Developing fraction screeners to identify children at risk for mathematics difficulties

Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
Fractions are a core topic in the mathematics curriculum in the intermediate grades. Competence with fractions is crucial for success in more advanced mathematics courses, such as algebra. Yet many students struggle to learn fractions and are at risk for later mathematics difficulties. To help prevent such difficulties, effective screening tools must identify students who are likely to struggle with fractions before they experience failure. To address this issue, the present study investigated the effectiveness of three fraction measures (i.e., general fraction concepts, fraction number line estimation, and fraction arithmetic) for screening fourth-, fifth-, and sixth-graders, respectively, who will go on to have trouble with mathematics. In particular, the study used data from a larger longitudinal study to assess the accuracy of the measures for identifying students who will not meet state standards on the end-of-the-year high-stakes mathematics test. Receiver operating characteristic (ROC) curve analyses were used to assess the accuracy of fourth-grade fraction measures to predict mathematics achievement in the spring of fourth grade (n = 411), fifth grade (n = 362), and sixth grade (n = 304); the fifth-grade fraction measures to predict mathematics achievement in the spring of fifth grade (n = 384) and sixth grade (n = 318); and the sixth-grade fraction measures to predict mathematics achievement in the spring of sixth grade (n = 327). ☐ Analyses revealed that the general fraction concepts and fraction number line estimation measures consistently emerged as accurate screeners of risk status across the grades while the fractions arithmetic measure did not consistently meet accuracy standards. That is, only the general fraction concepts measure and the fraction number line measure consistently demonstrated high diagnostic accuracy for predicting the outcome measure as determined by the area under the curve (AUC). In fourth and sixth grades, the general fraction concepts measure and fraction number line estimation measure did not significantly differ for the prediction of the outcome; the two measures were thus combined at each of these grades. In fifth grade, the general fraction concepts measure alone emerged as the best fifth-grade screener. To improve practicality for classroom use, the length of each screener was reduced using best subsets automatic linear modeling. Items with low predictive values for predicting the outcome were eliminated from the final best subset screeners. ☐ Screener statistics are reported for all six best subset screeners in ways that allow researchers and practitioners to administer the screeners with their own sample of students and make predictive interpretations of students’ scores. Specifically, the present study demonstrates a method for reporting ROC curve statistics for a single best subset screener that has not yet been introduced in the educational literature. First, a table is provided that reports ROC curve statistics for all cut scores along the screener, allowing researchers and practitioners to select any cut score based on their available resources and research goals. Second, a helpful figure called a probability nomogram is provided that allows readers to easily determine predictive interpretations of students’ screener scores. A separate method is demonstrated for reporting a screener that combines two best subset measures. Using logistic regression, a predicted probabilities matrix is provided that allows readers to make interpretations of a student’s later mathematics achievement based on the student’s scores on both measures. ☐ Addressing an important gap in the literature, the study provides recommendations for mathematics screening in the intermediate grades. The study also demonstrates how to report educational screeners in ways that allow researchers and practitioners to translate screener statistics into readily usable information. The following documents are appended: (a) the full general fraction concepts measure, (b) the full fraction arithmetic measure, and (c) a glossary of statistical terms.
Description
Keywords
Education, At risk, Fraction concepts, Fractions, Mathematics difficulties, Mathematics screeners
Citation