Structural validity and reliability of two observation protocols in college mathematics
Undergraduate mathematics education is being challenged to improve, with peer evaluation, student evaluations, and portfolio assessments as the primary methods of formative and summative assessment used by instructors. Observation protocols like the Mathematics Classroom Observation Protocol for Practices (MCOP^2) and the abbreviated Reformed Teaching Observation Protocol (aRTOP) are another alternative. However, before these observation protocols can be used in the classroom with confidence, a study needed to be conducted to examine both the aRTOP and the MCOP^2. This study was conducted at three large doctorate-granting universities and eight masters and baccalaureate institutions. Both the aRTOP and the MCOP^2 were evaluated in 110 classroom observations during the Spring 2016, Fall 2016, and Spring 2017 semesters. The data analysis allowed conclusions regarding the internal structure, internal reliability, and relationship between the constructs measured by both observation protocols. The factor loadings and fit indices produced from a Confirmatory Factor Analysis (CFA) found a stronger internal structure of the MCOP^2. Cronbach's alpha was also calculated to analyze the internal reliability for each subscale of both protocols. All alphas were in the satisfactory range for the MCOP^2 and below the satisfactory range for the aRTOP. Linear Regression analysis was also conducted to estimate the relationship between the constructs of both protocols. We found a positive and strong correlation between each pair of constructs with a higher correlation between subscales that do not contain Content Propositional Knowledge. This leads us to believe that Content Propositional Knowledge of the aRTOP is measuring something completely different, but not very well, and it needs to be assessed using another method. As noted above and detailed in the body of the work, we find support for the Mathematics Classroom Observation Protocol for Practices (MCOP^2) as a useful assessment tool for undergraduate mathematics classrooms.