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• W106766469 abstract "Interviewing students, though a common and popular activity in teacher education programs has been scarcely researched as a strategy to prepare prospective teachers for mathematics teaching. This study explores the role of interviews as occasions for prospective elementary school teachers to learn three essential practices in the teaching of mathematics—questioning, listening, and responding. Two orientations to interviewing students used by the participants in the study are described and illustrated. Their reported insights focused more prominently on the practice of listening and interpreting students’ mathematical ideas which raises questions about structures and designs of the interview experience so that the practices of questioning and responding become more prominent. Teaching in the ways that are envisioned in the mathematics reform documents (NCTM, 2000) where teachers ask for, listen to, and make sense of students’ ideas require a host of skills, knowledge and dispositions that are not well understood. They require teachers to “comprehend students’ thinking, their interpretations of problems, their mistakes ... and they must have the capacity to probe thoughtfully and tactfully” (Cohen, 1989, p. 75). Learning about students and their ways of thinking, therefore, is inarguably one of the most important domains of knowledge for teaching (Shulman, 1987). From planning lessons, to asking questions, to facilitating class discussion, teachers’ knowledge of and ability to investigate students’ thinking, can make a difference in the kinds of learning opportunities that are offered to students in the classroom (Henningsen & Stein, 1999; Fenemma et al, 1996). How and where teachers learn these competencies, however, has proven to be an elusive question. Conducting interviews with students is one strategy that has been proposed to help prospective teachers practice and learn questioning techniques (Moyer & Milewicz, 2002) and learn about students’ mathematical thinking (Schorr & Ginsburg, 2000). Similar to previous proponents we consider interviews as a valuable strategy in preservice teacher education. Although conducting interviews differ in significant ways from the challenges and demands of actual classroom practice, it is a context for learning and practicing skills such as questioning, listening, and responding that are essential in the classroom. Although research in recent years has seen a surge of interest in strategies to help prospective teachers learn these essential strategies (e.g., first author, 2000; second author, 1999), interviews with students though a very common and popular strategy in teacher education courses, have been scarcely researched both in terms of their design and their effectiveness or impact. In this study we explore preservice teachers’ approaches to interviewing students as well as the kinds of insights they report as having gained from their interview experience. Data Sources and Analysis To explore the question of how interviewing students could become occasions for prospective teachers to learn to investigate students’ mathematical ideas we draw upon our own experience teaching elementary and secondary mathematics education courses. The data we report here comes from one group of prospective teachers in the first author’s elementary mathematics methods course. This course is field-based, that is, the TE students are placed in a local school 2 hours/week and attend class 3 hours/week. The participants of this study were attending a course that was offered during the fall of one academic year. Participants were 18 elementary preservice teachers attending the course in their senior year as undergraduates and prior to their year-long internship placement. The Interview Task The preservice teachers conducted mathematics interviews with children from their local field placement elementary schools. Number sense was the topic chosen for the interviews, in particular, the interview protocol provided to the prospective teachers focused on a doubling task (Kelleher, 1996) which investigates students’ mental computational strategies when doubling numbers. The interview task was presented to the students as follows: Look in your field classroom and in their mathematics textbook to learn about how these help students develop number sense and collect student work to find out about how children make sense of numbers. Write: (1) Describe an activity from your field placement classroom, or from their textbook and/or teachers’ guide, and explain how it helps students develop number sense. (2) Write about what you learned from interviewing a student about what they understand and can do with numbers. Use the sample interview in the back as a resource and use Chapter 6 and 9 to help you interpret your findings. (3) Talk about what you learned, found challenging and insightful as an interviewer The sample interview provided to the preservice teachers did not include the specific questions that they were to ask or in what order they were to ask them, instead it stated the goal of the interview and what they might investigate with the task. It also included some advice about interviewing, such as a reminder to consistently use probes, to give students adequate time to think, and avoid validating student's responses by saying “That's right”, or “Good!” If you are compelled to say something, you may use less evaluative feedback such as “That's interesting.” Sample Interview Task This task asks students to mentally double numbers. It is designed to help us learn about the students' comfort and facility with numbers as well as to explore the students' strategies for doing mental computations. You might begin by asking the students to double 2, then 4, then 8, and so on. Always remember to ask students to explain how they figured their answers. Beware that some students might need clarification of what is meant by doubling and might need an example (using fingers or counters). In terms of what to look for in your analysis, it is interesting to note: (a) What is the largest number that the student can double mentally? (b) How does the student handle the numbers that are “easier” to double (e.g.:, multiples of 5 and 10) as opposed to the “tougher” numbers (e.g., numbers that require “carrying” or regrouping such as 17)? (c) Is the student’s strategy a broad or a limited strategy? (d) What sort of manipulatives (including how the student uses his/her fingers) does the student use to figure out the question? (e) What do the student’s facial expressions and non-verbal cues suggest about his/her level of confidence and engagement with the task? In preparation to their interviewing experience, several in-class experiences were designed to help preservice teachers plan and prepare their interviews. Preservice teachers watched three sets of video clips showing one-on-one interviews with students. The first two clips were two 5-7 minutes of videos of the first author interviewing two first grade students with the doubling task. The third clip was a video from the MACT (1990) materials where an interviewer is asking fourth through sixth grade students to calculate subtractions mentally and with paper and pencil. Following the viewing of the videos, the preservice teachers and instructor discussed examples of questions that gave good insight into students’ thinking, whether the students’ responses were conceptual or procedural in nature, and to discuss which questions they would like to ask the students that were not asked by the interviewer. Data sources and analysis The class discussion around the aforementioned videoclips was audiotaped. Observation notes from two graduate students were also collected to gather impressions of the participants’ orientations towards interviewing. These first impressions were used as an analytical lens and guide to the later analysis of the written reports. These reports were typically 3-5 pages in length. These written reflections were read and examined for constructs, themes, and patterns in preservice teachers’ orientations towards interviewing students and their reported insights. The researchers coded the themes using a constant comparative method (Strauss, 1987). The data were clustered around the most salient and recurring theme across the 18 participants. A framework that has been previously used by the authors to look at preservice teachers’ learning in other contexts and that focus on their “questioning, listening, responding” practices (see second author, 1999) also emerged as a useful framework to organize and cluster the patterns that arose in this context." @default.
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• W106766469 title "Learning to Investigate Students' Mathematical Thinking: The Role of Student Interviews." @default.
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