Comparing Fraction Magnitudes: Adults’ Verbal Reports Reveal Strategy Flexibility and Adaptivity, but Also Bias

Abstract

Many studies have used fraction magnitude comparison tasks to assess people’s abilities to quickly assess fraction magnitudes. However, since there are multiple ways to compare fractions, it is not clear whether people actually reason about the holistic magnitudes of the fractions in this task and whether they use multiple strategies in a flexible and adaptive way. We asked 72 adults to solve challenging fraction comparisons (e.g., 31/71 vs. 13/23) on a computer. In some of these comparisons, using benchmarks (i.e., reference numbers such as 1/2) was potentially beneficial. After each trial, participants provided verbal reports of their strategies. We found that participants used a large variety of strategies. The majority of strategies were holistic and relied on fraction magnitudes, and most of these strategies were based on benchmarks. Participants sometimes used gap comparison (i.e., comparing the differences between each fraction’s numerator and denominator), a heuristic that is not always valid and that does not rely on fraction magnitudes. Participants used strategies flexibly: they used many different strategies, they used highly efficient strategies most often, and they adapted their strategy use to features of the items. However, participants sometimes used gap comparison on items for which it did not yield the correct response, and this lack of adaptivity partly explained the “natural number bias” observed in this study.

Keywords

• fraction comparison
• strategy use
• natural number bias
• trial-by-trial assessment