Design, Validation, and Dissemination of Measures of Content Knowledge for Teaching Mathematics

关于教师学习的研究一直受到一些长期的方法论困难的困扰。尽管一再呼吁提高学术水平，提出更多基于经验的政策建议，但该领域受到学者们能够衡量的因素的限制：学习机会本身的特征；这些机会所产生的教师态度和信念；在某种程度上，教师的实践也会在这样的遭遇之后出现。然而，通常无法测量的是一个组成部分，它调解了这些因素，本身就是许多干预措施的重要目标，即教师的内容知识。这里提出的项目旨在帮助解决K-8数学领域的这一问题，在以前的工作基础上，继续开发教师数学知识的教学措施。然后，这些措施将提供给MSP数学项目，希望改善那些有教师学习和准备计划的项目的评估。建议开展五类工作：(1)向上扩展现有措施，以捕获中学数学教学内容，并在重点内容领域制定新的措施；(2)通过与MSP参与者和其他教师的访谈、数学家和数学教育者的评论以及其他方式来验证这些措施；(3)通过工具（数据库、核心量表）和对MSP评估者的技术援助，支持这些措施的高质量使用；（四）建立自给自足的措施使用体系；(5)通过试点和验证工作建立和测试理论。随着这五个方面的工作进展，我们将从理论和测量的角度仔细考虑公平问题。我们还将与计量和统计专家协商，以促进制定技术上最健全和最有效的措施。这一建议将有助于促进两个相关领域的知识和理解：定义K-8数学教学知识的组成要素，以及理解旨在提高这些知识的专业发展的影响。作者凭借过去在理论和措施开发方面的经验，有资格做这项工作，并制定了为期五年的仪器开发计划。本建议加强了教师专业发展研究的基础设施。基于对现有措施的兴趣，作者期望这些措施不仅对msp有用，而且对其他寻求理解教师学习的人也有用。这些指标可用于评价职前教师教育项目中教师的学习情况；比较传统教师教育课程的准备和其他认证途径；判断以提高教师教学内容知识为目的的专业发展效果；并评估课程材料设计的效果，以提高教师和学生的数学知识。最后，这个项目对理论发展做出了根本性的贡献，它提出了这样一个问题：“为了教数学，教师需要知道什么和能够做什么？”随着工作的进展，通过项目写作和心理测量分析来回答这个问题，作者试图为这一领域的理论、实践和政策的进步做出贡献。

Research on teacher learning has suffered from a number of chronic methodological difficulties. Despite repeated calls for improved scholarship and more empirically grounded policy recommendations, the field been constrained by what scholars have been able to measure: characteristics of the learning opportunities themselves; teacher attitudes and beliefs which result from those opportunities; and, to some extent, teacher practices which emerge after such encounters. Typically left unmeasured, however, is a component which mediates each of these and is itself a significant target of many interventions, namely, teachers' content knowledge. The project proposed here would aim to help redress this problem in the area of K-8 mathematics, building on previous work to continue developing measures of teachers' mathematical knowledge for teaching. These measures will then be made available to MSP mathematics projects in hopes of improving the evaluation of those with programs for teacher learning and preparation. Five categories of work are proposed: (1) expanding existing measures upward to capture middle grade mathematics content for teaching, and developing new measures in key content areas; (2) validating these measures through interviews with MSP participants and other teachers, reviews by mathematicians and mathematics educators, and other means; (3) supporting high-quality uses of these measures via tools (database, core scales) and technical assistance to MSP evaluators; (4) building a self-sustaining system of measures use; and (5) building and testing theory through piloting and validation work. As these five aspects of work progress, we will carefully consider issues of equity, both from the theoretical and measurement perspectives. We will also consult with measurement and statistical experts to promote the production of the most technically sound and valid measures possible. Intellectual MeritThis proposal will help advance knowledge and understanding in two related fields: in defining the component elements of knowledge for teaching K-8 mathematics, and in understanding the effects of professional development meant to improve that knowledge. The authors are qualified to do this work through their past experiences with theory and measures development, and have laid out a careful plan of instrument development over a five-year period. Broader Impact This proposal enhances the infrastructure for research into teacher professional development. Based on interest in existing measures, the authors expect these measures to be useful not only to MSPs, but also to others who seek to understand teacher learning. These measures can be used to evaluate teachers' learning in pre-service teacher education programs; to make comparisons between preparation in traditional teacher education programs and alternative routes to certification; to judge the efficacy of professional development aimed at improving teachers' content knowledge for teaching; and to estimate the effects of curriculum materials designed to improve teachers' knowledge of mathematics and students. Finally, this project contributes fundamentally to theory development, asking the question, "What do teachers need to know and be able to do with mathematics in order to teach mathematics?" By answering this question through item-writing and psychometric analyses as work progresses, the authors seek to contribute to progress in theory, practice, and policy in this field.