Mathematical expertise modulates the architecture of dorsal and cortico-thalamic white matter tracts

Math on cortex-enhanced delta phase synchrony in math experts during long and complex math demonstrations

Neural oscillations are important for working memory and reasoning and they are modulated during cognitively challenging tasks, like mathematics. Previous work has examined local cortical synchrony on theta (4-8 Hz) and alpha (8-13 Hz) bands over frontal and parietal electrodes during short mathematical tasks when sitting. However, it is unknown whether processing of long and complex math stimuli evokes inter-regional functional connectivity. We recorded cortical activity with EEG while math experts and novices watched long (13-68 seconds) and complex (bachelor-level) math demonstrations when sitting and standing. Fronto-parietal connectivity over the left hemisphere was stronger in math experts than novices reflected by enhanced delta (0.5-4 Hz) phase synchrony in experts. Processing of complex math tasks when standing extended the difference to right hemisphere, suggesting that other cognitive processes, such as maintenance of body balance when standing, may interfere with novice's internal concentration required during complex math tasks more than in experts. There were no groups differences in phase synchrony over theta or alpha frequencies. These results suggest that low-frequency oscillations modulate inter-regional connectivity during long and complex mathematical cognition and demonstrate one way in which the brain functions of math experts differ from those of novices: through enhanced fronto-parietal functional connectivity.

The development of simple addition problem solving in children: Reliance on automatized counting or memory retrieval depends on both expertise and problem size

In an experiment, 98 children aged 8 to 9, 10 to 12, and 13 to 15 years solved addition problems with a sum up to 10. In another experiment, the same children solved the same calculations within a sign priming paradigm where half the additions were displayed with the "+" sign 150 ms before the addends. Therefore, size effects and priming effects could be considered conjointly within the same populations. Our analyses revealed that small problems, constructed with addends from 1 to 4, presented a linear increase of solution times as a function of problem sums (i.e., size effect) in all age groups. However, an operator priming effect (i.e., facilitation of the solving process with the anticipated presentation of the "+" sign) was observed only in the group of oldest children. These results support the idea that children use a counting procedure that becomes automatized (as revealed by the priming effect) around 13 years of age. For larger problems and whatever the age group, no size or priming effects were observed, suggesting that the answers to these problems were already retrieved from memory at 8 to 9 years of age. For this specific category of large problems, negative slopes in solution times demonstrate that retrieval starts from the largest problems during development. These results are discussed in light of a horse race model in which procedures can win over retrieval.

Modulation of resting-state networks following repetitive transcranial alternating current stimulation of the dorsolateral prefrontal cortex

Transcranial alternating current stimulation (tACS) offers a unique method to temporarily manipulate the activity of the stimulated brain region in a frequency-dependent manner. However, it is not clear if repetitive modulation of ongoing oscillatory activity with tACS over multiple days can induce changes in grey matter resting-state functional connectivity and white matter structural integrity. The current study addresses this question by applying multiple-session theta band stimulation on the left dorsolateral prefrontal cortex (L-DLPFC) during arithmetic training. Fifty healthy participants (25 males and 25 females) were randomly assigned to the experimental and sham groups, half of the participants received individually adjusted theta band tACS, and half received sham stimulation. Resting-state functional magnetic resonance (rs-fMRI) and diffusion-weighted imaging (DWI) data were collected before and after 3 days of tACS-supported procedural learning training. Resting-state network analysis showed a significant increase in connectivity for the frontoparietal network (FPN) with the precuneus cortex. Seed-based analysis with a seed defined at the primary stimulation site showed an increase in connectivity with the precuneus cortex, posterior cingulate cortex (PCC), and lateral occipital cortex. There were no effects on the structural integrity of white matter tracts as measured by fractional anisotropy, and on behavioral measures. In conclusion, the study suggests that multi-session task-associated tACS can produce significant changes in resting-state functional connectivity; however, changes in functional connectivity do not necessarily translate to changes in white matter structure or behavioral performance.

A perceptual field test in object experts using gaze-contingent eye tracking

A hallmark of expert object recognition is rapid and accurate subordinate-category recognition of visually homogenous objects. However, the perceptual strategies by which expert recognition is achieved is less known. The current study investigated whether visual expertise changes observers' perceptual field (e.g., their ability to use information away from fixation for recognition) for objects in their domain of expertise, using a gaze-contingent eye-tracking paradigm. In the current study, bird experts and novices were presented with two bird images sequentially, and their task was to determine whether the two images were of the same species (e.g., two different song sparrows) or different species (e.g., song sparrow and chipping sparrow). The first study bird image was presented in full view. The second test bird image was presented fully visible (full-view), restricted to a circular window centered on gaze position (central-view), or restricted to image regions beyond a circular mask centered on gaze position (peripheral-view). While experts and novices did not differ in their eye-movement behavior, experts' performance on the discrimination task for the fastest responses was less impaired than novices in the peripheral-view condition. Thus, the experts used peripheral information to a greater extent than novices, indicating that the experts have a wider perceptual field to support their speeded subordinate recognition.

Nonlinear and machine learning analyses on high-density EEG data of math experts and novices

Current trend in neurosciences is to use naturalistic stimuli, such as cinema, class-room biology or video gaming, aiming to understand the brain functions during ecologically valid conditions. Naturalistic stimuli recruit complex and overlapping cognitive, emotional and sensory brain processes. Brain oscillations form underlying mechanisms for such processes, and further, these processes can be modified by expertise. Human cortical functions are often analyzed with linear methods despite brain as a biological system is highly nonlinear. This study applies a relatively robust nonlinear method, Higuchi fractal dimension (HFD), to classify cortical functions of math experts and novices when they solve long and complex math demonstrations in an EEG laboratory. Brain imaging data, which is collected over a long time span during naturalistic stimuli, enables the application of data-driven analyses. Therefore, we also explore the neural signature of math expertise with machine learning algorithms. There is a need for novel methodologies in analyzing naturalistic data because formulation of theories of the brain functions in the real world based on reductionist and simplified study designs is both challenging and questionable. Data-driven intelligent approaches may be helpful in developing and testing new theories on complex brain functions. Our results clarify the different neural signature, analyzed by HFD, of math experts and novices during complex math and suggest machine learning as a promising data-driven approach to understand the brain processes in expertise and mathematical cognition.

Common Neural Functions during Children's Learning from Naturalistic and Controlled Mathematics Paradigms

Two major goals of human neuroscience are to understand how the brain functions in the real world and to measure neural processes under conditions that are ecologically valid. A critical step toward these goals is understanding how brain activity during naturalistic tasks that mimic the real world relates to brain activity in more traditional laboratory tasks. In this study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in a naturalistic setting.

Resting-State Functional Connectivity in Mathematical Expertise

To what extent are different levels of expertise reflected in the functional connectivity of the brain? We addressed this question by using resting-state functional magnetic resonance imaging (fMRI) in mathematicians versus non-mathematicians. To this end, we investigated how the two groups of participants differ in the correlation of their spontaneous blood oxygen level-dependent fluctuations across the whole brain regions during resting state. Moreover, by using the classification algorithm in machine learning, we investigated whether the resting-state fMRI networks between mathematicians and non-mathematicians were distinguished depending on features of functional connectivity. We showed diverging involvement of the frontal-thalamic-temporal connections for mathematicians and the medial-frontal areas to precuneus and the lateral orbital gyrus to thalamus connections for non-mathematicians. Moreover, mathematicians who had higher scores in mathematical knowledge showed a weaker connection strength between the left and right caudate nucleus, demonstrating the connections' characteristics related to mathematical expertise. Separate functional networks between the two groups were validated with a maximum classification accuracy of 91.19% using the distinct resting-state fMRI-based functional connectivity features. We suggest the advantageous role of preconfigured resting-state functional connectivity, as well as the neural efficiency for experts' successful performance.

Hierarchy processing in human neurobiology: how specific is it?

Although human and non-human animals share a number of perceptual and cognitive abilities, they differ in their ability to process hierarchically structured sequences. This becomes most evident in the human capacity to process natural language characterized by structural hierarchies. This capacity is neuroanatomically grounded in the posterior part of left Broca's area (Brodmann area (BA) 44), located in the inferior frontal gyrus, and its dorsal white matter fibre connection to the temporal cortex. Within this neural network, BA 44 itself subserves hierarchy building and the strength of its connection to the temporal cortex correlates with the processing of syntactically complex sentences. Whether these brain structures are also relevant for other human cognitive abilities is a current debate. Here, this question will be evaluated with respect to those human cognitive abilities that are assumed to require hierarchy building, such as music, mathematics and Theory of Mind. Rather than supporting a domain-general view, the data indicate domain-selective neural networks as the neurobiological basis for processing hierarchy in different cognitive domains. Recent cross-species white matter comparisons suggest that particular connections within the networks may make the crucial difference in the brain structure of human and non-human primates, thereby enabling cognitive functions specific to humans. This article is part of the theme issue 'What can animal communication teach us about human language?'