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Roi Cohen Kadosh - One of the best experts on this subject based on the ideXlab platform.
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the neurocognitive bases of Numerical Cognition
2018Co-Authors: Francesco Sella, Charlotte Hartwright, Roi Cohen KadoshAbstract:Numerical Cognition describes the processes that one uses to assimilate, ascribe, and manipulate Numerical information. This chapter is organized into two sections. The first draws heavily on data from developmental and cognitive psychology. We use this to outline core findings related to Numerical‐information processing in humans. In particular, we describe the trajectory of the acquisition of basic Numerical skills. Starting in early infancy, we outline the processes that are believed to underlie nonsymbolic representation. Next, we summarize core studies that examine the representation of symbolic quantities (Arabic system). Lastly, we briefly report on the relationship between basic Numerical processing and mathematical achievement. The second part of the chapter explores evidence from neuropsychology and neuroscience. The core methodological approaches used are briefly outlined with signposting to relevant literature. Next, we examine data from early lesion studies, followed by a short review of one of the most influential models in the study of Numerical Cognition, the triple‐code model. Lastly, we look at the neurocognitive features of number, such as different modes of representation and the processing of quantity. Throughout, the core literature plus recent advances are summarized, giving the reader a thorough grounding in the neurocognitive bases of Numerical Cognition.
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transcranial electrical stimulation and Numerical Cognition
Canadian Journal of Experimental Psychology, 2016Co-Authors: Amar Sarkar, Roi Cohen KadoshAbstract:Processing, representing, and manipulating numbers and quantities is one of the most advanced cognitive abilities humans possess. This ability is becoming increasingly important with the rising dependence of society on technology, and rising educational and occupational focus on quantitative aptitude. Moreover, deficits in Numerical Cognition may impair both individual and societal achievement (Beddington et al., 2008; Duncan et al., 2007; Parsons & Bynner, 2005).Recently, there has been increasing academic and public attention on the applications of transcranial electrical stimulation (tES) for cognitive enhancement. Improvements have been observed in a range of psychological variables in healthy populations, including high-level Cognition such as visual short term memory (Tseng et al., 2012), working memory (Fregni et al., 2005; Richmond et al., 2014), planning (Dockery et al., 2009), language learning (Floel et al., 2008; Meinzer et al., 2014), analogical reasoning (Santarnecchi et al., 2013), and Numerical Cognition. The application of tES to Numerical Cognition is the focus of this review.Research on the use of tES for cognitive enhancement is very new, and within this emerging field, tES for enhancing Numerical Cognition is itself a nascent field of enquiry. The use of tES is both of scientific importance in understanding Numerical Cognition, and also of immense practical importance in the enhancement of typical and atypical Numerical Cognition. There are as yet no reviews on the use of tES for enhancing Numerical Cognition, though there are several on tES and general cognitive enhancement (e.g., Cohen Kadosh, 2013, in press; Jacobson, Koslowsky, & Lavidor, 2012; Krause & Cohen Kadosh, 2013; Kuo & Nitsche, 2012). An area of particular interest is the combination of tES and cognitive training, which seems to produce long-lived effects that are apparent even up to 6 months after the last stimulation session (e.g., Cappelletti et al., 2013; Cohen Kadosh et al., 2010; Looi et al., 2015; Reis et al., 2009; Snowball et al., 2013). Cognitive training leads to particular neuroanatomical and neurophysiological changes (Boyke et al., 2008; Draganski et al., 2004; Klingberg, 2010; Slagter et al., 2007). tES is combined with training to facilitate these neural changes, acting as an ingredient to sensitize the neural environment to the effects of training, thereby facilitating the acquisition of the practice effects to a greater degree than training by itself (Cohen Kadosh et al., 2012).This article attempts to bring together several important findings in this (small) body of research to provide a general picture of this emerging field. The material is divided into three sections: (a) A short overview of two relevant forms of tES; (b) the application of tES in the enhancement of three aspects of Numerical Cognition: numerosity, magnitude processing, and arithmetic operations; and (c) an agenda for future research.Principles of tESThe technology is portable, painless, easy to use, and safe when appropriate screening procedures are conducted (e.g., excluding participants with a personal or family history of epilepsy). The impact of the stimulation on neuronal activity depends on the shape of the current, and in this regard, there are several forms of tES that produce different effects based on the nature of the current. All the forms of tES can be accompanied by appropriate placebo conditions, in which the current is simply turned off after a brief period (e.g., 30 s), which serves as an effective placebo by generating physical sensations indistinguishable from real stimulation (Gandiga, Hummel, & Cohen, 2006), but no neural changes (Fritsch et al., 2010).Two forms of tES have been used in Numerical Cognition research, transcranial direction current stimulation (tDCS), and transcranial random noise stimulation (tRNS), and some of their features are described below.tDCSThis is the most well-known and most frequently used form of tES. …
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transcranial electrical stimulation and the enhancement of Numerical Cognition
Development of Mathematical Cognition#R##N#Volume 2: Neural Substrates and Genetic Influences, 2016Co-Authors: Amar Sarkar, Roi Cohen KadoshAbstract:Transcranial electrical stimulation (tES) is being employed as a tool for cognitive enhancement in an increasing number of research studies. Its effects have been noted in a range of psychological functions, including Numerical Cognition and learning. This chapter first presents the historical background, technical principles, and limitations that contextualize modern tES experiments, and then considers how this technology has been applied in the enhancement of Numerical Cognition. The populations considered here include individuals with normal Numerical abilities, such as judging numerosity, perceiving and comparing magnitudes, and carrying out more advanced arithmetic operations, as well as individuals with serious difficulties in working with numbers, as seen in mathematics anxiety and developmental dyscalculia. The chapter concludes with a consideration of important directions that research may take in the future. The emphasis throughout is the need to test the ecological validity of tES-induced cognitive benefits, which is particularly important in the context of an ever-increasing number of positive reports, both in the media and in academia. However, enhancements in healthy individuals have been restricted entirely to controlled laboratory settings. The essential bridge between using tES to enhance Numerical Cognition in the laboratory and the enhancement of mathematical achievement in educational or occupational settings has yet to be built. As this chapter illustrates, the steady accumulation of evidence is providing firmer ground to begin explorations of the ecological validity of tES interventions.
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oxford handbook of Numerical Cognition
2015Co-Authors: Roi Cohen Kadosh, Ann DowkerAbstract:SECTION I: INTRODUCTION SECTION II: HUMAN Cognition SECTION III: PHYLOGENY AND ONTOGENY OF MATHEMATICAL AND Numerical UNDERSTANDING SECTION IV: CULTURE AND LANGUAGE SECTION V: NEUROSCIENCE OF MATHEMATICS SECTION VI: Numerical IMPAIRMENTS, CO-MORBIDITY, AND REHABILITATION SECTION VII: INDIVIDUAL DIFFERENCES SECTION VIII: EDUCATION
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Numerical Cognition reading numbers from the brain
Current Biology, 2009Co-Authors: Roi Cohen Kadosh, Vincent WalshAbstract:How the human brain encodes numbers is revealed by a new analysis of patterns of brain activity. The findings address the nature of Numerical representations and homology between humans and non-human primates.
Daniel Ansari - One of the best experts on this subject based on the ideXlab platform.
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integrating Numerical Cognition research and mathematics education to strengthen the teaching and learning of early number
British Journal of Educational Psychology, 2021Co-Authors: Rebecca Merkley, Zachary Hawes, Christine L Stager, Daniel AnsariAbstract:Background Research into Numerical Cognition has contributed to a large body of knowledge on how children learn and perform mathematics. This knowledge has the potential to inform mathematics education. Unfortunately, Numerical Cognition research and mathematics education remain disconnected from one another, lacking the proper infrastructure to allow for productive and meaningful exchange between disciplines. The present study was designed to address this gap. Aim This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for Kindergarten to Grade 3 educators and their students. A central goal of the PD was to better integrate Numerical Cognition research and mathematics education. Sample A total of 45 K-3 educators and 180 of their students participated. Methods To test the reproducibility and replicability of the model, the study was carried out across two different sites, over a two-year period, and involved a combination of two different study designs: a quasi-experimental pre-post-research design and a within-group crossover intervention design. Result The results of the first implementation (Year 1), indicated that compared to a control group, both teachers and students benefited from the intervention. Teachers demonstrated gains on both a self-report measure and a test of Numerical Cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on the self-report measure, but not the test of Numerical Cognition knowledge. At the student level, there was some evidence of gains in numeration. Conclusion The current PD model is a promising approach to better integrate research and practice. However, more research is needed to determine in which school contexts the model is most effective.
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contributions of functional magnetic resonance imaging fmri to the study of Numerical Cognition
Journal of Numerical Cognition, 2018Co-Authors: Anna A Matejko, Daniel AnsariAbstract:Using neuroimaging as a lens through which to understand Numerical and mathematical Cognition has provided both a different and complementary level of analysis to the broader behavioural literature. In particular, functional magnetic resonance imaging (fMRI) has contributed to our understanding of Numerical and mathematical processing by testing and expanding existing psychological theories, creating novel hypotheses, and providing converging evidence with behavioural findings. There now exist several examples where fMRI has provided unique insights into the cognitive underpinnings of basic number processing, arithmetic, and higher-level mathematics. In this review, we discuss how fMRI has contributed to five critical questions in the field including: 1) the relationship between symbolic and nonsymbolic processing; 2) whether arithmetic skills are rooted in an understanding of basic Numerical concepts; 3) the role of arithmetic strategies in the development of arithmetic skills; 4) whether basic Numerical concepts scaffold higher-level mathematical skills; and 5) the neurobiological origins of developmental dyscalculia. In each of these areas, we review how the fMRI literature has both complemented and pushed the boundaries of our knowledge on these central theoretical issues. Finally, we discuss limitations of current approaches and future directions that will hopefully lead to even greater contributions of neuroimaging to our understanding of Numerical Cognition.
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beyond magnitude judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic
Cognition, 2016Co-Authors: Celia Goffin, Daniel AnsariAbstract:In the field of Numerical Cognition, ordinality, or the sequence of numerals, has received much less attention than cardinality, or the number of items in a set. Therefore it is unclear whether the Numerical effects generated from ordinality and cardinality tasks are associated, and whether they relate to math achievement and more domain-general variables in similar ways. To address these questions, sixty adults completed ordinality, cardinality, visual-spatial working memory, inhibitory control and math achievement tasks. The Numerical distance effect from the cardinality task and the reverse distance effect from the ordinality task were both relatively reliable but not statistically significantly associated with one another. Additionally, both distance effects predicted independent unique variance in math scores, even when visual-spatial working memory and inhibitory control were included in the regression model. These findings provide support for dissociation in the mechanisms underlying cardinal and ordinal processing of number symbols and thereby highlight the critical role played by ordinality in symbolic Numerical Cognition.
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the symbol grounding problem in Numerical Cognition a review of theory evidence and outstanding questions
Canadian Journal of Experimental Psychology, 2016Co-Authors: Tali Leibovich, Daniel AnsariAbstract:How do Numerical symbols, such as number words, acquire semantic meaning? This question, also referred to as the "symbol-grounding problem," is a central problem in the field of Numerical Cognition. Present theories suggest that symbols acquire their meaning by being mapped onto an approximate system for the nonsymbolic representation of number (Approximate Number System or ANS). In the present literature review, we first asked to which extent current behavioural and neuroimaging data support this theory, and second, to which extent the ANS, upon which symbolic numbers are assumed to be grounded, is Numerical in nature. We conclude that (a) current evidence that has examined the association between the ANS and number symbols does not support the notion that number symbols are grounded in the ANS and (b) given the strong correlation between numerosity and continuous variables in nonsymbolic number processing tasks, it is next to impossible to measure the pure association between symbolic and nonsymbolic numerosity. Instead, it is clear that significant cognitive control resources are required to disambiguate Numerical from continuous variables during nonsymbolic number processing. Thus, if there exists any mapping between the ANS and symbolic number, then this process of association must be mediated by cognitive control. Taken together, we suggest that studying the role of both cognitive control and continuous variables in numerosity comparison tasks will provide a more complete picture of the symbol-grounding problem.
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neurocognitive approaches to developmental disorders of Numerical and mathematical Cognition the perils of neglecting the role of development
Learning and Individual Differences, 2010Co-Authors: Daniel AnsariAbstract:Abstract The present paper provides a critical overview of how adult neuropsychological models have been applied to the study of the atypical development of Numerical Cognition. Specifically, the following three assumptions are challenged: 1. Profiles of strength and weaknesses do not change over developmental time. 2. Similar neuronal structures are activated in children and adults, as well as the notion that 3. Similarities in behavioral performance imply equivalence in underlying neurocognitive mechanisms. Data from behavioral and neuroimaging studies with both typically and atypically developing children is reviewed to illustrate the pitfalls of these assumptions. The present review proposes that, instead of resting on adult neuropsychological models, the use of both cross-sectional and longitudinal methods is required to elucidate the age-related changes in brain and behavior that give rise to the breakdown of numeracy and mathematics. Empirical data derived from such studies will generate explanatory models of the development of atypical Numerical Cognition.
François Osiurak - One of the best experts on this subject based on the ideXlab platform.
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Numerical Cognition: A meta-analysis of neuroimaging, transcranial magnetic stimulation and brain-damaged patients studies
Neuroimage-Clinical, 2019Co-Authors: Alexandrine Faye, Sophie Jacquin-courtois, Emanuelle Reynaud, Mathieu Lesourd, Jérémy Besnard, François OsiurakAbstract:This article offers the first comprehensive review examining the neurocognitive bases of Numerical Cognition from neuroimaging, Transcranial Magnetic Stimulation (TMS) and brain-damaged patients studies. We focused on the predictions derived from the Triple Code Model (TCM), particularly the assumption that the re- presentation of Numerical quantities rests on a single format-independent representation (i.e., the analogical code) involving both intraparietal sulci (IPS). To do so, we conducted a meta-analysis based on 28 neuroimaging, 12 TMS and 12 brain-damaged patients studies, including arithmetic and magnitude tasks in symbolic and non- symbolic formats. Our findings generally agree with the TCM predictions indicating that both IPS are engaged in all tasks. Nonetheless, the results of brain-damaged patients studies conflicted with neuroimaging and TMS studies, suggesting a right hemisphere lateralization for non-symbolic formats. Our findings also led us to discuss the involvement of brain regions other than IPS in the processing of the analogical code as well as the neural substrate of other codes underlying Numerical Cognition (i.e., the auditory-verbal code).
Alexandrine Faye - One of the best experts on this subject based on the ideXlab platform.
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Numerical Cognition: A meta-analysis of neuroimaging, transcranial magnetic stimulation and brain-damaged patients studies
Neuroimage-Clinical, 2019Co-Authors: Alexandrine Faye, Sophie Jacquin-courtois, Emanuelle Reynaud, Mathieu Lesourd, Jérémy Besnard, François OsiurakAbstract:This article offers the first comprehensive review examining the neurocognitive bases of Numerical Cognition from neuroimaging, Transcranial Magnetic Stimulation (TMS) and brain-damaged patients studies. We focused on the predictions derived from the Triple Code Model (TCM), particularly the assumption that the re- presentation of Numerical quantities rests on a single format-independent representation (i.e., the analogical code) involving both intraparietal sulci (IPS). To do so, we conducted a meta-analysis based on 28 neuroimaging, 12 TMS and 12 brain-damaged patients studies, including arithmetic and magnitude tasks in symbolic and non- symbolic formats. Our findings generally agree with the TCM predictions indicating that both IPS are engaged in all tasks. Nonetheless, the results of brain-damaged patients studies conflicted with neuroimaging and TMS studies, suggesting a right hemisphere lateralization for non-symbolic formats. Our findings also led us to discuss the involvement of brain regions other than IPS in the processing of the analogical code as well as the neural substrate of other codes underlying Numerical Cognition (i.e., the auditory-verbal code).
Hans-christoph Nuerk - One of the best experts on this subject based on the ideXlab platform.
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on the limits of language influences on Numerical Cognition no inversion effects in three digit number magnitude processing in adults
Frontiers in Psychology, 2015Co-Authors: Julia Bahnmueller, K. Orbinian Moeller, Anne Mann, Hans-christoph NuerkAbstract:The inversion of number words influences Numerical Cognition even in seemingly non-verbal tasks, such as Arabic number comparison. However, it is an open question whether inversion of decades and units also influences number processing beyond the two-digit number range. The current study addresses this question by investigating compatibility effects in both German- (a language with inverted) and English-speaking (a language with non-inverted number words) university students (mean age 22 years) in a three-digit number comparison task. We observed reliable hundred-decade as well as hundred-unit compatibility effects for three-digit number comparison. This indicates that, comparable two-digit numbers, three-digit numbers are processed in a parallel decomposed fashion. However, in contrast to previous results on two-digit numbers as well as on children’s processing of three-digit numbers, no reliable modulation of these compatibility effects through language was observed in adults. The present data indicate that inversion-related differences in multi-digit number processing are limited. They seem to be restricted to the number range involving those digits being inverted (i.e., tens and units in two-digit numbers) but do not generalize to neighboring digits. Possible reasons for this lack of generalization are discussed.
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Considering structural connectivity in the triple code model of Numerical Cognition: differential connectivity for magnitude processing and arithmetic facts.
Brain structure & function, 2014Co-Authors: Elise Klein, K. Orbinian Moeller, Julia Suchan, Hans-otto Karnath, André Knops, Guilherme Wood, Hans-christoph Nuerk, Klaus WillmesAbstract:The current study provides a generalizable account of the anatomo-functional associations as well as the connectivity of representational codes underlying Numerical processing as suggested by the triple code model (TCM) of Numerical Cognition. By evaluating the neural networks subserving Numerical Cognition in two specific and substantially different Numerical tasks with regard to both grey matter localizations as well as white matter tracts we (1) considered the possibility of additional memory-related cortex areas crucial for arithmetic fact retrieval (e.g., the hippocampus); (2) specified the functional involvement of prefrontal areas in number magnitude processing, and, finally; (3) identified the connections between these anatomo-functional instantiations of the representations involved in number magnitude processing and arithmetic fact retrieval employing probabilistic fiber tracking. The resulting amendments to the TCM are summarized in a schematic update, and ideas concerning the possible functional interplay between number magnitude processing and arithmetic fact retrieval are discussed.
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nirs in motion unraveling the neurocognitive underpinnings of embodied Numerical Cognition
Frontiers in Psychology, 2014Co-Authors: Hans-christoph Nuerk, Julia Bahnmueller, Thomas Dresler, Annchristine Ehlis, Ulrike CressAbstract:The central representation of numeri- cal Cognition is commonly considered an abstract magnitude representation serving as one key precursor for higher mathe- matical thinking. However, recent research indicates that the representation might not be purely abstract. In fact, accumulating evidence suggests that Numerical represen- tations are rooted in and shaped by spe- cific motor activities and sensory-bodily experiences and, therefore, are influenced by so-called embodied Numerical repre- sentations. If we want to understand how Numerical understanding develops, it is crucial to elucidate the basic cognitive tools with which we develop a sense of number. We argue that it is necessary to address this issue on both a behavioral and an eural level. Contrasting the view of functional magnetic resonance imaging (fMRI) being the generally preferable neuroimaging technique, we argue that particularly in embodied Cognition, restrictions and ben- efits of different imaging methods should guide the chosen research question. In our opinion, near-infrared spectroscopy (NIRS) is optimally suited to investi- gate embodied Cognition paradigms that explicitly involve motion. In the follow- ing, recent research will be outlined show- ing that Numerical Cognition is not purely abstract, but influenced by embodied rep- resentations. NIRS will then be introduced as a feasible technique for the investigation of embodied Cognitions. Since research in this domain is largely restricted to the perception of embodied experiences, but fails to address motion itself, we willfinally argue that NIRS offers a good opportunity to fill this research gap.
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influences of cognitive control on Numerical Cognition adaptation by binding for implicit learning
Topics in Cognitive Science, 2013Co-Authors: K. Orbinian Moeller, Elise Klein, Hans-christoph NuerkAbstract:Recently, an associative learning account of cognitive control has been suggested (Verguts & Notebaert, 2009). In this so-called adaptation by binding theory, Hebbian learning of stimulus-stimulus and stimulus-response associations is assumed to drive the adaptation of human behavior. In this study, we evaluated the validity of the adaptation-by-binding account for the case of implicit learning of regularities within a stimulus set (i.e., the frequency of specific unit digit combinations in a two-digit number magnitude comparison task) and their association with a particular response. Our data indicated that participants indeed learned these regularities and adapted their behavior accordingly. In particular, influences of cognitive control were even able to override the Numerical distance effect--one of the most robust effects in Numerical Cognition research. Thus, the general cognitive processes involved in two-digit number magnitude comparison seem much more complex than previously assumed. Multi-digit number magnitude comparison may not be automatic and inflexible but influenced by processes of cognitive control being highly adaptive to stimulus set properties and task demands on multiple levels.
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one language two number word systems and many problems Numerical Cognition in the czech language
Research in Developmental Disabilities, 2011Co-Authors: Silvia Pixner, K. Orbinian Moeller, Hans-christoph Nuerk, Liane Kaufmann, Julia Zuber, V HeřmanovaAbstract:Comparing Numerical performance between different languages does not only mean comparing different number-word systems, but also implies a comparison of differences regarding culture or educational systems. The Czech language provides the remarkable opportunity to disentangle this confound as there exist two different number-word systems within the same language: for instance, "25" can be either coded in non-inverted order "dvadsetpat" [twenty-five] or in inverted order "patadvadset" [five-and-twenty]. To investigate the influence of the number-word system on basic Numerical processing within one culture, 7-year-old Czech-speaking children had to perform a transcoding task (i.e., writing Arabic numbers to dictation) in both number-word systems. The observed error pattern clearly indicated that the structure of the number-word system determined transcoding performance reliably: In the inverted number-word system about half of all errors were inversion-related. In contrast, hardly any inversion-related errors occurred in the non-inverted number-word system. We conclude that the development of Numerical Cognition does not only depend on cultural or educational differences, but is indeed related to the structure and transparency of a given number-word system.
