We describe the theorization and validation of an instrument to measure mathematical knowledge for teaching college algebra at community colleges, through five different studies that use different data sources: (1) expert review of the items, (2) cognitive interviews with community college instructors, analysis of psychometric properties of data from (3) community college instructors and from (4) mathematics majors with no teaching experience, and (5) associations of the scores with teaching experience and frequency of engaging in specific tasks of teaching. This work contributes to efforts in developing instruments that measure mathematical knowledge for teaching at community colleges, and to validate the interpretation of what these instruments measure. Future studies can assess the extent to which high and low performance on the instrument is related to other measures of quality instruction and with student performance, and to assess changes in knowledge for teaching mathematics after participation in instructional development programs with this population.
Mesa et al. (Fri,) studied this question.