Toward a Common Metric for Mathematics Teaching Quality: A Many-Facet Rasch Calibration Framework for Scalable MCOP 2 Use

Mathematics teacher education programs increasingly need to compare teaching quality across raters, cohorts, programs, and sites for evaluation, accreditation, and professional development; yet classroom observation ratings cannot be meaningfully compared across contexts without a calibration framework. The Mathematics Classroom Observation Protocol for Practices (MCOP2), validated using Classical Test Theory, is widely adopted but lacks the psychometric infrastructure for comparable assessment at scale. This study employs Many-Facet Rasch Modeling (MFRM) to develop a provisional calibration framework placing rater severity, item difficulty, and rating scale thresholds on a common metric. Using 159 classroom observations across two disconnected sites with 11 raters, we demonstrate that (a) both MCOP2 subscales meet unidimensionality and model-fit requirements, (b) calibrated item and threshold parameters provide candidate anchor values that future raters can test, refine, and use for linking, and (c) rater-item bias patterns, particularly for Student Engagement items, identify targets for enhanced rater training. Sensitivity analyses indicate the central Teacher Facilitation findings are robust to alternative anchoring specifications. This framework represents a step toward transforming MCOP2 from a locally interpreted rubric into a common metric supporting more comparable cross-site evaluation and personalized professional development, conditional on the anchoring assumptions made explicit herein.