Error Patterns in Ordering Fractions among At-Risk Fourth-Grade Students

Abstract

The study had four purposes: (a) to describe fraction ordering errors among 227 at-risk 4th-grade students; (b) to examine performance differences among 3 cohorts; (c) to determine whether errors differed by problem type; and (d) to assess the effect of part-whole and measurement understanding on the probability of committing errors. Students completed a 9-item ordering test. There were no performance differences among cohorts. Students correctly answered 19% of problems. Same numerator problems were easier than problems with different numerators and different denominators. Part-whole and measurement understanding significantly predicted the probability of correctly answering a problem, although measurement understanding had a greater effect. The most common error was whole number ordering errors. This error was just as likely on both problem types. Superior measurement understanding dramatically decreased whole number ordering errors, but part-whole understanding had no significant effect. Smallest denominator – biggest fraction ordering errors infrequently occurred. Practical implications are discussed.