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theses

In recent years knowledge required for effective mathematics teaching has become more defined. A key area is the importance of teachers’ attending to student reasoning (e.g., Hiebert et al., 1997). There is increasing evidence that students are capable of constructing “proof-like” forms of reasoning to justify their solutions to tasks (e.g., Maher & Martino, 1996). These and other findings have been influential in shaping national policy by developing Standards for Practice, behaviors that students engage in while doing mathematics, and are best taught in the context of meaningful mathematical activity, including collaboration and discourse (Carpenter et al., 1989). Consequently, there is need for teachers to become aware of the importance of these practices and ways of attending to students mathematical reasoning. There is extensive work documenting that there is much to be gained by teachers studying episodes of children’s learning (e.g., Fennema, et al., 1996). There is also a substantial body of research in mathematics education and the learning sciences suggesting that creating opportunities for people to engage in generative and constructive ways with video has potential to support teacher learning. Research studies in teacher education suggest that both pre and in-service teachers can learn to recognize student reasoning by engaging in collaborative problem solving and then studying videos of children working on the same task (Maher, 2011). This study describes a course model, designed to examine teacher shifts in knowledge related to recognizing children’s mathematical reasoning. The design-based research was carried out over five years in a required course for mathematics education graduate students. The course addresses a review and study of literature in mathematics education research and practice, with special attention to collaborative problem solving, student learning, and emphasis on building knowledge within a designed setting. The results showed both pre (PST) and in-service teachers (IST) grew in their ability to recognize children’s reasoning. Analysis of course data provided insight into how teachers developed knowledge about student reasoning and how beliefs shifted in the process. Differences were identified between how PST and IST’s situated their experience. Implications of the study include recommendations for PST courses and PD programs.

ETD_7172

Ph.D.

Includes bibliographical references

by Robert Sigley

doi:10.7282/T3TQ63QQ

ETD doctoral

The author owns the copyright to this work.