Designing Cognitively Diagnostic Assessment for Algebraic Content Knowledge and Thinking Skills

Abstract

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory model and the quantitative assessment structure. Simulated data was applied to the model to illustrate the purpose. The diagnostic assessment model was represented by a Bayesian network model. Four explanatory variables and nine evidential variables were identified. These were developed to describe the content domain and cognitive structure in an algebra learning process. The diagnostic assessment model both exhibited learning progresses and provided diagnostic feedback. Through students’ performance examples model-based achievement scores were reported at three levels: 1) evidential variable level, 2) explanatory variable lower level, and 3) explanatory variable higher level. This study revealed that the diagnostic assessment model can effectively report learners’ progress in algebra learning in both content knowledge and thinking skills.