CAREER: Knowledge for Teaching Mathematics: The Impact of Mathematics Courses on Prospective Elementary Teachers' Mathematical Knowledge

拟议的研究计划的重点是数学未来的小学教师有机会在他们的本科教育和他们实际上学到的结果，他们的数学课程学习。虽然研究已经确定的问题，教师的知识作为一个显着的贡献因素，在K-6数学教育的质量普遍不足，更多的是知道什么教师不知道比他们知道什么或有机会学习。这项研究将着眼于整个机构和国家，以研究未来的教师正在教什么，他们实际上在学习什么。该项目将通过一组多方法，多层次的案例研究来调查学习和学习本科数学课程的机会。这项工作将包括分析为未来的小学教师编写的本科数学课程教科书;审查教科书的专题范围及其与各州数学学生学习标准的关系;对选定州的数学系和这些课程的教员进行调查;对各州机构选定课程进行个案研究;以及学生（副教师）在这些课程中学习的前后评估。重点数学领域将是乘法，分数，推理和证明。这项研究将有助于了解未来的小学教师是否接触到他们需要成功教学的内容，以及他们是否正在学习这些内容。 调查结果将包括教师是否以及在多大程度上教授有助于教学的数学知识的内容。这是一个新的研究领域，对此知之甚少，对教师教育具有重要意义。提议者的教育计划包括在密歇根州立大学教授小学教师的本科数学课程，使用目前由数学系支持的两种方法，并将该教学作为学习机会和教师知识的研究场所。她将修改课程，向博士生介绍评估教师知识和学习机会的理论和实践问题。

The proposed program of research focuses on the mathematics prospective elementary teachers have opportunities to learn during their undergraduate education and what they actually learn as a result of their mathematics courses. Although research has identified the problem of teacher knowledge as a significant contributing factor in the generally inadequate quality of K-6 mathematics education, more is known about what teachers do not know than about what they know or have had opportunities to learn. This study will look across institutions and states to examine what prospective teachers are being taught and what they are actually learning. The project will investigate both opportunities to learn and learning from undergraduate mathematics courses through a set of multi-method, multilevel case studies. The work will include an analysis of textbooks written for undergraduate mathematics courses for prospective elementary teachers; an examination of textbook topical coverage and how that correlates with states' mathematics student learning standards; surveys of mathematics departments and instructors of those courses in selected states; case studies of selected courses at institutions within the states; and pre- and post-assessments of student (preservice teacher) learning in those courses. The focal mathematical domains will be multiplication, fractions, and reasoning and proof. This research will contribute to understanding whether prospective elementary teachers are exposed to content that they need for successful teaching, and whether they are learning that content. The findings will include whether, and to what extent, instructors are teaching content that contributes to mathematical knowledge for teaching. This is new research in areas about which little is known, with important implications for teacher education.The proposer's education plan includes teaching undergraduate mathematics courses for elementary teachers at Michigan State University using two approaches currently supported by the Mathematics Department and using that teaching as a site for studying opportunity to learn and teacher knowledge. She will revise a course to introduce PhD students to theoretical and practical issues in assessing teacher knowledge and opportunities to learn.