Abstract:   Learning progressions are descriptions of students’ increasingly sophisticated ways of thinking about or understanding a topic during a period. It’s an iterative process to build learning progressions, beginning with hypothetical learning progressions and then validated by empirical approaches. Psychometric models, such as item response models, multidimensional item response models and cognitive diagnosis models, combine learning progressions with the function of assessing students. These models provide evidence for validating learning progressions and also make diagnosis about students. In addition, learning progressions have provided new perspectives for vertical scaling and adaptive learning. But we should be aware of some questions, such as differential item functioning.

Key words: learning progressions, item response models, cognitive diagnosis models, vertical scaling, adaptive learning, differential item functioning