This proposal draws on existing efforts to develop measures of elementary and middle school mathematical knowledge for teaching. Different from 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. For instance, these measures assess not only whether teachers know that 1 3/4 1/2 = 3 1/2, but also whether they can explain what this equation means, can construct a concrete representation or word problem which corresponds to it, and can understand and generalize from an unusual solution method for this problem. This proposal responds to a number of challenges that have arisen while disseminating these measures to researchers.
Currently, the Learning Mathematics for Teaching project (LMT) disseminates pre-piloted forms and technical information for evaluating teacher learning in K-8 number and operations, pre-algebra and algebra, and geometry. Teacher learning opportunities, however, frequently focus on more narrowly defined topic areas for instance, rational number concepts and operations. Yet items capturing teacher knowledge of rational number compose only one component of LMT's number concepts and operations measures. Because these current measures include other topics, they are unlikely to be appropriately sensitive to the content and effects of such professional development.
In response, this proposal argues for the construction of evaluation modules designed to be sensitive to and allow research and evaluation in the following areas: rational numbers; proportional reasoning; geometry; data analysis and probability. In all but the last topic area, for which LMT will create an entirely new set of items, the project will review and supplement existing items, create a form composed of items that capture key teacher competencies in these areas, pilot this form, then compose technical materials that support these modules' use. These technical materials will include two parallel forms and pre-equated raw-score-to-standardized-score conversion tables, to facilitate straightforward scoring.
This proposal also describes plans to improve the quality of dissemination training by exploring the nature of problems that arise when outside evaluators use these measures, and describes work to improve measures of teachers' knowledge of student learning around content. Intellectual Merit
This proposal grows from a well-established measures development project. At every step in this project's history, the provision of high-quality measures has coincided with and in some ways, depended upon progress in building theory about content knowledge for teaching mathematics, and exploring new areas in measurement design and scaling. This will be the case in the work proposed here, as well.
Broader Impact
This proposal enhances the infrastructure for research on 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. These measures are accessible to users with limited technical expertise, comparable across programs and approaches to professional development, and of high technical quality.
