CAREER: Examining prospective teachers' learning of three mathematics teaching practices-posing, interpreting, and responding-during teacher preparation

本项目侧重于三种数学教学练习--提出数学问题，回应学生的数学思想，解释学生的数学思维--教师准备课程中讨论的直接影响学生学习的练习。这些实践对数学教与学的改进至关重要，需要在教学的背景下对数学有深刻的理解。研究发现，这些做法在未来的数学教师中还不够发达，而且学习起来很有挑战性。尽管它们往往在教师准备课程中受到大量关注，但人们对这些做法在教师职业生涯开始阶段是如何发展的知之甚少。这意味着数学教师教育领域对于如何最好地帮助未来的教师走向对这些实践的更复杂的理解和制定缺乏完整的知识。本项目中提出的研究和教育议程对于改进数学教师培养计划和经验的设计和实施至关重要。这个项目将使用横断面和纵向研究设计来研究摆姿势、口译和回答的实践。这项横断面研究将描述密歇根州立大学小学教师培训计划三个阶段中每一个阶段的重点实践。这项纵向研究将重点放在未来小学教师通过教师培训计划进入第一年和第二年教学过程中重点实践的发展。还将通过对10名参与者的深入案例研究，审查这些做法发展的负担和制约因素。该项目的教育目标是为数学教师教育指导者提供专业发展。这一专业发展将包括整个项目期间的定期讲师会议，这将与研究小组的活动平行。例如，当研究小组致力于开发研究工具时，教师小组将专注于使研究工具适应他们的教师教育课堂。这些教育活动的目的是与实践数学教育教师合作，使本项目产生的研究工具和结果对数学教师教育工作者的教学实践有用。

This project focuses on three mathematics teaching practices --posing mathematical problems, responding to students' mathematical ideas, and interpreting students' mathematical thinking -- that are discussed in teacher preparation courses as practices that directly affect student learning. These practices are essential to the improvement of mathematics teaching and learning and demand a deep understanding of mathematics in the context of teaching. Research has found these practices to be underdeveloped in prospective teachers of mathematics and to be challenging to learn. In spite of the amount of attention they tend to receive in teacher preparation courses little is known about how these practices develop at the beginning stages of a teacher's career. This means that the field of mathematics teacher education has incomplete knowledge about how best to help prospective teachers move towards more sophisticated understandings and enactments of these practices. The research and educational agenda proposed in this project are critical to improving the design and implementation of mathematics teacher preparation programs and experiences. This project will study the practices of posing, interpreting, and responding using cross-sectional and longitudinal research designs. The cross-sectional study will characterize the focal practices at each of three stages in the elementary teacher preparation program at Michigan State University. The longitudinal study will focus on the development of the focal practices as prospective elementary school teachers move through the teacher preparation program and into their first and second year of teaching. Factors that afford and constrain the development of these practices will also be examined through in-depth case studies of ten participants. The educational goal of the project is to provide professional development for mathematics teacher education instructors. This professional development will consist of regular instructor meetings throughout the length of the project that will parallel the activities of the research group. As the research group works to develop the research instruments, for example, the instructor group will focus on adapting the research instruments to their teacher education classrooms. The goal of these educational activities is to, in collaboration with practicing mathematics education instructors, make the research tools and findings generated by this project useful to the teaching practice of mathematics teacher educators.