Development of a New Learning Progression Verification Method based on the Hierarchical Diagnostic Classification Model: Taking Grade 5 Students’ Fractional Operations as an Example

Abstract Learning progressions can reflect students’ continuous in‐depth thinking development paths, and their establishment is an iterative process from the construction of hypothetical learning progressions to the verification of that hypotheses. Considering the limitations of the existing verification method of learning progressions based on a rule space model, this study put forward a new validating method based on the hierarchical diagnostic classification model (HDCM) and developed a learning progression with grade 5 students’ fraction operations as an example. An expert group first abstracted the attributes and then developed a hypothesized learning progression. Next, the HDCM was used to analyze the test data collected from 817 fifth‐grade students, followed by the revision of the learning progression hypothesis. Results showed that (1) the fractional operations involved five attributes: basic operation (A1), reduction of a fraction (A2), changing fractions to a common denominator (A3), split with mix number (A4), and borrowing (A5); (2) the constructed learning progression featured four levels: Level 1 with A1, Level 2 with both A1 and A2, Level 3 with the first four attributes, and Level 4 with all five attributes.