Students' knowledge states and learning pathways of parallelism concept based on cognitive diagnostic assessment

Despite the importance of parallelism concept in understanding advanced geometric concepts, past studies have constantly reported poor mastery of this concept. To pinpoint students' current states in the progression of parallelism concept acquisition, this study aimed to profile students' knowledge states and model their learning pathways. Conducted using a cross-sectional research design, the study involved 1069 Grade Four students selected through two-stage cluster sampling. The findings revealed six distinct knowledge states exhibited by the students. Although the students obtained the same score on the test, they might demonstrate different knowledge states. Among the three identified learning pathways, the majority of students who have yet to reach the highest competency level are expected to follow Learning Pathway 1. This pathway indicates a transition of knowledge states from mastering the simplest attribute , corresponding to Geometric Thinking Level 0 , to the most complex attribute , corresponding to Geometric Thinking Level 1 , in ascending order.