Measuring Mathematical Knowledge for Teaching Using Computerized Adaptive Testing

使用计算机自适应测试测量教学数学知识

• 批准号: 0634306
• 负责人: Stephen Schilling
• 金额: $ 71.14万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0634306&HistoricalAwards=false
• 关键词: Measuring; Mathematical; Knowledge; Teaching; Using

This proposal draws on efforts beginning in 2000 of researchers at the University of Michigan to develop measures of elementary and middle school mathematical knowledge for teaching; this work comprises the bulk of the NSF funded Learning Mathematics for Teaching (LMT) project. In contrast to conventional assessments of mathematical knowledge (e.g., the SAT or Woodcock-Johnson assessment), these measures investigate the special mathematical knowledge teachers use to work in classrooms with students. One of the key outcomes of this work from the point of view of the NSF Math and Science Partnerships (MSP's) is the flexibility afforded by a library of more than 300 items ranging across the content areas of number concepts, operations, patterns, functions and algebra, and geometry, allowing project directors and evaluators to custom tailor assessment instruments to meet their specific needs and the content and effects of professional development efforts. This proposal seeks to fully exploit the extensive library of items developed as part of the LMT project and the psychometric information gathered using IRT as part of that effort through the creation of a web-based computerized adaptive testing (CAT) assessment. Computerized adaptive testing dynamically assesses subject performance in a particular domain by sequentially selecting items from the library in order to maximize the precision of measurement. After a subject has responded to a selected item, her/his scale score is updated, and a new item is chosen to match her/his updated scale score estimate. This process is then iterated until a specified level of precision is reached. The additional precision and reduction in testing time and effort afforded by computerized adaptive measures of teacher knowledge should enhance the ability of MSP project directors and evaluators 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. These CAT measures will be accessible to users with limited technical expertise, comparable across a wide variety of programs and approaches to professional development, and will employ the most modern and technically up to date approaches for CAT assessments.

该提案借鉴了密歇根大学研究人员自 2000 年开始制定的中小学数学知识教学衡量标准的努力；这项工作构成了 NSF 资助的教学数学 (LMT) 项目的大部分内容。与传统的数学知识评估（例如 SAT 或 Woodcock-Johnson 评估）相比，这些措施调查教师在课堂上与学生一起使用的特殊数学知识。从 NSF 数学和科学合作伙伴 (MSP) 的角度来看，这项工作的主要成果之一是由 300 多个项目组成的库所提供的灵活性，涵盖数字概念、运算、模式、函数和代数以及几何等内容领域，允许项目主管和评估人员定制评估工具，以满足他们的特定需求以及专业发展工作的内容和效果。该提案旨在通过创建基于网络的计算机自适应测试（CAT）评估，充分利用作为 LMT 项目一部分开发的广泛项目库以及使用 IRT 收集的心理测量信息，作为该工作的一部分。计算机化自适应测试通过从库中顺序选择项目来动态评估受试者在特定领域的表现，以最大限度地提高测量精度。在受试者对所选项目做出反应后，她/他的量表分数被更新，并且选择一个新项目来匹配她/他更新的量表分数估计。然后迭代这个过程，直到达到指定的精度水平。计算机化的教师知识适应性测量所带来的额外精确性以及测试时间和精力的减少，应提高 MSP 项目主管和评估人员判断旨在提高教师教学内容知识的专业发展效果的能力；并评估旨在提高教师和学生数学知识的课程材料的效果。这些 CAT 衡量标准将可供技术专业知识有限的用户使用，可在各种专业发展计划和方法中进行比较，并将采用最现代、技术上最新的方法进行 CAT 评估。