Inventing Data Structures for Representational Purposes: Elementary Grade Students' Classification Models

Abstract

This study concerns the development of children's understanding of data and classification. Three intact classrooms of students and their teachers (18 at 1st and 2nd grade, 25 at 4th grade, and 22 at 5th grade) worked over several sessions to categorize drawings made by other children and to progressively "mathematize" their categorization rules. The goal was to develop a model that would make explicit their initial guesses about the grade level of the artists. In small groups, students developed, applied, and made iterations of revisions to their data models. The details of instruction and duration varied somewhat in accord with the capabilities and needs of students of different ages. The youngest children evolved systems of attributes that described their categories in a post hoc fashion but failed to come to regard those rules as a model to guide classification. In contrast, 4th and 5th graders considered their category systems as models that logically constrained the members admitted to categories. These students came to appreciate dimensional attribute-value structure, although many continued to include redundant or extraneous information. They incorporated and discussed a variety of kinds of decision rules, including ways of combining information, such as differentially weighing diagnostic attributes. By engaging with data characterized by prototypic rather than crisp membership values, students had the opportunity to see the intellectual work performed by practices of data modeling.

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