The purpose of this study was to examine secondary mathematics teachers' questioning, responses, and perceived influences upon their instructional decisions regarding questioning and response to students' ideas. This study also compared the questioning practices, responses, and influences of beginning teachers to more experienced teachers. Previous studies on teacher quality in mathematics education have focused on general characteristics of mathematics teachers' instructional practice including a broad range of instructional strategies. Little is known about mathematics teachers' questioning practices and responses to students' ideas that research has repeatedly reported are critical to student mathematics learning in secondary classrooms. Furthermore, it is not clear how different novice teachers are in questioning and responding to students from experienced teachers. This understanding can provide significant insights into teacher education programs for mathematics teachers. With those issues in mind, this study was designed to answer the following questions: (1) What similarities and differences exist in questioning patterns between novice and experienced teachers when guiding a classroom mathematical discussion? (2) What similarities and differences exist in responses to students during pivotal teaching moments between novice and experienced teachers when guiding a classroom mathematical discussion? (3) What perceived factors impact the responses teachers give to students' ideas, and how are these factors of influence different among novice and experienced teachers?
This study employed a multiple case study research design to compare the questioning practices and responses of three beginning teachers and three experienced teachers. Multiple sources of data were collected, including two interviews (i.e., initial interview and follow-up interview) for each teacher, five days of classroom video footage for each teacher, and field notes by the researcher for each interview and observation. The researcher conducted initial interviews with each teacher to gain a general sense of the teacher's philosophy and use of questions in guiding classroom discussion. Five instructional days of observation followed the initial interview, and then the researcher conducted a follow-up interview by use of video-stimulated response. All interviews were transcribed verbatim for analysis. The data was analyzed mainly using the constant comparative method to identify regularities and patterns emerging from the data. Results showed differences between beginning and experienced teachers in the frequency and variety of questions asked. Although all teachers showed the largest number of questions in the Socratic questioning category, differences were prominent in the semantic tapestry and framing categories. Results regarding teacher responses to pivotal teaching moments showed that four teachers favored a procedural emphasis in their responses to students, and two teachers used responses to direct students to make clear connections within or outside of mathematics. Perceived influences identified include: (1) reflection on experience and mathematical knowledge for teaching, (2) time, and (3) relationship with students, teachers, and parents, and knowledge of student background.
Practicing teachers can expand the types of questions they use in the classroom, making particular efforts to include those areas that this study showed to be most lacking: semantic tapestry questions that help students build a coherent mental framework related to a mathematical concept, and framing questions that help frame a problem and structure the discussion that follows. The comparison between beginning and experienced teachers also shed light on important practices for teacher education. The beginning teacher participants from this study had no trouble noticing pivotal teaching moments in their lessons but were less developed in their responses to them. Recommendations for mathematics teacher education programs are to provide opportunities to develop content, pedagogical knowledge including specific instruction on questioning strategies, and also to provide parallel field experiences where pre-service teachers can apply the knowledge and skill they are learning.