Measuring Mathematical Knowledge for Teaching Using Computerized Adaptive Testing

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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.