Developing a Learning Progression for Probability Based on the GDINA Model in China

This research focuses on developing a learning progression of probability for middle school students, and it applies the GDINA model in cognitive diagnosis models to data analysis. GDINA model analysis firstly extracted nine cognitive attributes and constructed their attribute hierarchy and the hypothesized learning progression according to previous studies, curriculum standards, and textbooks. Then the cognitive diagnostic test was developed based on Q-matrix theory. Finally, we used the GDINA model to analyze a sample of 1624 Chinese middle school students' item response patterns to identify their attribute master patterns, verify and modify the hypothesized learning progression. The results show that, first of all, the psychometric quality of the measurement instrument is good. Secondly, the hypothesized learning progression is basically reasonable and modified according to the attribute mastery probability. The results also show that the level of probabilistic thinking of middle school students is improving steadily. However, the students in grade 8 are slightly regressive. These results demonstrate the feasibility and superiority of using cognitive diagnosis models to develop a learning progression.