Mutually Informative Measures of Knowledge: Concept Maps Plus Problem Sorts in Statistics

Abstract

This case study examines the validity of 1 measure of representation and employs multiple measures to examine whether they provide mutually informative or independent pieces of information. These measures include (a) concept maps, which measure how individuals represent their content knowledge of a domain as a whole; (b) problem sorts, which measure how individuals represent a specific aspect of their knowledge on word problems; and (c) structured interviews, which identify the reasons underlying sorting and concept mapping performance. Data from statistics instructors showed that the sorting task was a useful measure of representation when supplemented with instructors' explanations of their rationales. Moreover, concept maps assisted in the interpretation of performance on the sorting task. Concept maps and problem sorts were mutually informative, with the former providing a broader picture and the latter illustrating how particular concepts became salient when applied to a different context.