What they notice in photographs: A study of preservice teachers' noticing in a formative assessment cycle

Noticing is an essential skill for all teachers of mathematics. Mathematics teacher educators have utilized a variety of tools to practice and develop preservice teachers' (PSTs') ability to notice, which we extend to include photographs and learning trajectories. This article explores PSTs' noticing skills by analyzing work samples from a methods course assignment that examined teacher noticing and planning for future instruction. The work samples were analyzed using structural coding. Results indicate that PSTs can: (a) notice students' mathematical thinking in photographs they captured; (b) attend to and interpret the mathematics in photographs, but need additional support to consider how to respond to the mathematical thinking; and (c) use learning trajectories or progressions to help them notice, but there is less evidence of them using learning trajectories or progressions as a tool to respond to students' mathematical thinking. Implications for mathematics teacher education and future research are considered.