Constructing Concepts of Average

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The goal of this project is to examine how people develop, construct, interpret, and represent concepts of central tendency, or average. From this understanding, more effective directions for the teaching and learning of statistics at the elementary and middle school levels will be derived. Given the major educational thrust toward statistical literacy for all, and given the clear lack of research on what children understand about statistics, this study represents an important step in linking research to emerging mathematics teaching practices. During the first year of the project, fourth, sixth, and eighth graders as well as teachers of these grades will be interviewed to determine how they find and interpret average. Participants will use a variety of materials to solve and represent problems involving engaging, familiar quantitative data. Analysis of these interviews will identify the concepts, approaches, misconceptions, representations, and rules exhibited by individuals at these ages. A theoretical model of conceptions of average will be constructed from the first year's analysis. Based on this model, a series of teaching interviews, using concrete and software-based representations, will be devised. The second year's research will focus on investigating how inadequate cognitive models of average can become more complete and flexible.