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

通过知识和实践的结合促进教师发展和数学学习。这项建议的广泛目标是更好地了解学生和教师群体的数学教与学过程，并改进这一过程。这项研究将利用一系列定性和定量的方法，探索个人理解与人们学习的更广泛社区之间的关系。将对3所高中进行深入的、纵向的案例研究，共同关注教师和学生。其中两所学校既教授传统的数学课程，也教授改革的数学课程；第三所学校提供的课程结合了不同的方法。这3所学校将对大约1000名学生从一年级到四年级的不同项目进展情况进行监测。此外，教与学之间的关系将在每个学校的一些重点课程中进行考察。将对数学教与学过程进行综合分析。它将考察构成学习的知识、信念和实践之间的关系，这些知识、信念和实践传统上被视为不同的。这种分析的复杂性将通过使用一个分析框架来实现，该框架将解决教师和学生在数学教与学经验中发展的身份。研究结果将有助于为未来的数学教师和教师教育工作者定义新的课程。课程将以实践分析中学习的原则为基础。将确定各种问题，如教学方法、技术、评估和文化多样性。对于每个问题，教育研究结果将与从案例研究学校中精心挑选的一个或多个特定样本相结合。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。样本将通过课堂教学的录像带呈现给实习教师，以及教师的反思和计划、学生的作业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。使用案例研究学校的特定案例将通过提供共享的参考点和发展共同的词汇来鼓励这种调查。未来的教师和教师教育工作者将有机会讨论和学习个人和学生群体复杂的相关教与学实践。这样的对话可以为教师提供一种手段，不仅可以发展和澄清他们自己的理解，而且还可以建立作为专业贡献成员的身份。除了斯坦福大学将开发的新课程外，还将向更广泛的数学教育界传播基于案例的教与学分析。

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.