Fractions are defined by numerical relationships, and comparing two fractions’ magnitudes requires within-fraction (holistic) and/or between-fraction (componential) relational comparisons. To better understand how individuals spontaneously reason about fractions, we collected eye-tracking data while they performed a fraction comparison task with conditions that promoted or obstructed different types of comparisons. We found evidence for both componential and holistic processing in this mixed-pairs task, consistent with the hybrid theory of fraction representation. Additionally, making within-fraction eye movements on trials that promoted a between-fraction comparison strategy was associated with slower responses. Finally, participants who performed better on a non-numerical test of reasoning took longer to respond to the most difficult fraction trials, which suggests that those who had greater facility with non-numerical reasoning attended more to numerical relationships. These findings extend prior research and support the continued investigation into the mechanistic links between numerical and non-numerical reasoning.

Reasoning ability supports the development of mathematics proficiency, as demonstrated by correlational and longitudinal evidence, and yet this skill is not emphasized in traditional elementary mathematics curricula. We propose that targeting reasoning skills from elementary school onward could help more students succeed in advanced mathematics courses. Here, we review the links between reasoning and mathematics, discuss the neural basis and development of reasoning ability, and identify promising school curricula. © 2014 Elsevier GmbH.

Patterns of correlated activity among brain regions reflect functionally relevant networks that are widely assumed to be stable over time. We hypothesized that if these correlations reflect the prior history of coactivation of brain regions, then a marked shift in cognition could alter the strength of coupling between these regions. We sought to test whether intensive reasoning training in humans would result in tighter coupling among regions in the lateral frontoparietal network, as measured with resting-state fMRI (rs-fMRI). Rather than designing an artificial training program, we studied individuals who were preparing for a standardized test that places heavy demands on relational reasoning, the Law School Admissions Test (LSAT). LSAT questions require test takers to group or sequence items according to a set of complex rules. We recruited young adults who were enrolled in an LSAT course that offers 70 h of reasoning instruction (n = 25), and age- and IQ-matched controls intending to take the LSAT in the future (n = 24). rs-fMRI data were collected for all subjects during two scanning sessions separated by 90 d. An analysis of pairwise correlations between brain regions implicated in reasoning showed that fronto-parietal connections were strengthened, along with parietal-striatal connections. These findings provide strong evidence for neural plasticity at the level of large-scale networks supporting high-level cognition.

We have reported previously that intensive preparation for a standardized test that taxes reasoning leads to changes in structural and functional connectivity within the frontoparietal network. Here, we investigated whether reasoning instruction transfers to improvement on unpracticed tests of reasoning, and whether these improvements are associated with changes in neural recruitment during reasoning task performance. We found behavioral evidence for transfer to a transitive inference task, but no evidence for transfer to a rule generation task. Across both tasks, we observed reduced lateral prefrontal activation in the trained group relative to the control group, consistent with other studies of practice-related changes in brain activation. In the transitive inference task, we observed enhanced suppression of task-negative, or default-mode, regions, consistent with work suggesting that better cognitive skills are associated with more efficient switching between networks. In the rule generation task, we found a pattern consistent with a training-related shift in the balance between phonological and visuospatial processing. Broadly, we discuss general methodological considerations related to the analysis and interpretation of training-related changes in brain activation. In summary, we present preliminary evidence for changes in brain activation associated with practice of high-level cognitive skills.

The capacity to keep multiple items in short-term memory (STM) improves over childhood and provides the foundation for the development of multiple cognitive abilities. The goal of this study was to measure the extent to which age differences in STM capacity are related to differences in task engagement during encoding. Children (n = 69, mean age = 10.6 years) and adults (n = 54, mean age = 27.5 years) performed two STM tasks: the forward digit span test from the Wechsler Intelligence Scale for Children (WISC) and a novel eyetracking digit span task designed to overload STM capacity. Building on prior research showing that task-evoked pupil dilation can be used as a real-time index of task engagement, we measured changes in pupil dilation while participants encoded long sequences of digits for subsequent recall. As expected, adults outperformed children on both STM tasks. We found similar patterns of pupil dilation while children and adults listened to the first six digits on our STM overload task, after which the adults' pupils continued to dilate and the children's began to constrict, suggesting that the children had reached their cognitive limits and that they had begun to disengage from the task. Indeed, the point at which pupil dilation peaked at encoding was a significant predictor of WISC forward span, and this relationship held even after partialing out recall performance on the STM overload task. These findings indicate that sustained task engagement at encoding is an important component of the development of STM.

This review provides an introduction to two eyetracking measures that can be used to study cognitive development and plasticity: pupil dilation and spontaneous blink rate. We begin by outlining the rich history of gaze analysis, which can reveal the current focus of attention as well as cognitive strategies. We then turn to the two lesser-utilized ocular measures. Pupil dilation is modulated by the brain's locus coeruleus-norepinephrine system, which controls physiological arousal and attention, and has been used as a measure of subjective task difficulty, mental effort, and neural gain. Spontaneous eyeblink rate correlates with levels of dopamine in the central nervous system, and can reveal processes underlying learning and goal-directed behavior. Taken together, gaze, pupil dilation, and blink rate are three non-invasive and complementary measures of cognition with high temporal resolution and well-understood neural foundations. Here we review the neural foundations of pupil dilation and blink rate, provide examples of their usage, describe analytic methods and methodological considerations, and discuss their potential for research on learning, cognitive development, and plasticity.