| This dissertation contains three independently conducted studies on factors that affect the math achievement scores of preschool-aged children. The first study examined the associations between children's executive-functioning (EF) and math achievement scores at 54 months of age. Results suggest that EF is strongly associated with children's overall math skills and that, as children follow the developmental trajectory of counting to operations (Sarama & Clements, 2009), the relationship to EF changes. Counting skills are more highly associated with short-term memory and, as children move from counting to operations, the association with short-term memory becomes weakened and that of planning becomes more strongly associated. Implications for future research into the association between EF and math achievement, particularly in terms of joint interventions, are discussed. The second study examines the association between teachers' judgments of children's math skills in preschool and the direct assessments of children's math skills. Approximately 40% of the variance in teachers' report of children's math skills is attributable to factors other than the child. Overall, teachers misestimate the skills of children by approximately one-half a standard. Children who are one standard deviation above the mean are rated as only one-half a standard deviation above the mean and those who are one standard deviation below the mean are rated as only one-half a standard deviation below the mean. Implications for teacher education, particularly regarding the familiarity with the National Council of Teachers of Mathematics Standards 2000 and appropriate behavioral markers, are discussed. The third study addresses the association between the quality of preschool, defined as the quality of the general, social interactions between teacher and student and the quality of the physical environment, and children's math achievement scores. Results suggest that social interaction and physical environment quality in the preschool environment are not associated with children's math skills and do not have differential associations for subgroups of children. However, when this is considered with other research showing a positive effect of math-specific social interaction, it suggests that, though general social interaction is not associated with math skills, social interactions that are focused on math concepts can improve children's scores in math. |
