CAREER: Advancing Teacher Development and Mathematics Learning Through the Integration of Knowledge and Practice

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Advancing Teacher Development and Mathematics Learning through the Integration of Knowledge and Practice.The broad aim of this proposal is to better understand the mathematics teaching and learning process for communities of students and teachers and to improve that process. The research will explore the relationship between individual understanding and the broader communities in which people learn, drawing upon a range of qualitative and quantitative methods. In-depth, longitudinal case studies of 3 high schools will be conducted, focusing jointly upon teachers and students. Two of the schools teach both 'traditional' and 'reform' mathematics programs; the third offers a curriculum that combines different approaches. Approximately 1000 students will be monitored in the 3 schools as they progress through their different programs from freshman to senior years. In addition, the relationships between teaching and learning will be examined in a number of focus classes in each school. An integrated analysis of the mathematics teaching and learning process will be conducted. This will examine the relationships among the knowledge, beliefs, and practices that constitute learning, and that have traditionally been treated as distinct. The complexity of such an analysis will be made possible through the use of an analytical framework that will address the identities that teachers and students develop within the mathematics teaching and learning experience.The results of the research will help define new courses for prospective mathematics teachers and teacher educators. The courses will be based upon the principle of learning through analysis of practice. A variety of issues will be identified, such as teaching methods, technology, assessment, and cultural diversity. For each issue, educational research findings will be combined with one or more particular exemplars, carefully selected from the case-study schools. An exemplar could illustrate, for example, a student-teacher interaction; an example of innovative teaching or assessment; a departmental conflict or a particular use of technology. Exemplars will be presented to student teachers using videotapes of classroom lessons, along with teachers' reflections and plans, student work, and student reflections on their learning. One of the aims of the new programs is to cultivate sustained professional discourse. The use of particular cases drawn from the case study schools will encourage such inquiry by providing shared reference points and the development of a common vocabulary. The prospective teachers and teacher educators will have the opportunity to discuss and learn from complexly related practices of teaching and learning for individuals and groups of students. Such conversations can provide a means for teachers not only to develop and clarify their own understandings, but also to develop an identity as a contributing member of a profession. In addition to the new courses that will be developed at Stanford, case-based analyses of teaching and learning will be disseminated to the broader mathematics education community.