Disentangling magnitude processing, natural number biases, and benchmarking in fraction comparison tasks: A person-centered Bayesian classification approach

Abstract

Research on fraction comparison shows that students often follow biased comparison strategies, in particular such strategies that build on their knowledge of natural numbers. On the other hand they also apply successful comparison strategies such as benchmarking or fraction magnitude processing. Which strategies are applied or even combined depends on the students’ knowledge and on the task type. To investigate these complex relationships, we developed a balanced 2 × 2-dimensional itemset (congruent vs. incongruent items; benchmarking vs. non-benchmarking items) and a Bayesian classification of individual students’ performance (solution patters, response time, and individual distance effect), which we applied to an assessment of N = 350 sixth graders. We could show that the classification of the students with respect to possible solution strategies matched our hypotheses: We could replicate existing patterns and found additional composite strategies such as ‘benchmarking or bias‘ with a bias only in solution rates of non-benchmark items. In further analyses we found ‘benchmarking or suppressed bias-strategies (i.e., a bias in problem solving time of non-benchmarking items). Our study extends previous knowledge on individual strategies in fraction comparison and proposes a new person-centered approach to classify individual student profiles even with small profile sizes.