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The significance of children’s mathematical competence during the early years is well established; however, the methods for developing such competencies remain less understood. This study employed innovative analytical techniques to evaluate the scoring and interpretation of an existing domain-specific observational measure: the Classroom Observation of Early Mathematics Environment and Teaching (COEMET). We applied non-linear modeling approaches (i.e., Random Forest and Generalized Additive Models [GAM]) to investigate and provide a comprehensive overview of the relationships between COEMET’s measures—at both the scale and item levels—of teachers’ practices and children’s mathematical competencies. The analysis revealed that certain teaching practices, as indicated by the COEMET items, exhibited non-linear and even non-monotonic associations with children’s mathematical competencies.