Search

The present study uses a short, computerized task to investigate individual differences among middle school students in terms of the intuitions and strategies that they use to compare fractions. To tap into their intuitions about fractions, students were presented with pairs of fractions on the screen for a limited time of 10 s. Fraction pairs to be compared were controlled as to whether fractions shared or not a common component (numerator or denominator), as well as whether the greater fraction was the one with greater components or not. Data from about 500 students were processed with a clustering analysis based on these four item types, revealing distinct patterns of answers that we interpret in terms of strategies for answering the task. Half of the sample followed a simple "larger-component-larger-fraction" strategy as suggested by a congruency-based implementation of the natural number bias, although several clusters showed opposite patterns. These results show that a short, simple task can provide valuable information about students' individual differences in comparing fractions, useful for both research and practice in mathematics education. We discuss implications of these results for research and practice related to mathematics cognition and education.

Purpose: We investigated whether rhythm discrimination is mainly driven by the native language of the listener or by the fundamental design of the human auditory system and universal cognitive mechanisms shared by all people irrespective of rhythmic patterns in their native language. Method: In multiple experiments, we asked participants to listen to 2 continuous acoustic sequences and to determine whether their rhythms were the same or different (AX discrimination). Participants were native speakers of 4 languages with different rhythmic properties (Spanish, French, English, and German) to understand whether the predominant rhythmic patterns of a native language affect sensitivity, bias, and reaction time in detecting rhythmic changes in linguistic (Experiment 2) and in nonlinguistic (Experiments 1 and 2) acoustic sequences. We examined sensitivity and bias measures, as well as reaction times. We also computed Bayes factors in order to assess the effect of native language. Results: All listeners performed better (i.e., responded faster and manifested higher sensitivity and accuracy) when detecting the presence or absence of a rhythm change when the 1st stimulus in an AX test pair exhibited regular rhythm (i.e., a syllable-timed rhythmic pattern) than when the 1st stimulus exhibited irregular rhythm (i.e., stress-timed rhythmic pattern). This result pattern was observed both on linguistic and nonlinguistic stimuli and was not modulated by the native language of the participant. Conclusion: We conclude that rhythm change detection is a fundamental function of a processing system that relies on general auditory mechanisms and is not modulated by linguistic experience.

Individual differences in inhibitory control have been shown to relate to general mathematics achievement, but whether this relation varies for specific areas within mathematics is a question that remains open. Here, we evaluate if inhibitory processes play a specific role in the particular case of fraction comparison, where learners must ignore the potentially misleading information provided by the natural numbers composing fractions (e.g. 2/3 > 4/7 despite 2 < 4 and 3 < 7). To do this, we presented a sample of Chilean children (N = 450) from 5th, 6th, and 7th grade with a numerical comparison task tapping inhibitory and other processes. Results showed that both general math achievement and accuracy in comparing fractions were significantly predicted by inhibition. The former association, however, turned out to mediate the latter one. Another process, related to visual priming, predicted children's likelihood to answer fraction comparison items focusing exclusively on the fraction components. This relation was, furthermore, not mediated by general math achievement. Altogether, these findings shed light on the mental processes underlying the early stages of the learning of fractions.