Characterizing Behavioral and Brain Changes Associated with Practicing Reasoning Skills

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.National Science Foundation (U.S.). Graduate Research FellowshipEunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.) (F32HD079143-01

Neurodevelopment of relational reasoning: Implications for mathematical pedagogy

a b s t r a c t 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

Gaussian Tunneling Model of c-Axis Twist Josephson Junctions

We calculate the critical current density $J^J_c$ for c-axis Josephson tunneling between identical high temperature superconductors twisted an angle $\phi_0$ about the c-axis. We model the tunneling matrix element squared as a Gaussian in the change of wavevector q parallel to the junction, $<|t({\bf q})|^2>\propto\exp(-{\bf q}^2a^2/2\pi^2\sigma^2)$. The $J^J_c(\phi_0)/J^J_c(0)$ obtained for the s- and extended-s-wave order parameters (OP's) are consistent with the Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ data of Li {\it et al.}, but only for strongly incoherent tunneling, $\sigma^2\ge0.25$. A $d_{x^2-y^2}$-wave OP is always inconsistent with the data. In addition, we show that the apparent conventional sum rule violation observed by Basov et al. might be understandable in terms of incoherent c-axis tunneling, provided that the OP is not $d_{x^2-y^2}$-wave.Comment: 6 pages, 6 figure

Adolescent brain development

Adolescence starts with puberty and ends when individuals attain an independent role in society. Cognitive neuroscience research in the last two decades has improved our understanding of adolescent brain development. The evidence indicates a prolonged structural maturation of grey matter and white matter tracts supporting higher cognitive functions such as cognitive control and social cognition. These changes are associated with a greater strengthening and separation of brain networks, both in terms of structure and function, as well as improved cognitive skills. Adolescent-specific sub-cortical reactivity to emotions and rewards, contrasted with their developing self-control skills, are thought to account for their greater sensitivity to the socio-affective context. The present review examines these findings and their implications for training interventions and education

Task-evoked pupillometry provides a window into the development of short-term memory capacity

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&apos; pupils continued to dilate and the children&apos;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

The unique contributions of verbal analogical reasoning and non-verbal matrix reasoning to science and maths problem-solving in adolescence

Relational reasoning, the ability to detect meaningful patterns, matures through adolescence. The unique contributions of verbal analogical and non-verbal matrix relational reasoning to science and maths are not well understood. Functional magnetic resonance imaging data were collected during science and maths problem-solving, and participants (N=36, 11-15 years) also completed relational reasoning and executive function tasks. Higher verbal analogical reasoning associated with higher accuracy and faster reaction times in science and maths, and higher activation in the left anterior temporal cortex during maths problem-solving. Higher non-verbal matrix reasoning associated with higher science accuracy, higher science activation in regions across the brain, and lower maths activation in the right middle temporal gyrus. Science associations mostly remained significant when individual differences in executive functions and verbal IQ were taken into account, while maths associations typically did not. The findings indicate the potential importance of supporting relational reasoning in adolescent science and maths learning

Bridging Cognitive and Education Research to Gain Insights on Fractions Learning

Symbolic fractions are notoriously difficult to learn, and this difficulty has been characterized in terms of cognitive, mathematical, and educational challenges. In this dissertation I present evidence from several eye-tracking studies that illuminate participants’ cognitive approaches to proportional reasoning, and analyze them from the perspectives of psychological research on relational reasoning, as well as modern education research. In my first two studies, I had participants perform fraction comparison tasks while I measured their eye movements to assess how they approached various types of problems. In the first of these studies, I compared the performance and eye gaze patterns of 5th-graders, who were just beginning to learn fractions, with those of college students. I sought to test the hypothesis, based on relational complexity theory, that children have difficulty learning fractions in part because they have difficulty integrating relationships among mental representations. This effect was present in the data, however, there were additional performance decrements unrelated to relational complexity that are better explained by the development of inhibition and cognitive flexibility. Further, I found that children who did not comprehend fraction concepts, as evidenced by their performance, still exhibited similar eye movements to those who performed well, suggesting that they encoded the relevant numerical relations even though they were not able to interpret them correctly. These findings underscore the cognitive and mathematical complexities inherent in proportional reasoning. In the second fraction comparison study, I investigated the extent to which adults applied various relational integration skills to proportional reasoning problems, and whether doing so impacted their performance. I found that they performed better on trials that could be solved more easily by componential than magnitude processing. Specifically, when there was a readily-available multiplicative factor between the two fractions, they made fewer within-fraction saccades consistent with magnitude calculation – and when they made fewer of these saccades, they performed more efficiently. This work highlights the ways in which relational thinking can support proportional reasoning. In the dissertation, I place the results of these first two studies in the context of prior research on fraction understanding, and point to possible implications for pedagogy. In a third study, I collaborated on an investigation of children’s learning trajectories during the acquisition of fraction knowledge, comparing two curricular approaches. We found that individual prior knowledge, classroom environment, and the curriculum with which the students engaged all influenced their acquisition of fractions knowledge. As is evident in this dissertation, experimental psychology and educational research provide different, and equally productive, lenses with which to explore the learning of fractions. By integrating across these theories and methods of analysis, we can more fully characterize and promote the development of proportional reasoning