Abandoning questions with unpredictable answers
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Abandoning questions with unpredictable answers Cat Gaspard1 · Julie Gainsburg1
© Springer Nature B.V. 2019
Abstract This study investigated the types of questions that prospective teachers of mathematics asked their students during whole-class discussions, how these questions changed over time, and why. Four prospective teachers were interviewed at the beginning and end of a 10-week period of student teaching to elicit their views about the kinds of questions mathematics teachers should ask. One lesson per week, for eight lessons, was video recorded for each prospective teacher. These videos were analyzed for the kinds of questions the prospective teachers asked and the nature of the responses from their high-school students. We found that the prospective teachers initially expressed the view that it was important to ask questions that required students to explain their thinking—a view that aligned with what was promoted in their teacher-preparation program—and that they attempted to ask questions with unpredictable answers in the early weeks. Over time, however, they asked fewer questions overall, with an even greater reduction in the number of questions with unpredictable answers. Interviews revealed that the prospective teachers’ views about what kinds of questions to ask were influenced, over time, by the responses of their students. The videos offered additional insights into the nature of the students’ responses. Keywords Mathematics education · Teacher education · Pedagogical knowledge · Preservice teacher education · Secondary mathematics education · Questioning practices A common focus of teacher-preparation programs (TPPs) is to develop teachers’ questioning skills and an understanding of how different types of questions serve different pedagogical purposes. In mathematics education, teacher questions that generate mathematical discussion among students have been increasingly emphasized. For example, the Common Core State Standards for Mathematical Practices (Common Core State Standards Initiative 2010) expect students to “construct viable arguments and critique the reasoning of others” and “express regularity in repeated reasoning”—practices that require mathematical talk among students and teacher. Whole-class discussions can support mathematical talk and, * Cat Gaspard [email protected] Julie Gainsburg [email protected] 1
Department of Secondary Education, Michael D. Eisner College of Education, California State University, Northridge, 18111 Nordhoff St, Northridge, CA 91330, USA
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as such, are important pedagogical components of mathematics lessons. However, student talk does not ensure learning; teachers must ask generative questions at strategic times in order to elicit, build on, and extend student thinking about a mathematical point (Sleep 2012; Smith and Stein 2011). To orchestrate a productive whole-class discussion about mathematics, a teacher must possess a repertoire of types of questions to draw a range of students into
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