From Whole Number Bias to Gap Thinking: University Students’ Strategy Choices in Fraction Comparison and Relations to Math and Cognitive Abilities

Abstract Fractions pose a significant challenge for many students. Several flawed strategies have been identified in elementary and secondary students when selecting the larger of two fractions: the whole number strategy (choosing the larger numerals), the reverse strategy (choosing the smaller numerals), and the gap strategy (choosing the smaller difference between numerator and denominator). The prevalence of these strategies among university students is unknown. In the present study, we used specially designed stimuli and cluster analysis to identify fraction comparison strategy use among 90 university students. We assessed potential contributing factors to fraction understanding: general math achievement, inhibitory control, and visuospatial working memory. The results revealed three clusters: a Whole-Number-Strategy group (14%), who primarily used the whole number strategy; a Partial-Reverse-Strategy group (30%), who used the reverse strategy for challenging fractions; and a Gap-Tendency group (56%), who showed high accuracy when the gap strategy succeeds, and lower but above chance accuracy when the gap strategy fails. Regarding the contributing factors, the Gap-Tendency group performed better than the Whole-Number-Strategy group, but did not differ from the Partial-Reverse-Strategy group, on all measures. These findings extend prior research on strategies by showing that many university students have overcome whole number bias but have not yet achieved a complete understanding of fraction magnitude. Moreover, the lack of differences in math and cognitive factors between the better-performing groups shows that strong math and cognitive abilities are necessary but not sufficient for full fraction understanding among university students.