UC Berkeley

Learning progressions are one of the most important curriculum and assessment design ideas to be introduced in the past decade. A well-constructed learning progression can incorporate the knowledge needed to define the “track” that students may or should be on. This can inform teachers about when to teach what to whom. For the development of sound learning progressions, researchers investigate how learning typically unfolds in a particular area of study, and should empirically test and validate it. A learning progression of Number Sense was developed in a research project, Special Education Learning Progressions in Math (SELPM). The progression includes hypothesized levels of achievement for grades K to 3 for four sub-domains of Number Sense: Place Value, Addition, Magnitude Comparison, and Transcoding. This research was concerned with the validation of the learning progression. The study used three student assessment data sets to investigate the validity of the proposed learning progressions using item response theory, specifically the Rasch model and its extension. This research consists of three validation studies – Phase I: Preliminary Study, Phase II: Testing Validity of Learning Progression, and Phase III: Validation of Alternative Learning Progression. Through the iterative validation process, this research aimed to provide an empirically-validated and theoretically-based Number Sense learning progression and a set of assessments for the education community