If students are to pursue the mathematical strategies they devise, teachers must be able to notice these strategies in-the-moment, attending to what a student did and interpreting what they understand. Otherwise, teachers might urge students to pursue a different approach. Novice teachers may find it particularly challenging to notice strategies in-the-moment as they have had few opportunities to develop the knowledge of children's thinking believed necessary to do so. We conducted video stimulated-recalls with four novice teachers, in which teachers shared what they had noticed during moments from a previous lesson. In recalling these moments, teachers often attended to specific details in students' strategies and made precise claims about students' understandings. This noticing was supported by contextual knowledge teachers had about their students and prior lessons. We propose that teacher educators prepare teachers to notice strategies by preparing them to develop contextual knowledge in addition to knowledge of children's thinking.