Measuring Mathematical Knowledge for Teaching Using Computerized Adaptive Testing

这项建议借鉴了密歇根大学研究人员从2000年开始的努力，开发用于教学的小学和中学数学知识的衡量标准；这项工作构成了NSF资助的用于教学的学习数学(LMT)项目的大部分。与传统的数学知识评估(如SAT或Woodcock-Johnson评估)不同，这些措施调查教师在课堂上与学生一起工作时使用的特殊数学知识。从NSF数学与科学伙伴关系(MSP)的角度来看，这项工作的主要成果之一是一个包含300多个项目的图书馆提供了灵活性，涵盖了数字概念、运算、模式、函数、代数和几何等内容领域，允许项目主任和评估者定制评估工具，以满足他们的具体需求以及专业发展努力的内容和效果。这项提议旨在通过建立基于网络的计算机化自适应测验(CAT)评估，充分利用作为LMT项目一部分开发的广泛题库和使用IRT收集的心理测量信息，作为这一努力的一部分。计算机化的适应性测试通过从库中顺序地选择项目来动态评估特定领域的受试者的表现，以便最大限度地提高测量的精度。在受试者对所选项目作出响应之后，她/他的量表分数被更新，并且选择新的项目以匹配他/她的更新的量表分数估计。然后迭代此过程，直到达到指定的精度级别。教师知识的计算机化适应措施提供了更高的精确度和测试时间和工作量，这将加强MSP项目主任和评估员的能力，以判断旨在改善教师教学内容知识的专业发展的有效性，并评估旨在改善教师和学生的数学知识的课程材料的效果。这些CAT措施对技术专长有限的用户来说将是可获得的，在各种方案和专业发展方法中具有可比性，并将采用最现代和技术上最新的方法进行CAT评估。

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.