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Abstract This paper presents the development and validation of the 17-item mathematics Graduate Student Instructor Observation Protocol (GSIOP) at two universities. The development of this instrument attended to some unique needs of novice undergraduate mathematics instructors while building on an existing instrument that focused on classroom interactions particularly relevant for students’ development of conceptual understanding, called the Mathematical Classroom Observation Protocol for Practices (MCOP²). Instrument validation involved content input from mathematics education researchers and upper-level mathematics graduate student instructors at two universities, internal consistency analysis, interrater reliability analysis, and structure analyses via scree plot analysis and exploratory factor analysis. A Cronbach-Alpha level of 0.868 illustrated a viable level for internal consistency. Crosstabulation and correlations illustrate high level of interrater reliability for all but one item, and high levels across all subsections. Collaborating a scree plot with the exploratory factor analysis illustrated three critical groupings aligning with the factors from the MCOP²(student engagement and teacher facilitation) while adding a third factor, lesson design practices. Taken collectively, these results indicate that the GSIOP measures the degree to which instructors’ and students’ actions in undergraduate mathematics classrooms align with practices recommended by the Mathematical Association of America (MAA) using a three-factor structure of teacher facilitation, student engagement, and design practices. 

In this study, two universities created and implemented a student-centered graduate student instructor observation protocol (GSIOP) and a post-observational Red-Yellow-Green feedback structure (RYG feedback). The GSIOP and RYG feedback was used with novice graduate student instructors (GSIs) by experienced GSIs through a peer-mentorship program. Ten trained mentor GSIs completed 50 sets of three observations of novice GSIs. Analyzing 151 GSIOPs and 151 RYG feedback meetings longitudinally provided insight to identify what types of feedback informed and influenced GSIOP scores. After qualitatively coding feedback along multiple dimensions, we found certain forms of feedback were more influential for GSI development than others with respect to change in GSIOP score. Our results indicate contextually-specific feedback leads to more observed changes and improvement across multiple observations than decontextualized feedback. 

In this study, two universities created and implemented a student-centered graduate student instructor observation protocol (GSIOP) and a post-observational Red-Yellow-Green feedback structure (RYG feedback). The GSIOP and RYG feedback was used with novice mathematics graduate student instructors (GSIs) by experienced GSIs through a peer-mentorship program. Ten trained mentor GSIs observed novice GSIs, completed a GSIOP, and provided RYG feedback as part of an observation-feedback cycle. This generated 50 semester-long data sets of three observation-feedback cycles of novice GSIs. Analyzing these data sets helped identify how certain feedback influenced GSIOP scores. 

We developed and implemented a peer-mentoring program at two US universities whereby nine experienced mathematics graduate student instructors (GSIs) each mentored three or four first- and second-year GSIs (novices). Mentors facilitated bi-weekly small group meetings with context-specific support to help novices use active-learning techniques and augment productive discourse (Smith & Stein, 2011). Meeting discussion topics were informed by novices’ interests, concerns raised by both mentors and novices, and ideas from other small groups. We examined what topics from small-group peer-mentoring meetings novices valued and timing of the topics that mentors suggested for future cycles. We qualitatively coded meeting topics and analyzed novices’ ratings of topics discussed. Results indicate specific topics novices valued and the importance of timing some topics appropriately, informing future professional development for GSIs. These results offer insight and synergy between educating GSIs and improving undergraduate mathematics teacher pedagogy.