The Application of Diagnostic Tree Model to Mathematics Assessment with Constructed-Response Items

Abstract

This study aimed to analyze mathematics assessments with constructed-response items using diagnostic tree model (DTM), which accommodates polytomous responses with multiple strategies and obtain diagnostic information about examinees’ attribute mastery. A cognitive diagnostic assessment evaluating the “absolute inequality” domain with constructed-response items was designed based on the DTM and administered to students attending a science high school for gifted children. The findings from cognitive diagnosis of examinees indicate that students face more challenges in mastering the Cauchy-Schwarz inequality compared with the arithmetic-geometric mean inequality, with the greatest difficulty being in the application of the substitution method. The analysis revealed that for certain test items, the estimated guess and slip parameters vary depending on the nodes of the path selected by the chosen strategy, thus indicating that the difficulty to solve the problem may depend on the strategy that the students choose. Additionally, this study suggests several methods to visualize the item response of each examinee using a tree structure and estimated parameters for the DTM and to utilize it for individualized diagnostic feedback.