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Abstract
Twenty-nine preservice teachers in a mathematics content course for early childhood education majors participated in an Interview Project. The preservice teachers worked in pairs (and one group of 3) to conduct an interview where they asked a child to solve additive structured story problems. Then they were asked to describe and analyze the childs mathematics using frameworks that were presented to them in class and to discuss any instructional decisions that they made prior to the interview, during the interview, and in a hypothetical second meeting with the child. The goals of the Interview Project were for the preservice teachers to develop knowledge of the frameworks around additive structured story problems and to apply these frameworks in real time and retrospectively while teaching children and for the preservice teachers to develop the ability to listen to and learn from childrens mathematical thinking. The purpose of the study was to evaluate whether or not the project met these goals. Pre-Interview Project and post-Interview Project data were collected in order to observe any changes. Data were collected in the form of class products, interviews, and observations. I found that the preservice teachers engaged in a Mathematics Teaching Cycle similar to that described by Simon (1997). The preservice teachers showed a significant improvement in their ability to describe a childs mathematics, to analyze a childs mathematics, and to use their listening to make appropriate instructional decisions. In addition, I found that the preservice teachers were rethinking their definitions of teaching and learning mathematics. They moved away from a view of teaching as telling and toward a view of teaching as posing appropriate tasks. They saw the benefit of incorporating theory into their practice. They also rethought their views of learning mathematics. They began to value reasoning strategically and using intuition to solve problems, rather than relying on traditional algorithms.