Block-based programming environments are widely used in computer science education. However, these environments pose significant challenges for student modeling. Given a series of problem-solving actions taken by students in block-based programming environments, student models need to accurately infer problem-solving students' programming abilities in real time to enable adaptive feedback and hints that are tailored to students' abilities. While student models for block-based programming offer the potential to support student-adaptivity, creating student models for these environments is challenging because students can develop a broad range of solutions to a given programming activity. To address these challenges, we introduce a progression trajectory-based student modeling framework for modeling novice student block-based programming across multiple learning activities. Student trajectories utilize a time series representation that employs code analysis to incrementally compare student programs to expert solutions as students undertake block-based programming activities. This paper reports on a study in which progression trajectories were collected from more than 100 undergraduate students engaging in a series of block-based programming activities in an introductory computer science course. Using progression trajectory-based student modeling, we identified three distinct trajectory classes: Early Quitting, High Persistence, and Efficient Completion. Analysis of these trajectories revealed that they exhibit significantly different characteristics with respect to students' actions and can be used to accurately predict students' programming behaviors on future programming activities compared to competing baseline models. The findings suggest that progression trajectory-based student models can accurately model students' block-based programming problem solving and hold potential for informing adaptive support in block-based programming environments.
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