Computational thinking (CT) is a concept of growing importance to pre-university education. Yet, CT is often assessed through results, rather than by looking at the CT process itself. Process-based assessments, or assessments that model how a student completed a task, could instead investigate the process of CT as a formative assessment. In this work, we proposed an approach for developing process-based assessments using constructionist tasks specifically for CT assessment in K-12 contexts, with a focus on directly connecting programming artifacts to aspects of CT. We then illustrated such an assessment with 29 students who ranged in CT and programming experience. These students completed both a constructionist task and a traditional CT assessment. Data from the constructionist task was used to build a process-based assessment and results were compared between the two assessment methods. The process-based assessment produced groups of students who differed in their approach to the task with varying levels of success. However, there was no difference between groups of students in the scores on the traditional CT assessment. Process-based assessment from our approach may be useful as formative assessment to give process feedback, localized to the task given to students.