Applying an IRT-Based Cognitive Diagnostic Model to Diagnose Students' Knowledge States in Multiplication and Division with Exponents
Menucha Birenbaum, Kikumi K. Tatsuoka · Applied Measurement in Education · 1993
The study applied a psychometric model-the rule-space model-to diagnose students' states of knowledge about how the exponents behave in multiplication and division of quantities with exponents. A 38-item test was administered to 431 Grade 10 students. Each item was characterized by a list of task attributes required for answering the item correctly, and each student was classified, based on his or her item-score pattern, into the most likely knowledge, state (i.e., attribute-mastery pattern) corresponding to an ideal item-score pattern. The following outcomes of the rule-space model were presented: (a) the results of the classification of examinees to knowledge states at the group level along with individual examples, (b) the mastery level of the underlying task attributes as evaluated at three different test-score groups, and (c) a tree diagram of the transitional relationships among the knowledge states that can guide the design of effective remediation. Implications for utilizing the feedback, provided by the rule-space model in the context of instruction and assessment are discussed.