The goal of this exploratory study was to analyze how beginning prospective secondary school teachers approached the analysis of student written responses to formative assessment probes. We sought to identify what elements of students' written work were noticed, what types of inferences of student understanding were built, and what these noticed elements and inferences told us about levels of sophistication in assessing student understanding. Our results are based on the qualitative analysis of the written evaluations of student work made by 32 prospective secondary school teachers enrolled in an introductory teacher preparation course at our institution. The results of this study suggest that analyzing teachers' assessment of student understanding requires paying attention to both domain-neutral and domain-dependent aspects of teacher reasoning. Domain-neutral dimensions help characterize how a teacher frames the assessment of student understanding. Domain-dependent dimensions characterize how the teacher attends to relevant disciplinary ideas. Our prospective teachers often focused on the description and qualification of student work, making fewer attempts to make sense of student ideas. However, study participants' abilities to generate inferences were varied and influenced by the nature of students' responses. Findings from this study provide a framework for scaffolding and evaluating progress in teachers' abilities to notice and interpret student work.