Source: Journal of Teacher Education, Volume 60 No. 4, 380-392 (September/October 2009).
(Reviewed by the Portal Team)
Cognitively guided instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students’ mathematical thinking, they struggle with how to follow up on student ideas. In this article, the authors focus on three classrooms and the ways the teachers asked questions to help students make public and extend their mathematical thinking. The authors detail teachers’ questions and how they relate to students’ making explicit their complete and correct explanations.
Three teachers who had engaged in algebraic reasoning CGI professional development participated in this study. The teachers taught elementary school classrooms (two second grade, one third grade) at a large urban school district in Southern California. The district, in its 2nd year of new leadership when the study began, had a history of poor performance and a long-standing sense from those outside the district that it would never do well.
The authors chose these teachers for observation and analysis because they came from similar schools, taught similar concepts and skills, used similar classroom structures
(a combination of collaborative group and whole-class discussion of problem-solving strategies), but showed substantial differences in student achievement on posttests of algebraic thinking.
The authors videotaped and audiotaped conversations in these classrooms in ways that allowed them to document what students said to the teacher and to each other, so that they could closely analyze the relationship between teacher practice and student participation.
This study provides evidence about how teachers’ questions can support students to be more explicit and detailed in their explanations (Sfard & Kieran, 2001). In the classrooms examined here, the teachers frequently followed up on students’ initial responses, and they did so in a variety of different ways. At times they probed one student in a focused manner over a series of turns. At other times they asked one specific question related to something the student had said, or they asked a general question to prompt the student give additional explanation. Sometimes they asked leading questions, and sometimes they did none of these.
Follow-up questions, however, did not guarantee further student explanation. We found that the particular moves teachers made after their initial question seeking an explanation mattered for students’ opportunities to make their explanations explicit. Most important, uncovering details of students’ strategies often required multiple specific questions, each one focused on an element of a student’s explanation. In this way, the teachers focused on what students said in relation to the critical mathematical ideas and pressed students to make their thinking explicit.
This study shows that teachers’ questions can position the student thinking in relation to the mathematics in ways that support student understanding. The analyses provide evidence that much questioning occurs after teachers’ initial questions asking students to explain how
they solved problems.