From replication to extension: Unveiling student profiles in fraction comparison tasks

Abstract

Students often encounter difficulties when learning and processing fractions. In fraction comparison tasks, they tend to rely on a mixture of successful strategies, e.g., fraction magnitude processing or benchmarking, and erroneous strategies, e.g., natural number-based reasoning or gap thinking. Reinhold et al. (2023) used a theory-driven approach to classify students into distinct profiles depending on their strategy choice based on their performance on a comparison task with 24 single-digit fractions. The authors identified single strategy profiles (e.g., typical natural number bias) and composite profiles (e.g., benchmarking or typical bias). The current study aimed to replicate this study (RO1) and extend its design by incorporating multi-digit fractions (i.e., the denominator has at least two digits; RO2) and additional biased comparison strategies, specifically gap thinking (RO3). A set of 101 fraction comparison tasks was administered to 285 fifth- and sixth-grade students in Flanders, Belgium, controlling for benchmarking to 1/2, numerical distance, natural number-based reasoning and gap thinking. A Bayesian classification approach based on students’ performance (accuracy, reaction time, and individual distance effect) replicated the distinct profiles identified by Reinhold et al. (2023), not only for single- (RO1) but also for multi-digit fractions (RO2). Furthermore, we identified additional single strategy and composite profiles (e.g., applying benchmarking where possible, otherwise gap thinking), both based on accuracy and reaction time data (RO3). This study enhances our understanding of individual differences in fraction processing and emphasizes the importance of controlling for gap thinking.