Mrs. Hobbs's fourth graders are struggling. And it is working. This year, instead of teaching the state standard on unit conversion by showing students a procedure to follow, Hobbs asked her students to work in groups to develop a method. She is excited to promote more reasoning, problem solving, and use of varied solution pathways, in line with the NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014). This is worthy work. But in some moments, for some students, the struggle does not feel productive. Several students are hesitant and lack confidence. A few give up easily. Hobbs does not want to go back to telling students a procedure, but she does not want to leave them to flounder.
Understanding mathematics teacher noticing has been the focus of a growing body of research, in which student work and classroom videos are often used as artifacts for surfacing teachers’ cognitive processes. However, what teachers notice through reflecting on artifacts of teaching may not be parallel to what they notice in the complex and demanding environment of the classroom. This article used a new technique, side-by-side coaching, to uncover teacher noticing in the moment of instruction. There were 21 instances of noticing aloud during side by side coaching which were analyzed and classified, yielding 6 types of teacher noticing aloud, including instances in which teachers expressed confidence, struggle, and wonder. Implications for coaching and future research on teacher noticing are discussed.