Contextual Research and Large Empirical Research? Developing the Theory of Mathematical Knowledge for Teaching by Investigating its Nature, Measurement, and Growth

密歇根大学安阿伯的一个研究小组进行的这项大型实证研究正在三个方面的工作中发展数学知识教学（MKT）的理论基础。主要重点是数学领域的初级教师和初任教师。第一股包括一套理论建设的研究，分析目前的理解，在文献和当前的课堂实践。对于这条链，研究人员通过识别构成构建体的不同方面来绘制MKT。第二部分是一个工具开发项目，从一些先前开发的多项选择措施开始。这条线的重点是开发新的替代评估项目和工具，使用不同的格式，将是有效和可靠的措施MKT在教师？职业生涯的不同阶段。在第三条链中，研究人员正在阐述教师在职业生涯中发展数学知识的学习进展。该项目有三个目标：（1）系统地绘制教学数学知识的地形图;（2）开发MKT的替代措施并分析所获得的数据;（3）概念化教师的轨迹？收购和使用MKT。正在采用多种方法来实现项目目标。三个研究团队正在同时工作，每个团队都致力于解决这三个方面中的一个。所有的研究小组都在对报告的研究进行广泛的审查，并大量借鉴了对数学课录像的分析。正在分析全国范围内进行的调查数据，以帮助确定教师的MKT轨迹？careers.在一至三年级，在学年的三个时间点连续五天对九名初任教师及其教室进行观察和录像。研究人员正在实施新的评估项目，并对60名教师进行认知访谈，以分析和完善项目的有效性。多学科专家正在进行八次为期多天的训练营，审查正在编写的材料（例如，项目和建议的轨迹），并合作和独立工作，以产生支持材料。一名外部评估人员正在收集、分析数据，并向研究小组报告数据，用于形成和总结目的。评估人员将以具体问题为指导，并将审查产品，视频分析和学者营地。将产生的主要产品是MKT地图，MKT的替代评估以及MKT的专业学习轨迹。这些产品和研究结果将通过同行评审期刊、会议介绍和多媒体内容指南传播。正如本研究小组制作的大量先前材料的传播和使用所证明的那样，这项工作将达到并影响数学教育领域的大量人员。

This large empirical study by a research team at the University of Michigan Ann Arbor is developing the theoretical foundations for mathematical knowledge for teaching (MKT) in three strands of work. The primary focus is on preservice and beginning teachers in the area of mathematics. The first strand includes a set of theory-building studies analyzing current understandings in the literature and current classroom practices. For this strand researchers map MKT by identifying the different aspects that constitute the construct. The second strand is an instrument-development project that began with some prior developed multiple-choice measures. The focus of this strand is developing new alternative assessment items and instruments using different formats that will be valid and reliable measures of MKT at teachers? different stages in their career. In the third strand, researchers are articulating a description of teachers' learning progressions over their careers as they develop mathematical knowledge for teaching. The project is guided by three goals: (1) to systematically map the terrain of mathematical knowledge for teaching; (2) to develop alternative measures of MKT and analyze the data obtained; and (3) to conceptualize the trajectory of teachers? acquisition and use of MKT. Multiple methods are being employed to achieve the project goals. Three teams of researchers are working concurrently, each one devoted to addressing one of the three strands. All research teams are doing an extensive review of reported research and are drawing heavily from analyses of video records of mathematics lessons. Data from surveys administered nationally are being analyzed to help identify a trajectory of MKT for teachers? careers. In Years 1-3 nine beginning teachers and their classrooms are being observed and video tapped for five consecutive days at three points during the school year. Researchers are administering new assessment items and conducting cognitive interviews of 60 teachers to analyze the validity of and refine the items. Eight camps of multiple days are being conducted of multidisciplinary experts to review materials being developed (e.g., items and proposed trajectories) and to work collaboratively and independently to produce supportive materials. An external evaluator is collecting, analyzing, and reporting data to the research teams for both formative and summative purposes. The evaluator is guided by specific questions and will review products, video analyses, and the camps of scholars. The main products that will be produced are a map of MKT, alternative assessments of MKT, and a professional learning trajectory for MKT. These products and findings are to be disseminated through peer-reviewed journals, conference presentations, and multimedia content guides. As evidenced by the large dissemination and use of prior materials produced by this research team, this work will reach and influence a significant number of those in the mathematics education field.