Characterizing pivotal teaching moments in beginning mathematics teachers\u27 practice

Although skilled mathematics teachers and teacher educators often know when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students\u27 mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers\u27 instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers\u27 decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers\u27 abilities to act in ways that would increase their students\u27 mathematical understanding. © 2012 Springer Science+Business Media B.V