Mathematical Knowledge Learning Trajectories: An International Comparative Study

Learning trajectories refer to the progression of students’ knowledge acquisition and skill development within a specific domain. By identifying students’ proficiency levels across specific knowledge points or attributes, cognitive diagnostic models (CDMs) allow researchers to systematically describe and analyze learning trajectories. This study utilized 42 eighth-grade mathematics items from the Trends in International Mathematics and Science Study (TIMSS) 2019 dataset and responses from 4,460 students across eight countries or regions. Based on seven attributes identified by the TIMSS framework, CDM was employed to investigate variations in learning trajectories across different content domains. Specifically, the study examined relationships between knowledge states and attribute patterns to identify distinct learning trajectories. The findings reveal that the United States and Dubai (UAE) exhibited only a single dominant learning trajectory, while other countries or regions demonstrated greater diversity in their students’ learning pathways. Across all contexts, most students tended to first master attributes related to geometry or data and probability, suggesting these areas as common starting points for skill development. These results highlight the potential of CDMs to uncover nuanced patterns of knowledge progression and inform tailored educational strategies.