This study examined elementary and secondary prospective teachers' (PTs') abilities to analyze a classroom lesson in order to make claims about student thinking around specific mathematical learning goals based on relevant and revealing evidence. Previous research suggests PTs have some skills in analyzing evidence but apply them inconsistently. Our goal was to describe in more detail the strengths and weaknesses in PTs' ability to analyze evidence of student thinking. Results indicate that PTs can make some appropriate claims about student learning in a lesson transcript, but more often make overly broad and general claims. PTs were able to support their claims with specific student work but often used poorly aligned evidence. PTs also often explicitly recognized the shortcomings of evidence from the lesson transcript, but then relied on that evidence to make claims about student thinking. Finally, PTs' background, such as number of teacher education courses completed, does not appear to strongly influence their ability to make claims and support them with evidence, though secondary PTs were more likely to recognize the limitations of evidence than elementary PTs. These results have implications for teacher educators, pointing to the importance of designing interventions to help PTs look beyond the most visible and salient features of a lesson when analyzing student thinking.