All analytical data.

As a new generation of assessment instrument, cognitive diagnosis integrates the measurement objectives into the cognitive model to diagnose the fine-grained knowledge of students. Taking the PISA 2012 dataset in mathematics from Shanghai, Hong Kong, Macau and Taiwan as the research subject, this study constructed a cognitive model with the attributes of Mathematical Abstraction, Logical Reasoning, Mathematical Modeling, Intuitive Imagination, Mathematical Operation and Data Analysis, and made an analysis of the mastery of students’ mathematical competencies of different attributes in four regions, and the learning paths of the students’ mathematical competencies were constructed. The results showed that Shanghai had the obvious advantages in each attribute; the mastery mode of Hong Kong, Macau and Taiwan showed a common trend, and they all indicated a relatively low percentages of competencies in Logical Reasoning and Intuitive Imagination. In terms of the learning paths, the learning paths in the four regions reflected diversities, but obvious main learning paths existed. Majority of the knowledge states’ abilities were below 0. While in Hong Kong, Taiwan, and Macau, more knowledge states’ abilities were above 0. This research provided a reference for the systematic analysis of students’ knowledge status and learning path.