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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.

School mathematics comprises a diversity of concepts whose cognitive complexity is still poorly understood, a chief example being fractions. These are typically taught in middle school, but many students fail to master them, and misconceptions frequently persist into adulthood. In this study, we investigate fraction comparison, a task that taps into both conceptual and procedural knowledge of fractions, by looking at performance of highly mathematically skilled young adults. Fifty-seven Chilean engineering undergraduate students answered a computerized fraction comparison task, while their answers and response times were recorded. Task items were selected according to a number of mathematically and/or cognitively relevant characteristics: (a) whether the fractions to be compared shared a common component, (b) the numerical distance between fractions, and (c) the applicability of two strategies to answer successfully: a congruency strategy (a fraction is larger if it has larger natural number components than another) and gap thinking (a fraction is larger if it is missing fewer pieces than another to complete the whole). In line with previous research, our data indicated that the congruency strategy is inadequate to describe participants' performance, as congruent items turned out to be more difficult than incongruent ones when fractions had no common component. Although we hypothesized that this lower performance for congruent items would be explained by the use of gap thinking, this turned out not to be the case: evidence was insufficient to show that the applicability of the gap thinking strategy modulated either participants' accuracy rates or response times (although individual-level data suggest that there is an effect for response times). When fractions shared a common component, instead, our data display a more complex pattern that expected: an advantage for congruent items is present in the first experimental block but fades as the experiment progresses. Numerical distance had an effect in fraction comparison that was statistically significant for items without common components only. Altogether, our results from experts' reasoning reveal nuances in the fraction comparison task with respect to previous studies and contribute to future models of reasoning in this task. [ABSTRACT FROM AUTHOR]

The distinction between non-symbolic and symbolic number is poorly addressed by the authors despite being relevant in numerical cognition, and even more important in light of the proposal that the approximate number system (ANS) represents rational numbers. Although evidence on non-symbolic number and ratios fits with ANS representations, the case for symbolic number and rational numbers is still open.

The present study examined neural responses associated with moral sensitivity in adolescents with a background of early social deprivation. Using high-density electroencephalography (hdEEG), brain activity was measured during an intentional inference task, which assesses rapid moral decision-making regarding intentional or unintentional harm to people and objects. We compared the responses to this task in a socially deprived group (DG) with that of a control group (CG). The event-related potentials (ERPs) results showed atypical early and late frontal cortical markers associated with attribution of intentionality during moral decision-making in DG (especially regarding intentional harm to people). The source space of the hdEEG showed reduced activity for DG compared with CG in the right prefrontal cortex, bilaterally in the ventromedial prefrontal cortex (vmPFC), and right insula. Moreover, the reduced response in vmPFC for DG was predicted by higher rates of externalizing problems. These findings demonstrate the importance of the social environment in early moral development, supporting a prefrontal maturation model of social deprivation.