others that are apt to be less accessible in the confines of this initial introduction to practices of statistical reasoning.

Authors

• Ryan Seth Jones, Vanderbilt University

• Richard Lehrer, Vanderbilt University