## Project Aspire: Defining and Assessing Mathematical Knowledge For Teaching Secondary Mathematics

This project focuses on mathematical knowledge for teaching at the secondary level, building upon and extending existing work for elementary mathematics. The project is developing two related assessment instruments: one for assessing teachers' mathematical knowledge for teaching secondary mathematics (MKTsm) and one for assessing the quality of secondary mathematics instruction (IQAsm). Used simultaneously, these instruments are capable of linking secondary teachers' mathematical knowledge with their instruction. The first instrument draws from prior research on teachers' and students' understanding of key mathematical ideas. The second extends the Instructional Quality Assessment (IQA), an existing assessment that focuses on the quality of elementary and middle school mathematics, so that it has a clearer focus on secondary mathematics and on the quality of mathematical ideas that a teacher's instruction fosters.

The instruments are being constructed, validated, and tested in three overlapping phases. Development of the MKTsm assessment draws on existing research on teachers' and students' understandings of foundational ideas in algebra and precalculus. The IQAsm extension draws from existing IQA validation studies, from the co-PIs' recent research on transforming secondary teachers' classroom mathematical practices, and from what is learned through the development process in designing the MKTsm instrument. The MKTsm and IQAsm instruments are being piloted in three projects of the Math and Science Partnership (MSP) program, to ensure that the instruments are broadly valuable to MSP projects and mathematics education in general. The instruments are being distributed online, and measures are being taken to ensure valid and appropriate usage by other researchers, or by administrators who might use the instruments for purposes that could include evaluation. In addition to the instruments, the project is developing training videos, scoring guidelines, and an overview for administrators, and also is creating a process by which the publisher will require certification of professional development for use of the instruments when they become commercialized.