Junior secondary students’ plane geometry learning: A cognitive diagnostic study

Junior secondary plane geometry requires students to coordinate diagrams, properties, and reasoning, yet classroom assessments often provide limited diagnostic information beyond total scores. Cognitive diagnostic assessment (CDA) can provide fine-grained evidence about students’ mastery, but its classroom-based application to plane geometry remains limited. This study used the sequential generalized deterministic inputs, noisy “and” gate (seq-GDINA) model to analyze responses to a school-based midterm examination in plane geometry completed by 534 grade 8 students at a junior secondary school in China. It examined students’ mastery of five cognitive attributes and inferred possible learning paths from the diagnosed knowledge states of 207 students in four focal classes. Diagnostic interpretation was supported by evidence of test quality, model fit, and attribute-level classification accuracy. The results indicated uneven mastery across the five attributes. The students showed stronger mastery of triangle concepts and axial symmetry but weaker mastery of congruent triangles, polygons and their interior angles, and especially angle-bisector properties. Subgroup and individual analyses showed that students with similar total scores could differ markedly in their geometric profiles. In the four focal classes, the diagnosed knowledge states suggested a dominant inferred path from no stable mastery, through triangle concepts and axial symmetry, then polygons and congruent triangles, and finally to full mastery of all five attributes. This path can be interpreted as a classroom-level inference. The study shows how CDA can help interpret students’ knowledge mastery and guide remedial instruction in plane geometry.