This paper reports a study to address two questions concerning children's understanding of average: how do children construct and interpret representativeness within the context of data sets? and How do children think about the mean as a particular mathematical definition and relationship? Twenty-one students (seven each of 4th, 6th, and 8th graders) were interviewed using a series of seven open-ended problems that examined the notion of average. The four that yielded the most results were identified and included in the report. These were two "Construction Problems," an "Interpretation Problem," and a "Weighted Means Problem." Analysis of transcripts and summaries of the interviews produced five approaches that children used for constructing and describing average. The approaches were: (1) Average as Mode; (2) Average as Algorithm; (3) The TERC Working Papers series consists of completed research, both published and unpublished, and workin-progress in the learning and teaching of science and mathematics. We are introducing the series with four papers and will add papers at regular intervals.
Whenever the need arises to describe a set of data in a succinct way, the issue of mathematical representativeness arises. The goal of this research is to understand the characteristics of fourth through eighth graders' constructions of “average” as a representative number summarizing a data set. Twenty-one students were interviewed, using a series of open-ended problems that called on children to construct their own notion of representativeness. Five basic constructions of representativeness are identified and analyzed. These approaches illustrate the ways in which students are (or are not) developing useful, general definitions for the statistical concept of average.
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