The number sense and the language instinct: Relating syntax and arithmetic in human cognition

Attitudes of Junior High School Pupils toward Arithmetic

Number sense is a fundamental component of meaningful mathematics learning, particularly in solving arithmetic operation problems. However, many students demonstrate procedural proficiency without adequate numerical understanding. This study aims to describe and analyze students’ number sense in solving arithmetic operation problems in relation to differences in mathematical ability. A mixed methods approach with an explanatory sequential design was employed. The participants were 60 seventh-grade students from MTs Miftahul Ulum Lumajang, who were categorized into high, medium, and low mathematical ability groups based on a mathematics ability test. Quantitative data were collected through a number sense test and analyzed using descriptive statistics and one-way ANOVA, while qualitative data were obtained through in-depth interviews and analyzed using the interactive model of Miles, Huberman, and Saldaña. The results indicate a statistically significant difference in students’ number sense across different levels of mathematical ability (p<0.05). Students with high mathematical ability demonstrated more developed number sense, characterized by effective estimation, flexible strategy use, and the ability to evaluate the reasonableness of results. Students with medium mathematical ability showed partial development with inconsistent use of estimation and strategies, whereas students with low mathematical ability relied heavily on mechanical procedures and exhibited limited understanding of numerical relationships. These findings highlight the importance of differentiated instruction in arithmetic operations that emphasizes the development of number sense according to students’ mathematical ability levels.

Previous work has shown relations between domain-general processes, domain-specific processes, and mathematical ability. However, the underlying neurophysiological effects of mathematical ability are less clear. Recent evidence highlighted the potential role of beta oscillations in mathematical ability. Here we investigate whether domain-general (working memory) and domain-specific (number sense) processes mediate the relation between resting-state beta oscillations and mathematical ability, and how this may differ as a function of development (children vs. adults). We compared a traditional analysis method normally used in EEG studies with a more recently developed parameterization method that separates periodic from aperiodic activity. Regardless of methods chosen, we found no support for mediation of working memory and number sense, neither for children nor for adults. However, we found subtle differences between the methods. Additionally, we showed that the traditional EEG analysis method conflates periodic activity with aperiodic activity; in addition, the latter is strongly related to mathematical ability and this relation differs between children and adults. At the cognitive level, our findings do not support previous suggestions of a mediation of working memory and number sense. At the neurophysiological level our findings suggest that aperiodic, rather than periodic, activity is linked to mathematical ability as a function of development.

Event Abstract Back to Event Mathematical abilities in development and neuroanatomical correlates GIULIA CRISTOFORETTI1*, Helena Verhelst1, Wim Fias1 and Denes Szucs2 1 Department of Experimental Psychology, Ghent University, Belgium 2 Centre for Neuroscience in Education, University of Cambridge, United Kingdom Currently, dominant cognitive neuroscience theories of developmental dyscalculia (DD) suggest that it is related to the domain-specific impairment of the simple number processing ability (number sense) of the brain, residing in the intraparietal sulcus (IPS) (Piazza et al., 2010; Isaac et al., 2001). However, behavioral and neuroimaging research also suggests that poor mathematical abilities are linked to the disruption of other functions of the IPS. Indeed, DD relates to a robust impairment of various cognitive functions implemented by the extended brain network underlying mathematics such as visuospatial short-term memory (STM) and working memory (WM), both linked to the IPS, and inhibition function (Szucs et al. 2013, Szucs et al., 2014). In the current imaging study, we investigate mathematical abilities and the neuroanatomical basis taking these cognitive functions into account. Structural and diffusion tensor imaging data from 33 children (9-10 years) were collected. Children were administered standardized test measures of mathematics abilities, reading, IQ; further measures on visuospatial STM and WM, number sense and inhibition function have been collected. At the behavioral level, mathematical performance has a positive correlation with visuospatial STM and WM and does not correlate with number sense measures. Preliminary results at the grey matter level in the right hemisphere show that mathematical performance and visuospatial WM scores correlate negatively with grey matter volume of the IPS. No correlation is observed between IPS volume and number sense measures. These results reveal new insights about poor mathematical abilities related to the impairment of visuospatial STM and WM rather than magnitude representation (number sense). References Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124, 1701–1707. Piazza M., Facoetti A., Trussardi A.N., Berteletti I., Conte S., Lucangeli D., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33-41. Szucs D., Devine A., Soltesz F., Nobes A., Gabriel F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 2674-88. Szűcs D., Devine A., Soltesz F., Nobes A., Gabriel F. (2014., Cognitive components of a mathematical processing network in 9-year-old children. Developmental Science, 17, 506-524 Keywords: number cognition, Visual working and short-term memory, Intraparietal sulcus (IPS), DTI, Developmental cognitive neurosceince Conference: 13th National Congress of the Belgian Society for Neuroscience , Brussels, Belgium, 24 May - 24 May, 2019. Presentation Type: Poster presentation Topic: Behavioral/Systems Neuroscience Citation: CRISTOFORETTI G, Verhelst H, Fias W and Szucs D (2019). Mathematical abilities in development and neuroanatomical correlates. Front. Neurosci. Conference Abstract: 13th National Congress of the Belgian Society for Neuroscience . doi: 10.3389/conf.fnins.2019.96.00040 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 24 Apr 2019; Published Online: 27 Sep 2019. * Correspondence: Mrs. GIULIA CRISTOFORETTI, Department of Experimental Psychology, Ghent University, Ghent, East Flanders, 9000, Belgium, giulia.cristoforetti@ugent.be Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers GIULIA CRISTOFORETTI Helena Verhelst Wim Fias Denes Szucs Google GIULIA CRISTOFORETTI Helena Verhelst Wim Fias Denes Szucs Google Scholar GIULIA CRISTOFORETTI Helena Verhelst Wim Fias Denes Szucs PubMed GIULIA CRISTOFORETTI Helena Verhelst Wim Fias Denes Szucs Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

The idea that human cognition is, or can be understood as, a form of computation is a useful conceptual tool for cognitive science. It was a foundational assumption during the birth of cognitive science as a multidisciplinary field, with Artificial Intelligence (AI) as one of its contributing fields. One conception of AI in this context is as a provider of computational tools (frameworks, concepts, formalisms, models, proofs, simulations, etc.) that support theory building in cognitive science. The contemporary field of AI, however, has taken the theoretical possibility of explaining human cognition as a form of computation to imply the practical feasibility of realising human(-like or -level) cognition in factual computational systems, and the field frames this realisation as a short-term inevitability. Yet, as we formally prove herein, creating systems with human(-like or -level) cognition is intrinsically computationally intractable. This means that any factual AI systems created in the short-run are at best decoys. When we think these systems capture something deep about ourselves and our thinking, we induce distorted and impoverished images of ourselves and our cognition. In other words, AI in current practice is deteriorating our theoretical understanding of cognition rather than advancing and enhancing it. The situation could be remediated by releasing the grip of the currently dominant view on AI and by returning to the idea of AI as a theoretical tool for cognitive science. In reclaiming this older idea of AI, however, it is important not to repeat conceptual mistakes of the past (and present) that brought us to where we are today.

During the summer of 2008 in Washington, DC, the Cognitive Science Society celebratedthe 30th anniversary of its seminal 1979 conference in San Diego. The 2008 conferenceorganizers—Bradley Love, Ken McRae, and Vladimir Sloutsky—commissioned a sympo-sium to celebrate the occasion. In discussing possibilities, we agreed that the symposiumshould not simply address the Society’s origins and subsequent history, but that it shouldfocus on contributions from the disciplines and theoretical perspectives central to CognitiveScience, along with their future directions.We originally settled on five disciplines and five theoretical perspectives, and then weinvited 10 active established researchers to address them at the conference. To accommo-date these 10 speakers, two symposia were presented, one on disciplines and one onperspectives. Each speaker was asked to address: (a) What was your discipline⁄perspectivelike at the time of the 1979 conference? (b) How has the discipline⁄perspective changedover the past 30 years to what it is today? (c) How do you foresee the discipline⁄perspectivechanging in the next 30 years?Because of time constraints, we could not include all disciplines and perspectives centralto Cognitive Science. Fortunately, however, we were able to remedy this limitation byasking additional researchers to contribute articles here. The resulting collection of articlescovers disciplines and perspectives that have been central to Cognitive Science for the past30 years and that are likely to be central for the next 30 years and beyond. Specifically, thedisciplines (and the authors addressing them) include the following:Psychology (Dedre Gentner)Artificial Intelligence (Kenneth D. Forbus)Philosophy (William Bechtel)Linguistics (Elissa L. Newport)

Mathematical language and mathematical abilities in preschool: A systematic literature review

The development of mathematical skills in early childhood relies on number sense, the foundational ability to discriminate among quantities. Number sense in early childhood is predictive of academic and professional success, and deficits in number sense are thought to underlie lifelong impairments in mathematical abilities. Despite its importance, the brain circuit mechanisms that support number sense learning remain poorly understood. Here, we designed a theoretically motivated training program to determine brain circuit mechanisms underlying foundational number sense learning in female and male elementary school-age children (7-10 years). Our 4 week integrative number sense training program gradually strengthened the understanding of the relations between symbolic (Arabic numerals) and nonsymbolic (sets of items) representations of quantity. We found that our number sense training program improved symbolic quantity discrimination ability in children across a wide range of math abilities including children with learning difficulties. Crucially, the strength of pretraining functional connectivity between the hippocampus and intraparietal sulcus, brain regions implicated in associative learning and quantity discrimination, respectively, predicted individual differences in number sense learning across typically developing children and children with learning difficulties. Reverse meta-analysis of interregional coactivations across 14,371 fMRI studies and 89 cognitive functions confirmed a reliable role for hippocampal-intraparietal sulcus circuits in learning. Our study identifies a canonical hippocampal-parietal circuit for learning that plays a foundational role in children's cognitive skill acquisition. Findings provide important insights into neurobiological circuit markers of individual differences in children's learning and delineate a robust target for effective cognitive interventions.SIGNIFICANCE STATEMENT Mathematical skill development relies on number sense, the ability to discriminate among quantities. Here, we develop a theoretically motivated training program and investigate brain circuits that predict number sense learning in children during a period important for acquisition of foundational cognitive skills. Our integrated number sense training program was effective in children across a wide a range of math abilities, including children with learning difficulties. We identify hippocampal-parietal circuits that predict individual differences in learning gains. Our study identifies a brain circuit critical for the acquisition of foundational cognitive skills, which will be useful for developing effective interventions to remediate learning disabilities.

What makes humans cognitively unique—and why are they unique in these ways? These are interesting questions not just because we are humans, but also because we have an outsized influence on the planet as a whole. To answer them, this book begins by providing a clearer characterization of the nature of human cognitive uniqueness: it sets out and justifies an inventory of key features of distinctively human cognition. On this basis, the book assesses the major existing theories seeking to explain distinctively human thought from across the cognitive, social, and human sciences and argues that a new account is needed, one that bridges nativist and learning-based approaches. It then presents exactly such an account. At the heart of this account is a positive feedback loop that links evolved representations, forms of cultural learning, and technology. With the help of this feedback loop, key examples of uniquely human cognition can be explained: distinctively human mindreading, distinctively human moral cognition, and the distinctively human propensity for trade. The book concludes with an application of this interactionist theory of distinctively human cognition to various issues of contemporary importance: the relationship between distinctively human cognition and increasingly sophisticated artificial intelligence, the role of religion in human thought and action, and the relationship between extensive patent regimes and human innovation. In doing all this, the book takes a simultaneous methodological and explanatory approach: it shows how to best conduct the study of human cognitive uniqueness and actually engages in this study itself.

This study aims to investigate whether there is a relationship between mathematical ability and mathematical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the relationship between the two constructs, we will trace groups of students that differ across mathematical ability and investigate the relationships amongst these students’ performance on a mathematical ability test and the components of mathematical creativity. Data were collected by administering two tests, a mathematical ability and a mathematical creativity test, to 359 elementary school students. Mathematical ability was considered as a multidimensional construct, including quantitative ability (number sense and pre-algebraic reasoning), causal ability (examination of cause–effect relations), spatial ability (paper folding, perspective and spatial rotation abilities), qualitative ability (processing of similarity and difference relations) and inductive/deductive ability. Mathematical creativity was defined as a domain-specific characteristic, enabling individuals to be characterized by fluency, flexibility and originality in the domain of mathematics. The data analysis revealed that there is a positive correlation between mathematical creativity and mathematical ability. Moreover, confirmatory factor analysis suggested that mathematical creativity is a subcomponent of mathematical ability. Further, latent class analysis showed that three different categories of students can be identified varying in mathematical ability. These groups of students varying in mathematical ability also reflected three categories of students varying in mathematical creativity.

Number Sense and mathematics across development and cultures

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

In this study, it was investigated how domain-specific (number sense) and domain-general (working memory, creativity) factors explain the variance in mathematical abilities in primary school children. A total of 166 children aged 8 to 10 years old participated. Several tests to measure math ability, mathematical creativity, number sense, verbal and visual spatial working memory and creativity were administered. Data were analyzed with a series of correlation and regression analyses. Number sense, working memory and creativity were all found to be important predictors of academic and creative mathematical ability. Furthermore, groups with math learning disabilities (MLD) and mathematical giftedness (MG) were compared to a typically developing (TD) group. The results show that the MLD group scored lower on number line estimation and visual spatial working memory than the TD group, while the MG group differed from the TD group on visual spatial working memory and creativity. It is concluded that creativity plays a significant role in mathematics, above working memory and number sense.

Towards a Cognitive Science of the Human: Cross-Cultural Approaches and Their Urgency.

Backgroundhuman cognition is not static. Early human cognition is different from modern human cognition. In the cognitive process of modern people, the information received by the senses from the external world is encoded and translated, and then presented in the form of abstract causal logic through the logical analysis and empirical verification of scientific thinking. However, the cognitive model of early human beings depended on mythological language and metaphorical thinking. Therefore, our purpose in this work is to study the basic operation principle of this mythical metaphorical thinking and the psychological motivation of human beings to use this way of thinking, and to explore the relationship and significance between human scientific cognition and myth. Metaphorical cognition, and emotional behavior.Subjects and MethodsBased on Cassirer's mythological metaphorical thinking theory, this study analyzes the comparative texts of ancient and modern human mythological language, and obtains a similar understanding of digital cognition, orientation cognition, attribute cognition and language cognition. Knowledge information is followed by comparative research. In this way, we can confirm the principles followed by human beings and the psychological motivation to apply these principles in the cognitive model of metaphorical thinking relying on mythological language. In order to better study the basic principles of metaphorical thinking and the changes of emotional behavior in mythological language, this study uses the measurement tool and the interpersonal emotion regulation scale (ierq) compiled by Hofmann et al. (2016) to measure how individuals regulate their emotions through others.The scale includes 4 factors and 20 items in total. Five point meter, The higher the score, the greater the degree of using interpersonal style to regulate emotion High. In this study, the results of confirmatory factor analysis are as follows: χ 2 / DF = 7.921, RMSEA = 0.077, CFI = 0.904, TLI = 0.889, indicating that the scale has good structural validity in this study. Internal one Consistence α The coefficient is 0.94, which is the sum of the above four factors α The coefficients are 0.84, 0.77, 0.84 and 0.82 respectively. At the same time, the implicit positive emotion subscale is adopted. The scale adopts the implicit positive emotion subscale compiled by Quirin et al. (2009) and revised by Dong Shanchuan (2016). The scale adopts 4-point scoring to evaluate the correlation between 6 meaningless synthetic words and 3 positive emotion words. The higher the total score, the higher the implicit positive emotion and the internal consistency α The coefficient is 0.93.Resultshumans who rely on mythological language and metaphorical thinking show a specific cognitive model. Mythology and early language reveal human cognition of themselves and the external world in an intuitive and concrete way. Modern languages are usually more abstract and logical. However, the comparison between scientific cognitive group and mythological metaphorical cognitive group reflects the principle of “replacing the whole with the part”. On the other hand, the psychological motivation of human beings to use this way of thinking is to replace all unfamiliar and difficult to understand abstract things with concrete real things. The results showed that there was a significant positive correlation between psychological expectation and emotion regulation ability (P < 0.01). Tested by multiple linear regression, interpersonal emotion regulation, regulation difficulty and their interaction items significantly predicted implicit positive emotion. Simple slope analysis showed that when the level of regulation difficulty was low (m-1sd), interpersonal emotion regulation significantly positively predicted implicit positive emotion, β= 0.33，t=12.54，p＜0.001; When the adjustment difficulty level is high (M + 1sd), the prediction coefficient is β= 0.26，t=8.93，p＜0.001. This shows that the predictive power of interpersonal emotion regulation on implicit positive emotion is significantly enhanced with the decrease of regulation difficulty level.Conclusionthe principle of “part rather than whole“ is the basic principle of mythological language and metaphorical thinking. It is rooted in and reflects the basic characteristics of primitive thinking, and runs through the early forms of human understanding of the world, such as myth, early language, primitive art and so on. Metaphorical thinking is an intuitive and concrete way of thinking and cognition. The psychological motivation for humans to use this way of thinking may be that they cannot understand abstract things. Therefore, they must replace these inexplicable abstract things with concrete real things. Therefore, the psychological activity process of early humans seems to be different from that of modern humans. Among them, direct Feiling is stronger than logical abstraction, and emotion is stronger than rational thinking. At the same time, in this study, we find that these principles and motives still exist in modern human cognition.