Pedagogical Content Knowledge and STEM Teacher Preparation

数学科学（21）本项目为STEM本科生开发一门为中学数学教学做准备的全年课程。该课程整合了精心设计的问题解决活动，儿童学习数学的视频案例研究，学术阅读和讨论。要求本科生重新考虑4 -12年级的数学内容，然后准备好概念化这些年级学生的数学发展。这种类型的研究产生了早期形式的教学内容知识，其中内容知识与对学生认知如何发展的理解相结合。在分析自己和4-12年级学生的作业时，本科生特别关注数学发展中标志着关键转变的表征、策略、语言和大思想。该项目的研究是分析本科生理解这些组成部分的能力，他们理解和解释儿童数学思维的能力，并迭代地开发这种类型的课程可以基于的学习序列。智力价值：该项目建立在先前对教师专业连续体的研究基础上，并拓宽了对教师在其作为大学生的关键职前几年发展的理解。本科学生学习在初中和初中数学中出现的重要数学概念、认知障碍、策略、模型和语言。最近开发的一些录像材料使用户能够非常详细地审查这些问题，并使他们能够观察和研究在真实教室中从事的儿童。该项目将提供一个理解，在多大程度上，在哪里，以及如何在本科课程中最好地使用这些材料。更广泛的影响：中学数学和科学教师的短缺一直是一个全国性的问题，因此，旨在让本科生更快进入教学的项目受到越来越多的关注。对于STEM本科生来说，将他们的数学研究与教与学的研究联系起来是很重要的，对于大学教育工作者来说，发展研究和传播方法来加强他们的准备是很重要的。此外，许多州标准要求4-8年级的学生学习比过去更严格的内容（包括代数），教师在教学中融入更高水平的推理是很重要的。本项目通过研究、开发和传播教学方法来解决这些问题，这些教学方法将STEM本科生的学习内容与4-12年级的关键主题联系起来。

Mathematical Sciences (21) This project is researching and developing a full year course for STEM undergraduates preparing for secondary mathematics teaching. The course integrates carefully structured problem solving activities, video case studies of children learning mathematics, academic readings, and discussions. Undergraduates are asked to reconsider the mathematical content of grades 4 -12 and then be ready to conceptualize the mathematical development of a student in these grades. This type of study results in early forms of pedagogical content knowledge, where content knowledge is blended with an understanding of how students' cognition develops. While analyzing their own work and that of grade 4-12 students, undergraduates pay specific attention to the representations, strategies, language, and big ideas that mark critical transitions in mathematical development. The project's research is analyzing the abilities of undergraduates to understand these components, their ability to understand and interpret children's mathematical thinking, and iteratively develop learning sequences upon which courses of this type can be based. Intellectual Merit: The project builds upon prior research on the teacher professional continuum, and is broadening understanding of the development of teachers during their critical pre-service years as university students. The undergraduates study the important mathematical ideas, cognitive obstacles, strategies, models, and language that surface in middle school and secondary mathematics. A number of recently developed video materials allow users to examine these issues in great detail and enable them to view and study children engaged in authentic classrooms. The project will provide an understanding of to what extent, where, and how such material can best be used in the undergraduate curriculum.Broader Impact: The shortage of secondary mathematics and science teachers is a continuing national concern and as a result, programs designed to move undergraduates more quickly into teaching are receiving increased attention. It is important for STEM undergraduates to connect their study of mathematics with the study of teaching and learning, and for collegiate educators to develop research and disseminate approaches that enhance their preparation. In addition, many state standards are requiring more rigorous material (including algebra) in grades 4-8 than in the past and it is important for teachers to incorporate higher level reasoning in their instruction. This project addresses these issues through research, development, and dissemination of instructional approaches that link STEM undergraduates' learning of content to critical themes in grade 4-12.