Measurement Model for Linking Individual Learning to Processes and Knowledge: Application to Mathematical Reasoning

Abstract

Contemporary instructional theories increasingly emphasize the importance of linking an individual's learning to changes in cognitive processes and knowledge structures. In this article, an extension of the multidimensional Rasch model for learning and change (MRMLC) is presented so as to permit theories of processes and knowledge structures to be incorporated into the item response model. Like the MRMLC, this extension (MRMLC+) resolves some basic problems in measuring individual change and permits adaptive testing so that precise estimates of learning may be obtained. Additionally, MRMLC+ permits individual learning to be linked to substantive changes in processing and knowledge. An application to a study on the impact of short‐term instruction on mathematical problem solving shows the potential of MRMLC + for interpretations. In this study, a theoretically plausible model of knowledge structures (Mayer, Larkin, & Kadane, 1984) provides the basis of individual learning interpretations.