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

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

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' 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

Intensive reasoning training alters patterns of brain connectivity at rest.

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

Intensive Reasoning Training Alters Patterns of Brain Connectivity at Rest

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 co-activation 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 fronto-parietal 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 hours 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 days. 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

Eye Gaze Patterns Reflect How Young Fraction Learners Approach Numerical Comparisons

Learning fractions is notoriously difficult, yet critically important to mathematical and general academic achievement. Eye-tracking studies are beginning to characterize the strategies that adults use when comparing fractions, but we know relatively little about the strategies used by children. We used eye-tracking to analyze how novice children and mathematically-proficient adults approached a well-studied fraction comparison paradigm. Specifically, eye-tracking can provide insights into the nature of differences: whether they are quantitative—reflecting differences in efficiency—or qualitative—reflecting a fundamentally different approach. We found that children who had acquired the basic fraction rules made more eye movements than did either adults or less proficient children, suggesting a thorough but inefficient problem solving approach. Additionally, correct responses were associated with normative gaze patterns, regardless of age or proficiency levels. However, children paid more attention to irrelevant numerical relationships on conditions that were conceptually difficult. An exploratory analysis points to the possibility that children on the verge of making a conceptual leap attend to the relevant relationships even when they respond incorrectly. These findings indicate the potential of eye-tracking methodology to better characterize the behavior associated with different levels of fraction proficiency, as well as to provide insights for educators regarding how to best support novices at different levels of conceptual development

Intensive reasoning training alters patterns of brain connectivity at rest.

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

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