Characterizing Teachable Moments in Classrooms of Experienced Mathematics Teachers
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It has been widely agreed upon within the mathematics education community that there are important moments within a mathematics lesson that a teacher needs to notice and act upon (Fennema, Carpenter, Franke, Levi, Jacobs & Epson, 1996; Stockero and Van Zoest, 2013). These moments are generally called teachable moments. There is more work about pre-service teachers than in-service teachers, and teachable moments have not been studied for the same teacher over extended period of time. The purposes of this qualitative study were to characterize the teachable moments in experienced mathematics teachers’ classrooms over a six-week period, and to describe their decisions in response to those teachable moments. Six mathematics teachers who each had at least five years of mathematics teaching experience agreed to participate in the study. For each teacher, the researcher videotaped and wrote field notes in the same class once per week for six weeks. Two researchers reviewed the videotapes and identified instances of teachable moments through consensus. Follow-up interviews with each teacher focused on video excerpts of the teachable moments and understanding the corresponding decisions made by the teacher. Carspecken’s (1996) first three stages for critical qualitative research, compiling the primary record, preliminary reconstructive analysis and dialogical data generation via teacher interviews framed the data collection and data analysis techniques, as did an earlier framework from Sun and Hanna (2013) that characterized teachable moments and teacher decisions. The coding process resulted in the same three types of teachable moments as identified by Sun and Hanna (2013). These types were: incorrect mathematics, sense-making, and mathematical confusion. Teachers’ decisions in response to teachable moments were classified into seven types, which was three more than the types of experienced teachers’ decisions in response to teachable moments identified by Sun and Hanna (2013). These types were: extend/make connections, pursue student thinking, emphasize mathematical meaning, wait to allow student to explore first, emphasize mathematical process, acknowledge but continue, and ignore or dismiss. The last three types of decisions were newly identified from the data of this study. The information provided by this study may be of value to teacher educators and professional development providers to help teachers recognize mathematically rich moments and productively use student thinking to increase learning.