Modern trends of education development and mathematical training of schoolchildren

The relevance of the research is due to the need to modernize mathematical training of schoolchildren in line with the key trends in the development of education: globalization, digitalization and population aging. Conceptual ideas ensuring the development of modern mathematical theories have been identified on the basis of the analysis, and a set of key elements that make up the base of modern mathematics have been presented: structures, properties, actions, abstractions, relationships, behavior and alternatives. The research problem is to determine the foundations of designing a system of mathematical education, focused on students gaining a broad understanding of mathematics as a cultural phenomenon, a language of science and a set of tools for real life. The purpose of the study is to describe ways to modernize the mathematical preparation of schoolchildren in the mainstream of digitalization and the practical orientation of education. In the research process the following methods have been used: study and analysis of literary sources, theoretical modeling and design. One of the most significant manifestations of the digitalization trend in mathematical education is the use of interactive geometric environments. Their technical and methodological capabilities make it possible to organize the process of teaching mathematics on the basis of a research approach, which is expressed in students independently putting forward hypotheses in the process of experimenting with geometric objects created in an interactive geometric environment. The necessity of including mathematical literacy as one of its important results in the mathematical preparation of schoolchildren has been justified. The necessary changes in the content of mathematical training have been determined by creating a system of special, competency-based tasks

Enhanced functional synchronization of medial and lateral PFC underlies internally-guided action planning

Actions are often internally guided, reflecting our covert will and intentions. The dorsomedial prefrontal cortex, including the pre-Supplementary Motor Area (pre-SMA), has been implicated in the internally generated aspects of action planning, such as choice and intention. Yet, the mechanism by which this area interacts with other cognitive brain regions such as the dorsolateral prefrontal cortex, a central node in decision-making, is still unclear. To shed light on this mechanism, brain activity was measured via fMRI and intracranial EEG in two studies during the performance of visually cued repeated finger tapping in which the choice of finger was guided by either a presented number (external) or self-choice (internal). A functional-MRI (fMRI) study in 15 healthy participants demonstrated that the pre-SMA, compared to the SMA proper, was more active and also more functionally correlated with the dorsolateral prefrontal cortex during internally compared to externally guided action planning (p < 0.05, random effect). In a similar manner, an intracranial-EEG study in five epilepsy patients showed greater inter-regional gamma-related connectivity between electrodes situated in medial and lateral aspects of the prefrontal cortex for internally compared to externally guided actions. Although this finding was observed for groups of electrodes situated both in the pre-SMA and SMA-proper, increased intra-cluster gamma-related connectivity was only observed for the pre-SMA (sign-test, p < 0.0001). Overall our findings provide multi-scale indications for the involvement of the dorsomedial prefrontal cortex, and especially the pre-SMA, in generating internally guided motor planning. Our intracranial-EEG results further point to enhanced functional connectivity between decision-making- and motor planning aspects of the PFC, as a possible neural mechanism for internally generated action planning

Neural traces of stress: cortisol related sustained enhancement of amygdala-hippocampal functional connectivity

Stressful experiences modulate neuro-circuitry function, and the temporal trajectory of these alterations, elapsing from early disturbances to late recovery, heavily influences resilience and vulnerability to stress. Such effects of stress may depend on processes that are engaged during resting-state, through active recollection of past experiences and anticipation of future events, all known to involve the default mode network (DMN). By inducing social stress and acquiring resting-state functional magnetic resonance imaging (fMRI) before stress, immediately following it, and 2 h later, we expanded the time-window for examining the trajectory of the stress response. Throughout the study repeated cortisol samplings and self-reports of stress levels were obtained from 51 healthy young males. Post-stress alterations were investigated by whole brain resting-state functional connectivity (rsFC) of two central hubs of the DMN: the posterior cingulate cortex (PCC) and hippocampus. Results indicate a ’recovery’ pattern of DMN connectivity, in which all alterations, ascribed to the intervening stress, returned to pre-stress levels. The only exception to this pattern was a stress-induced rise in amygdala-hippocampal connectivity, which was sustained for as long as 2 h following stress induction. Furthermore, this sustained enhancement of limbic connectivity was inversely correlated to individual stress-induced cortisol responsiveness (AUCi) and characterized only the group lacking such increased cortisol (i.e., non-responders). Our observations provide evidence of a prolonged post-stress response profile, characterized by both the comprehensive balance of most DMN functional connections and the distinct time and cortisol dependent ascent of intra-limbic connectivity. These novel insights into neuro-endocrine relations are another milestone in the ongoing search for individual markers in stress-related psychopathologies

Dual array EEG-fMRI : An approach for motion artifact suppression in EEG recorded simultaneously with fMRI

Objective: Although simultaneous recording of EEG and MRI has gained increasing popularity in recent years, the extent of its clinical use remains limited by various technical challenges. Motion interference is one of the major challenges in EEG-fMRI. Here we present an approach which reduces its impact with the aid of an MR compatible dual-array EEG (daEEG) in which the EEG itself is used both as a brain signal recorder and a motion sensor. Methods: We implemented two arrays of EEG electrodes organized into two sets of nearly orthogonally intersecting wire bundles. The EEG was recorded using referential amplifiers inside a 3 T MR-scanner. Virtual bipolar measurements were taken both along bundles (creating a small wire loop and therefore minimizing artifact) and across bundles (creating a large wire loop and therefore maximizing artifact). Independent component analysis (ICA) was applied. The resulting ICA components were classified into brain signal and noise using three criteria: 1) degree of two-dimensional spatial correlation between ICA coefficients along bundles and across bundles; 2) amplitude along bundles vs. across bundles; 3) correlation with ECG. The components which passed the criteria set were transformed back to the channel space. Motion artifact suppression and the ability to detect interictal epileptic spikes following daEEG and Optimal Basis Set (OBS) procedures were compared in 10 patients with epilepsy. Results: The SNR achieved by daEEG was 11.05 +/- 3.10 and by OBS was 8.25 +/- 1.01 (p <0.00001). In 9 of 10 patients, more spikes were detected after daEEG than after OBS (p <0.05). Significance: daEEG improves signal quality in EEG-fMRI recordings, expanding its clinical and research potential. (C) 2016 Elsevier Inc. All rights reserved.Peer reviewe

Never Resting Brain: Simultaneous Representation of Two Alpha Related Processes in Humans

Brain activity is continuously modulated, even at “rest”. The alpha rhythm (8–12 Hz) has been known as the hallmark of the brain's idle-state. However, it is still debated if the alpha rhythm reflects synchronization in a distributed network or focal generator and whether it occurs spontaneously or is driven by a stimulus. This EEG/fMRI study aimed to explore the source of alpha modulations and their distribution in the resting brain. By serendipity, while computing the individually defined power modulations of the alpha-band, two simultaneously occurring components of these modulations were found. An ‘induced alpha’ that was correlated with the paradigm (eyes open/ eyes closed), and a ‘spontaneous alpha’ that was on-going and unrelated to the paradigm. These alpha components when used as regressors for BOLD activation revealed two segregated activation maps: the ‘induced map’ included left lateral temporal cortical regions and the hippocampus; the ‘spontaneous map’ included prefrontal cortical regions and the thalamus. Our combined fMRI/EEG approach allowed to computationally untangle two parallel patterns of alpha modulations and underpin their anatomical basis in the human brain. These findings suggest that the human alpha rhythm represents at least two simultaneously occurring processes which characterize the ‘resting brain’; one is related to expected change in sensory information, while the other is endogenous and independent of stimulus change

Cortex-based inter-subject analysis of iEEG and fMRI data sets: Application to sustained task-related BOLD and gamma responses

Linking regional metabolic changes with fluctuations in the local electromagnetic fields directly on the surface of the human cerebral cortex is of tremendous importance for a better understanding of detailed brain processes. Functional magnetic resonance imaging (fMRI) and intra-cranial electro-encephalography (iEEG) measure two technically unrelated but spatially and temporally complementary sets of functional descriptions of human brain activity. In order to allow fine-grained spatio-temporal human brain mapping at the population-level, an effective comparative framework for the cortex-based inter-subject analysis of iEEG and fMRI data sets is needed.We combined fMRI and iEEG recordings of the same patients with epilepsy during alternated intervals of passive movie viewing and music listening to explore the degree of local spatial correspondence and temporal coupling between blood oxygen level dependent (BOLD) fMRI changes and iEEG spectral power modulations across the cortical surface after cortex-based inter-subject alignment. To this purpose, we applied a simple model of the iEEG activity spread around each electrode location and the cortex-based inter-subject alignment procedure to transform discrete iEEG measurements into cortically distributed group patterns by establishing a fine anatomic correspondence of many iEEG cortical sites across multiple subjects.Our results demonstrate the feasibility of a multi-modal inter-subject cortex-based distributed analysis for combining iEEG and fMRI data sets acquired from multiple subjects with the same experimental paradigm but with different iEEG electrode coverage. The proposed iEEG-fMRI framework allows for improved group statistics in a common anatomical space and preserves the dynamic link between the temporal features of the two modalities

Infants' preferences for native versus non-native rhythm

This project tests preferences for native versus non-native accents, realized primarily through temporal rhythm variations. It tests four groups of infants, 4-, 6-, 8-, and 10-month-olds, acquiring Czech as their native language