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

通过知识与实践的整合促进教师发展和数学学习。该提案的主要目的是更好地了解学生和教师社区的数学教学和学习过程，并改进该过程。这项研究将探讨个人理解与人们学习的更广泛社区之间的关系，利用一系列定性和定量方法。将对3所高中进行深入的纵向案例研究，共同关注教师和学生。其中两所学校同时教授“传统”和“改革”数学课程;第三所学校提供结合不同方法的课程。大约1000名学生将在这三所学校接受监测，因为他们从大一到大四的不同课程。此外，教与学之间的关系将在每所学校的一些重点班进行审查。对数学教与学的过程进行综合分析。这将检查知识之间的关系，信念，和实践，构成学习，并已被传统上视为不同的。这种分析的复杂性将成为可能，通过使用一个分析框架，将地址的身份，教师和学生的数学教学和learningexperiences.The研究的结果将有助于确定未来的数学教师和教师教育工作者的新课程。这些课程将以通过分析实践进行学习的原则为基础。将确定各种问题，如教学方法，技术，评估和文化多样性。对于每一期，教育研究结果将与从案例研究学校精心挑选的一个或多个特定范例相结合。例如，一个范例可以说明学生与教师的互动;创新教学或评估的例子;部门冲突或技术的特定使用。范例将使用课堂教学录像带，沿着教师的反思和计划，学生的工作，以及学生对他们学习的反思。新课程的目标之一是培养持续的专业话语。从案例研究学校中提取的特定案例的使用将通过提供共同的参考点和共同词汇的发展来鼓励这种探究。未来的教师和教师教育工作者将有机会讨论和学习的教学和学习的个人和学生团体的复杂相关的做法。这种对话不仅可以为教师提供一种发展和澄清自己的理解的手段，而且可以为教师提供一种身份认同，使其成为一个专业的贡献者。除了将在斯坦福大学开发的新课程外，还将向更广泛的数学教育界传播基于案例的教学分析。

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.