The significance of children’s mathematical competence during the early years is well established; however, the methods for developing such competencies remain less understood. Specifically, there is a need to identify what constitutes high-quality educational environments and effective instruction. Both the study and promotion of high-quality educational environments and teaching, through coaching and other professional development initiatives, necessitate the use of observational instruments that are reliable, efficient, and valid, including content, internal, external, and consequential validity. Moreover, domain-specific measures are essential, as general quality measures often fail to adequately assess curriculum content, scope, or sequence, and they do not reliably predict improvements in children’s learning outcomes. 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 [RF] and Generalized Additive Models [GAMs]) 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 study first employed the RF machine learning method to identify the most important COEMET items for prediction, followed by the use of GAMs to depict the non-linear relationships between COEMET predictors and the outcome variable. 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.
Dong, Y., Clements, D. H., Mulcahy, C., & Sarama, J. (2025). How teaching practices relate to early mathematics competencies: A non-linear modeling perspective. Education Sciences, 15(9). https://doi.org/10.3390/educsci15091175