Teachers’ Professional Noticing from a Perspective of Key Elements of Intensive, One-to-One Intervention

Abstract

Teaching practice, which uses student mathematical thinking to develop mathematical concepts, is valued by the mathematics education community, but the nuances of this practice are relatively unexplored (Leatham, Peterson, Stockero, & Van Zoest, 2015). We observed about 33 hours of video recordings of one-to-one instruction in the Mathematics Intervention Specialist Program (MISP), involving four teachers and six students, in order to identify patterns relating to how the teachers act in particular situations to achieve particular pedagogical goals. We conceptualized a set of instances of such patterns in one-to-one teaching sessions, called Key Elements (KEs)—micro-instructional strategies used by a teacher when interacting with a student solving an arithmetic task. Twenty-five KEs are described and incorporated into a framework consisting of four categories: before posing a task, during posing a task, during solving a task, and after solving a task. A scenario of one-to-one instruction is described and the teacher’s use of the following nine KEs is highlighted: Post-posing wait-time, post-responding wait-time, rephrasing the task, giving encouragement to a partly or nearly correct response, changing the setting during solving, scaffolding during, recapitulating, linking settings, and affirming. The three skills of professional noticing—attending, interpreting and deciding—are used to categorize the KEs of teaching occurring in the scenario. This highlights the linking of the KEs of instruction and the three skills of professional noticing. Thus, the study supports the notion that teacher development focusing on professional noticing can enhance teachers’ learning to use the KEs of one-to-one instruction.