Analyzing and interpreting student thinking through written work is a key, often challenging, practice of teaching. It entails noticing students' mathematical thinking and drawing on mathematical knowledge for teaching. This study investigates how pre-service secondary teachers at the beginning of their preparation reason about students' written work. In interviews, participants solved mathematical tasks and the analyzed student written work in order to make assertions about student understanding. Analysis of participants' assertions revealed three primary reasoning strategies: mathematical reasoning, pedagogical reasoning, and reasoning through self-comparison. Self-comparison involved participants comparing the student work directly with their own work on the task. This strategy showed promise, as it could be used to help make inferential assertions about student understanding. It also highlighted areas of caution around how beginning pre-service teachers might make use of evidence. This study contributes to the existing literature around noticing student thinking in written work by highlighting the significance of reasoning through self-comparison.