Publications & Resources

Assessing Expert Knowledge Representations of Introductory Statistics

Jun 2003

Nancy C. Lavigne and Robert Glaser

The assessment challenge today is to build assessments based on empirical and theoretical knowledge of learning and cognition. A cognitive proficiency that has received relatively little attention in statistics classrooms is how students represent their knowledge of statistical content. In this report, we focus on two assessments that are specifically designed to assess different but related aspects of individuals’ knowledge representations: (a) problem sorts which measure how individuals represent a specific aspect of their knowledge in the context of word problems (i.e., problem representation) and (b) concept maps which measure how individuals represent their knowledge of the discipline as a whole (i.e., domain representation). This case study is meant to assess a statistics expert’s representation of statistics as explicitly as possible. The participant was required to (a) group problems based on how he felt they best belonged together and explain his sorts after he was finished, (b) identify and explain various levels of problem groupings he expected introductory statistics students to generate, and (c) construct two concept maps, one representing statistics as a whole (includes descriptive and inferential statistics) and a second representing a specific aspect of statistics (inferential statistics), which was content emphasized in the problem sorting task. Explanations were audiotaped. The data suggest that the problem sorting task can be useful as a measure of representation when supplemented with an individual’s explanations for his or her sorts. Moreover, concept maps can assist in the interpretation of performance on the problem sorting task. The concept map and problem sorting measures can be mutually informative, with the concept map providing a broader picture and the problem sorts illustrating how certain concepts become salient when applied to different contexts.

Lavigne, N. C., & Glaser, R. (2003). Assessing expert knowledge representations of introductory statistics (CSE Report 600). Los Angeles: University of California, Los Angeles, National Center for Research on Evaluation, Standards, and Student Testing (CRESST).