A comparative study on cognitive diagnostic assessment of mathematical key competencies and learning trajectories

Abstract

Initiated by the Program for International Student Assessment (PISA), Mathematical Key Competencies (MKCs), which integrate into the process of solving situational problems, becomes a typical example of Mathematical Key Competencies assessment. Cognitive Diagnostic Assessment, as a new generation of measurement theory, integrates the measurement objectives into the cognitive process model via cognitive analysis, and helps increase understanding of students’ mastery over fine-grained knowledge points. This paper analyzed 12 PISA test items and calibrated their attributes, thus forming a cognitive model based on six PISA’s MKCs, which were namely Mathematical Abstraction, Logical Reasoning, Intuitive Imagination, Mathematical Modeling, Mathematical Operation and Data Analysis. Through the comparison of models fit for DINA, DINO, RRUM, ACDM, GDM, LCDM, LLM, G-DINA and Mixed Model, the LCDM with a good model fit was selected to analyze the data of 19, 454 students in eight countries, and comparisons of the six MKCs among these countries were obtained. Through analyzing the knowledge states, combing the prerequisite relationships between the attributes, and exploring the learning trajectories of students’ MKCs in different countries, we found that the students’ performance in China was the best among all countries for each of the six MKCs. In all other countries, the students’ performance in Logical Reasoning and Intuitive Imagination were weaker than the other attributes. An analysis of learning trajectories found that Russia, Singapore, Australia and Finland had very similar main learning trajectories (highlighted in red), and the main learning trajectories of Russia and Singapore are the same; however, there exist distinct differences in learning trajectories between China and the United States, where the learning trajectories in China is complicated with varied branches, while the ones in the United States is relatively simple with fewer branches.