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

拟议的研究计划侧重于数学准小学教师在本科教育期间有机会学习，以及他们在数学课程中实际学到了什么。尽管研究发现，教师知识问题是导致K-6数学教育质量普遍不高的一个重要因素，但人们更多地了解教师不知道的东西，而不是他们知道的或有机会学习的东西。这项研究将跨越机构和州，检查未来的教师被教授了什么，他们实际学到了什么。该项目将通过一组多方法、多层次的案例研究，调查从本科数学课程中学习和学习的机会。这项工作将包括对为未来小学教师编写的本科数学课程编写的教科书进行分析；检查教科书的主题覆盖面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师进行调查；对各州机构选定的课程进行案例研究；以及对学生(职前教师)在这些课程中的学习情况进行事前和事后评估。重点的数学领域将是乘法、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了他们成功教学所需的内容，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在教授有助于数学知识的内容，以及在多大程度上有助于教学。这是在鲜为人知的领域的新研究，对教师教育具有重要影响。建议的教育计划包括在密歇根州立大学为小学教师教授本科数学课程，使用目前得到数学系支持的两种方法，并将该教学作为研究学习机会和教师知识的场所。她将修改一门课程，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.