A new ontology for numerical cognition: Integrating evolutionary, embodied, and data informatics approaches.

Numerical cognition is a field that investigates the sociocultural, developmental, cognitive, and biological aspects of mathematical abilities. Recent findings in cognitive neuroscience suggest that cognitive skills are facilitated by distributed, transient, and dynamic networks in the brain, rather than isolated functional modules. Further, research on the bodily and evolutionary bases of cognition reveals that our cognitive skills harness capacities originally evolved for action and that cognition is best understood in conjunction with perceptuomotor capacities. Despite these insights, neural models of numerical cognition struggle to capture the relation between mathematical skills and perceptuomotor systems. One front to addressing this issue is to identify building block sensorimotor processes (BBPs) in the brain that support numerical skills and develop a new ontology connecting the sensorimotor system with mathematical cognition. BBPs here are identified as sensorimotor functions, associated with distributed networks in the brain, and are consistently identified as supporting different cognitive abilities. BBPs can be identified with new approaches to neuroimaging; by examining an array of sensorimotor and cognitive tasks in experimental designs, employing data-driven informatics approaches to identify sensorimotor networks supporting cognitive processes, and interpreting the results considering the evolutionary and bodily foundations of mathematical abilities. New empirical insights on the BBPs can eventually lead to a revamped embodied cognitive ontology in numerical cognition. Among other mathematical skills, numerical magnitude processing and its sensorimotor origins are discussed to substantiate the arguments presented. Additionally, an fMRI study design is provided to illustrate the application of the arguments presented in empirical research.

White and gray matter correlates of theory of mind in autism: a voxel-based morphometry study.

Autism spectrum disorder (ASD) is characterized by difficulties in theory of mind (ToM) and social communication. Studying structural and functional correlates of ToM in the brain and how autistic and nonautistic groups differ in terms of these correlates can help with diagnosis and understanding the biological mechanisms of ASD. In this study, we investigated white matter volume (WMV) and gray matter volume (GMV) differences between matching autistic and nonautistic samples, and how these structural features relate to age and ToM skills, indexed by the Reading the Mind in the Eyes (RMIE) measure. The results showed widespread GMV and WMV differences between the two groups in regions crucial for social processes. The autistic group did not express the typically observed negative GMV and positive WMV correlations with age at the same level as the nonautistic group, pointing to abnormalities in developmental structural changes. In addition, we found differences between the two groups in how GMV relates to ToM, particularly in the left frontal regions, and how WMV relates to ToM, mostly in the cingulate and corpus callosum. Finally, GMV in the left insula, a region that is part of the salience network, was found to be crucial in distinguishing ToM performance between the two groups.

A comparative study of machine learning methods for classifying ERP scalp distribution.

Objective. Machine learning (ML) methods are used in different fields for classification and regression purposes with different applications. These methods are also used with various non-invasive brain signals, including Electroencephalography (EEG) signals to detect some patterns in the brain signals. ML methods are considered critical tools for EEG analysis since could overcome some of the limitations in the traditional methods of EEG analysis such as Event-related potentials (ERPs) analysis. The goal of this paper was to apply ML classification methods on ERP scalp distribution to investigate the performance of these methods in identifying numerical information carried in different finger-numeral configurations (FNCs). FNCs in their three forms of montring, counting, and non-canonical counting are used for communication, counting, and doing arithmetic across the world between children and even adults. Studies have shown the relationship between perceptual and semantic processing of FNCs, and neural differences in visually identifying different types of FNCs.Approach.A publicly available 32-channel EEG dataset recorded for 38 participants while they were shown a picture of an FNC (i.e., three categories and four numbers of 1,2,3, and 4) was used. EEG data were pre-processed and ERP scalp distribution of different FNCs was classified across time by six ML methods, including support vector machine, linear discriminant analysis, naïve Bayes, decision tree, K-nearest neighbor, and neural network. The classification was conducted in two conditions: classifying all FNCs together (i.e., 12 classes) and classifying FNCs of each category separately (i.e., 4 classes).Results.The support vector machine had the highest classification accuracy for both conditions. For classifying all FNCs together, the K-nearest neighbor was the next in line; however, the neural network could retrieve numerical information from the FNCs for category-specific classification.Significance.The significance of this study is in exploring the application of multiple ML methods in recognizing numerical information contained in ERP scalp distribution of different finger-numeral configurations.

Incongruity in fraction verification elicits N270 and P300 ERP effects.

Understanding how the numerical magnitudes of fractions are accessed is a topic of major interest in numerical cognition and mathematics education. Only a few studies have investigated fraction processing using EEG methods. In the present study, 24 adult participants completed a fraction magnitude verification task while EEGs were recorded. Similar to other arithmetic verification tasks, behavioral results show increased response times to validate mismatching magnitudes compared to matching ones. ERP results show an early frontal N270 component to mismatching trials and a late parietal P300 component during matching trials. These ERP results highlight that participants treat matching fractions as targets and suggest that additional cognitive resources are needed to process mismatching targets. These results provide evidence that fractions processing shares a similar neurocognitive process as those observed during the processing of arithmetic operations and open the door to further explore fraction processing using ERP methods.

Structured versus free block play: the impact on arithmetic processing.

BACKGROUND: Block play is one type of intervention that improves visuospatial skills. There are multiple forms of block play and it is unclear whether they have differential cognitive effects. METHOD: Given the importance of visuospatial skills for mathematical performance, we studied the differential impact of two types of block playstructured (copying a block design) and free (building from imagination) on arithmetic processing, using behavioral and fMRI methods. Forty-three children aged 8.3±0.8 years participated (21 free play and 22 structured block play). RESULTS: Results showed that while both groups showed behavioral improvements, only the structured block play group showed significant improvements in both addition and subtraction performance. Additionally, the structured block play group showed increased activation in several regions linked to memory, motor, and arithmetic processing after training. CONCLUSION: The results inform choices for activities used in the classroom to improve visuospatial skills and suggest structured block play may be beneficial for arithmetic processing.

Gray matter volume in left intraparietal sulcus predicts longitudinal gains in subtraction skill in elementary school.

Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms.

Connecting levels of analysis in educational neuroscience: A review of multi-level structure of educational neuroscience with concrete examples.

In its origins educational neuroscience has started as an endeavor to discuss implications of neuroscience studies for education. However, it is now on its way to become a transdisciplinary field, incorporating findings, theoretical frameworks and methodologies from education, and cognitive and brain sciences. Given the differences and diversity in the originating disciplines, it has been a challenge for educational neuroscience to integrate both theoretical and methodological perspectives in education and neuroscience in a coherent way. We present a multi-level framework for educational neuroscience, which argues for integration of multiple levels of analysis, some originating in brain and cognitive sciences, others in education, as a roadmap for the future of educational neuroscience, with concrete examples in mathematical learning and moral education.

ERP differences in processing canonical and noncanonical finger-numeral configurations.

Finger-numeral configurations are used to represent numerosities, to count, and to do arithmetic across cultures. Previous research has distinguished between two forms of finger-numeral configurations; finger montring and finger counting. Montring refers to how people raise their fingers to show numerosities to others and usually serves a communicative function. Finger counting is used both for counting and arithmetic, and has a self-directed, facilitative function. In this study we compared the ERP markers for recognition of montring, counting, and noncanonical finger-numeral configurations with adult participants to explore differences in early perceptual and later semantic processing. Montring configurations were recognized faster and more accurately compared to counting and noncanonical. Recognition of montring configurations drew larger attentional resources, marked by higher positivity in the P1/N1 range, and montring and counting showed similar patterns of semantic processing, marked by higher positivity in the P3 range compared to noncanonical, possibly due to strategy differences (memory recall vs. counting). We also found some ERP evidence for participants' finger counting habits affecting their processing of counting configurations. Overall, the results show differences in perceptual and semantic processes involved in extracting numerical information across the three finger-numeral configurations.

Gray Matter Correlates of Finger Gnosis in Children: A VBM Study.

Accumulating evidence relates finger gnosis (also called finger sense or finger gnosia), the ability to identify and individuate fingers, to cognitive processing, particularly numerical cognition. Multiple studies have shown that finger gnosis scores correlate with or predict numerical skills in children. Neuropsychological cases as well as magnetic stimulation studies have also shown that finger agnosia (defects in finger gnosis) often co-occurs with cognitive impairments, including agraphia and acalculia. However, our knowledge of the structural and functional correlates, and the development of finger gnosis is limited. To expand our understanding of structural brain features that are associated with finger gnosis, we conducted a voxel-based morphometry study with 42 seven- to 10-year-old children, where we investigated the correlation between finger gnosis scores and whole-brain gray matter volume (GMV). Correlations between finger gnosis and GMV were found in a set of frontoparietal, striatal, and cerebellar areas. We also found sex differences in how GMV is associated with finger gnosis. While females showed a more distributed and extensive set of frontal and parietal clusters, males showed two striatal clusters. This study provides the first findings on structural brain features that correlate with finger gnosis.

An Embodied Approach to Understanding: Making Sense of the World Through Simulated Bodily Activity.

Even though understanding is a very widely used concept, both colloquially and in scholarly work, its definition is nebulous and it is not well-studied as a psychological construct, compared to other psychological constructs like learning and memory. Studying understanding based on third-person (e.g., behavioral, neuroimaging) data alone presents unique challenges. Understanding refers to a first-person experience of making sense of an event or a conceptual domain, and therefore requires incorporation of multiple levels of study, at the first-person (phenomenological), behavioral, and neural levels. Previously, psychological understanding was defined as a form of conscious knowing. Alternatively, biofunctional approach extends to unconscious, implicit, automatic, and intuitive aspects of cognition. Here, to bridge these two approaches an embodied and evolutionary perspective is provided to situate biofunctional understanding in theories of embodiment, and to discuss how simulation theories of cognition, which regard simulation of sensorimotor and affective states as a central tenet of cognition, can bridge the gap between biofunctional and psychological understanding.

Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study.

Fingers are used as canonical representations for numbers across cultures. In previous imaging studies, it was shown that arithmetic processing activates neural resources that are known to participate in finger movements. Additionally, in one dual-task study, it was shown that anatomically ordered finger tapping disrupts addition and subtraction more than multiplication, possibly due to a long-lasting effect of early finger counting experiences on the neural correlates and organization of addition and subtraction processes. How arithmetic task difficulty and tapping complexity affect the concurrent performance is still unclear. If early finger counting experiences have bearing on the neural correlates of arithmetic in adults, then one would expect anatomically and non-anatomically ordered tapping to have different interference effects, given that finger counting is usually anatomically ordered. To unravel these issues, we studied how (1) arithmetic task difficulty and (2) the complexity of the finger tapping sequence (anatomical vs. non-anatomical ordering) affect concurrent performance and use of key neural circuits using a mixed block/event-related dual-task fMRI design with adult participants. The results suggest that complexity of the tapping sequence modulates interference on addition, and that one-digit addition (fact retrieval), compared to two-digit addition (calculation), is more affected from anatomically ordered tapping. The region-of-interest analysis showed higher left angular gyrus BOLD response for one-digit compared to two-digit addition, and in no-tapping conditions than dual tapping conditions. The results support a specific association between addition fact retrieval and anatomically ordered finger movements in adults, possibly due to finger counting strategies that deploy anatomically ordered finger movements early in the development.

The impact of finger counting habits on arithmetic in adults and children.

Here, we explored the impact of finger counting habits on arithmetic in both adults and children. Two groups of participants were examined, those that begin counting with their left hand (left-starters) and those that begin counting with their right hand (right-starters). For the adults, performance on an addition task in which participants added 2 two-digit numbers was compared. The results revealed that left-starters were slower than right-starters when adding and they had lower forward and backward digit-span scores. The children (aged 5-12) showed similar results on a single-digit timed addition task-right-starters outperformed left-starters. However, the children did not reveal differences in working memory or verbal and non-verbal intelligence as a function of finger counting habit. We argue that the motor act of finger counting influences how number is represented and suggest that left-starters may have a more bilateral representation that accounts for the slower processing.