From whole number bias to gap thinking: College students’ strategy choices in fraction comparisons and relations to cognitive abilities

Fraction thinking poses a challenge for students, and several flawed comparison strategies have been identified: whole-number-strategy (choosing larger numerals), reverse-strategy (choosing smaller numerals), and gap-strategy (choosing the smaller difference between numerator and denominator). The prevalence of these strategies among college students is unknown. Here, we used cluster analysis to identify strategy use among 90 college students. Three cognitive factors were also assessed: general math achievement, inhibitory control, and working memory. The results revealed three clusters: Whole-Number-Strategy (14%), who used whole-number-strategy consistently; Partial-Reverse-Strategy (30%), who used reverse-strategy for more challenging fractions; and Gap-Tendency (56%), who performed well except when gap strategy fails. For cognitive factors, Gap-Tendency performed better than Whole-Number-Strategy, but did not differ from Partial-Reverse-Strategy, on any measure. These findings extended prior research on strategy choices to show that the majority of college students have overcome whole bias, but not yet achieved a complete understanding of fraction magnitude.