Predicting mathematics difficulties with an early number sense screener
Date
2021
Authors
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Publisher
University of Delaware
Abstract
Early numerical competencies support subsequent mathematical understanding and accurately predict later academic achievement (Duncan et al., 2007). However, wide variation in children’s abilities exists as early as preschool entry (DeFlorio and Beliakoff, 2015). Early identification of children who may be at-risk for mathematics difficulties (MD) is crucial. Yet development of early math screening tools has lagged far behind those developed for early literacy. ☐ The present study investigated the diagnostic accuracy of two forms of the Screener for Early Number Sense (SENS), a psychometrically sound screening tool for children in pre-K, kindergarten, and first grade. Construction of both forms of the SENS was guided by number sense research (National Mathematics Advisory Panel (NMAP), 2008; National Research Council (NRC), 2009). Children were assessed on the SENS (N = 450) and given a validated mathematics achievement test one year later. The longer version of the SENS was statistically compared to the shorter version at each grade level to determine if one screener produces higher diagnostic accuracy. Additionally, practical utility of the SENS was evaluated via item analyses, posttest probabilities, and growth analysis. ☐ Findings showed the SENS short-form to be as accurate as the SENS long-form at classifying children based on MD risk status (determined as at or below the 25th percentile in math achievement). ROC curve analyses revealed that the SENS short-form reached sufficient levels of diagnostic accuracy as measured by the Area Under the Curve (AUC). The SENS short-form discriminated between a child at-risk for MD and a child not-at-risk for MD in 90% of cases for pre-K, 76% of cases for kindergarten, and 86% of cases for first grade. ☐ Diagnostic metrics generated by ROC curve statistics (i.e., sensitivity and specificity) determined posttest probabilities that calculated children’s individual-level risk for failing the mathematics achievement measure. Posttest probabilities were calculated for low-income (LI) and middle-income (MI) children at each grade level, based on their screener results and pretest probability for MD. Results showed that a LI pre-K child with a 36% pretest probability who scored below the cut point on the SENS has a 69% chance of subsequently failing the mathematics achievement measure. Student growth analysis by MD risk status showed that at-risk and not-at-risk children made similar gains in number sense knowledge between the pre-K and kindergarten. A different pattern emerged for at-risk vs. not-at-risk children between kindergarten and first grade. During this span not-at-risk children made more gains than children identified as at-risk for MD. ☐ The present dissertation study provides verification that the SENS can be effectively shortened while maintaining sufficient diagnostic accuracy. The vertically-scaled grade-level forms are effective at capturing student growth over time and demonstrate how student performance can be evaluated for individual-level information using posttest probabilities. Future work could address existing limitations by including a nationally representative sample of participants and empirically validating the posttest probability thresholds used in analyses.
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Keywords
Kindergarten, Mathematics learning difficulties, Number sense, Preschool