Number Processing Abilities Research Articles

Typical Mathematical Education Cannot Predict Non‐Verbal Number Sense

ABSTRACTFormal education would promote symbolic number processing ability, but the relationship between non‐symbolic number sense and mathematical education remains controversial. The current investigation hypothesized that non‐symbolic number sense is independent from the limited human experience of mathematical education, while symbolic number processing could be influenced by related closely to mathematical education. Experiment 1 compared both non‐symbolic number sense and arithmetic computation of undergraduates majoring in STEM fields and humanities. Experiment 2 compared homologous undergraduates from China and Kyrgyzstan in non‐symbolic number sense and mathematical cognitive processing. Both of two experiments found that mathematical education was significantly associated with symbolic mathematics, but not with non‐symbolic number sense. The results suggest that while mathematical education might improve symbolic mathematics, it does not alter non‐symbolic number sense.

Mathematics anxiety and number processing: The link between executive functions, cardinality, and ordinality.

One important factor that hampers children's learning of mathematics is math anxiety (MA). Still, the mechanisms by which MA affects performance remain debated. The current study investigated the relationship between MA, basic number processing abilities (i.e., cardinality and ordinality processing), and executive functions in school children enrolled in grades 4-7 (N = 127). Children were divided into a high math anxiety group (N = 29) and a low math anxiety group (N = 31) based on the lowest quartile and the highest quartile. Using a series of analyses of variances, we find that highly math-anxious students do not perform worse on cardinality processing tasks (i.e., digit comparison and non-symbolic number sense), but that they perform worse on numerical and non-numerical ordinality processing tasks. We demonstrate that children with high MA show poorer performance on a specific aspect of executive functions-shifting ability. Our models indicate that shifting ability is tied to performance on both the numerical and non-numerical ordinality processing tasks. A central factor seems to be the involvement of executive processes during ordinality judgements, and executive functions may constitute the driving force behind these delays in numerical competence in math-anxious children.

The role of basic number processing in high mathematics achievement in primary school

While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high achievement in mathematics (above the 90th percentile) and 32 average-achieving peers (between the 25th and 75th percentile). Children completed measures of symbolic number processing (comparison and order). We additionally investigated the roles of spatial visualization and working memory. High mathematics achievers were faster and more accurate in order processing compared to average achievers, but no differences were found in magnitude comparison. High mathematics achievers demonstrated better spatial visualization ability, while group differences in working memory were less clear. Spatial visualization ability was the only significant predictor of group membership. Our results therefore highlight the role of high spatial visualization ability in high mathematics achievement.

Visual Occipito-Temporal N1 Sensitivity to Digits Across Elementary School.

Number processing abilities are important for academic and personal development. The course of initial specialization of ventral occipito-temporal cortex (vOTC) sensitivity to visual number processing is crucial for the acquisition of numeric and arithmetic skills. We examined the visual N1, the electrophysiological correlate of vOTC activation across five time points in kindergarten (T1, mean age 6.60 years), middle and end of first grade (T2, 7.38 years; T3, 7.68 years), second grade (T4, 8.28 years), and fifth grade (T5, 11.40 years). A combination of cross-sectional and longitudinal EEG data of a total of 62 children (35 female) at varying familial risk for dyslexia were available to form groups of 23, 22, 27, 27, and 42 participants for each of the five time points. The children performed a target detection task which included visual presentation of single digits (DIG), false fonts (FF), and letters (LET) to derive measures for coarse (DIG vs. FF) and fine (DIG vs. LET) digit sensitive processing across development. The N1 amplitude analyses indicated coarse and fine sensitivity characterized by a stronger N1 to digits than false fonts across all five time points, and stronger N1 to digits than letters at all but the second (T2) time point. In addition, lower arithmetic skills were associated with stronger coarse N1 digit sensitivity over the left hemisphere in second grade (T4), possibly reflecting allocation of more attentional resources or stronger reliance on the verbal system in children with poorer arithmetic skills. To summarize, our results show persistent visual N1 sensitivity to digits that is already present early on in pre-school and remains stable until fifth grade. This pattern of digit sensitivity development clearly differs from the relatively sharp rise and fall of the visual N1 sensitivity to words or letters between kindergarten and middle of elementary school and suggests unique developmental trajectories for visual processing of written characters that are relevant to numeracy and literacy.

Variations in psychological factors and experience-dependent changes in team-based video game performance

Success in many types of activities relies upon the performance of skilled individuals. Across formal and more informal environments, the amount of experience an individual has accumulated has been observed to predict skilled performance. Psychological traits have also been found to relate to the development of skilled performance. Questions remain regarding what factors influence the development of skilled performance within team-based activities. Factors including variations in psychological traits and how teammates are selected, in addition to the amount of accumulated experience, may differ in how strongly they influence changes in the skilled performance of individuals. In the present study, the degree to which psychological factors interacted with accumulated experience with regard to skilled performance was examined within a team-based activity. Personality, social, and cognitive measures were collected from players of a team-based online video game. Subsequently, their experience and performance playing video game matches where their teammates were selected by the players versus randomly assigned were assessed across a three-month period. Longitudinal models revealed that performance improved with the number of matches played, with the rate of improvement affected by how teammates were selected and individual differences in specific psychological measures, number processing ability, fluid intelligence, theory of mind ability, and neuroticism. These psychological factors and the method by which teammates were selected moderated the degree to which individuals improved their performance with experience. In line with previous research, these findings indicated that psychological factors, in addition to experience, contributed to the development of skilled performance within a team-based activity.

Mathematical abilities in development and neuroanatomical correlates

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.

Numerical and Non-numerical Predictors of First Graders' Number-Line Estimation Ability.

Children’s ability to map numbers into a spatial context has been shown to be a powerful predictor of math performance. Here, we investigate how three types of cognitive abilities – approximate number processing ability, symbolic number processing ability, and non-numerical cognitive abilities – predict 0–100 number-line estimation performance in first graders. While each type of measure predicts number-line performance when considered individually, when considered together, only symbolic number comparison and non-verbal reasoning predicted unique variance in number-line estimation. Moreover, the relation between symbolic number comparison and number-line ability was stronger for male students than for female students, suggesting potential gender differences in the way boys and girls accomplish mapping numbers into space. These results suggest that number-line estimation ability is largely reflective of the precision with which symbolic magnitudes are represented (at least among boys). Our findings therefore suggest that promoting children’s understanding of symbolic, rather than non-symbolic, numerical magnitudes may help children learn better from number-lines in the classroom.

A cognitive model for multidigit number reading: Inferences from individuals with selective impairments

We propose a detailed cognitive model of multi-digit number reading. The model postulates separate processes for visual analysis of the digit string and for oral production of the verbal number. Within visual analysis, separate sub-processes encode the digit identities and the digit order, and additional sub-processes encode the number's decimal structure: its length, the positions of 0, and the way it is parsed into triplets (e.g., 314987 → 314,987). Verbal production consists of a process that generates the verbal structure of the number, and another process that retrieves the phonological forms of each number word. The verbal number structure is first encoded in a tree-like structure, similarly to syntactic trees of sentences, and then linearized to a sequence of number-word specifiers. This model is based on an investigation of the number processing abilities of seven individuals with different selective deficits in number reading. We report participants with impairment in specific sub-processes of the visual analysis of digit strings – in encoding the digit order, in encoding the number length, or in parsing the digit string to triplets. Other participants were impaired in verbal production, making errors in the number structure (shifts of digits to another decimal position, e.g., 3,040 → 30,004). Their selective deficits yielded several dissociations: first, we found a double dissociation between visual analysis deficits and verbal production deficits. Second, several dissociations were found within visual analysis: a double dissociation between errors in digit order and errors in the number length; a dissociation between order/length errors and errors in parsing the digit string into triplets; and a dissociation between the processing of different digits – impaired order encoding of the digits 2–9, without errors in the 0 position. Third, within verbal production, a dissociation was found between digit shifts and substitutions of number words. A selective deficit in any of the processes described by the model would cause difficulties in number reading, which we propose to term “dysnumeria”.

Number processing ability is connected to longitudinal changes in multiplayer online battle arena skill

The popularity of multiplayer online battle arena (MOBA) games provides an opportunity to examine how cognitive skills are linked with changes in player performance within a team-based game genre. There is evidence that video game experience in other genres is connected with specific cognitive skills such as visuospatial attention and working memory capacity. Links have also been observed outside of video games such as numerical intelligence being correlated with the performance of chess experts. In the present study, we investigated whether numerical and working memory ability measured at an initial time-point predicted changes in MOBA skill and gameplay frequency measured five months later. We observed that participants who scored higher on a number processing task had greater improvements in MOBA skill and that this link depended on the social context of the gameplay. Specifically, numerical skill was linked to player rankings generated from matches where they were paired with random individuals; no connection was observed with gameplay that took place with a familiar set of teammates. The results of the present study extend previous research indicating video gameplay is linked to specific cognitive skills, in the case of MOBAs being numerical processing. We suggest that the difference in the connection with number ability to gameplay with novel and familiar players is in line with evidence that the importance of individual performance and the sense of achievement can be reduced in team settings. We suggest that future research should examine what types of quantitative abilities are indicative of MOBA skill and the impact of those factors relative to social skills.

Distinctive Role of Symbolic Number Sense in Mediating the Mathematical Abilities of Children with Autism.

Despite reports of mathematical talent in autism spectrum disorders (ASD), little is known about basic number processing abilities in affected children. We investigated number sense, the ability to rapidly assess quantity information, in 36 children with ASD and 61 typically developing controls. Numerical acuity was assessed using symbolic (Arabic numerals) as well as non-symbolic (dot array) formats. We found significant impairments in non-symbolic acuity in children with ASD, but symbolic acuity was intact. Symbolic acuity mediated the relationship between non-symbolic acuity and mathematical abilities only in children with ASD, indicating a distinctive role for symbolic number sense in the acquisition of mathematical proficiency in this group. Our findings suggest that symbolic systems may help children with ASD organize imprecise information.

The speed of magnitude processing and executive functions in controlled and automatic number comparison in children: an electro-encephalography study

BackgroundIn the numerical Stroop paradigm (NSP) participants decide whether a digit is numerically or physically larger than another simultaneously presented digit. This paradigm is frequently used to assess the automatic number processing abilities of children. Currently it is unclear whether an equally refined evaluation of numerical magnitude occurs in both controlled (the numerical comparison task of the NSP) and automatic (the physical comparison task of the NSP) numerical comparison in both children and adults. One of our objectives was to respond this question by measuring the speed of controlled and automatic magnitude processing in children and adults in the NSP. Another objective was to determine how the immature executive functions of children affect their cognitive functions relative to adults in numerical comparison.Methods and resultsThe speed of numerical comparison was determined by monitoring the electro-encephalographic (EEG) numerical distance effect: The amplitude of EEG measures is modulated as a function of numerical distance between the to-be-compared digits. EEG numerical distance effects occurred between 140–320 ms after stimulus presentation in both controlled and automatic numerical comparison in all age groups. Executive functions were assessed by analyzing facilitation and interference effects on the latency of the P3b event-related potential component and the lateralized readiness potential (LRP). Interference effects were more related to response than to stimulus processing in children as compared with adults. The LRP revealed that the difficulty to inhibit irrelevant response tendencies was a major factor behind interference in the numerical task in children.ConclusionThe timing of the EEG distance effect suggests that a refined evaluation of numerical magnitude happened at a similar speed in each age group during both controlled and automatic magnitude processing. The larger response interference in children than in adults suggests that despite the similar behavioural profile of children and adults, partially different cognitive processes underlie their performance in the NSP. Further, behavioural effects in the NSP depend on interactions between comparison, facilitation/interference and response-related processes. Our data suggest that caution is needed when using the NSP to compare behavioural markers of the numerical processing skills of children and adults.

Assessment of calculation and number processing using the EC301 battery: Cross-cultural normative data and application to left- and right-brain damaged patients

To provide referential normative data on simple tasks dealing with number processing and calculation which could be used in clinical investigations, 551 normal volunteers aged between 18 and 69 years from France and Belgium (n = 180). Italy (n = 212) and Germany (n = 159). performed the 31 tasks which constitute the EC301 calculation and number processing battery. Differences between countries were significant for 16 tasks and a Gender x Education interaction was observed for some tasks, with men performing better than women among subjects with low education only. To present an overview of preserved and impaired calculation and number processing abilities in left-brain damaged (LBD) aphasic patients and right-brain damaged (RBD) nonaphasic patients, the 31 subtests of the EC301 battery were proposed to 80 patients with cerebrovascular accident, 56 left and 24 right, for most cases in the territory of the middle cerebral artery. LBD aphasic patients showed low performance on oral and alphabetical spoken verbal and written verbal counting, transcoding when a written code was involved, and mental or written calculation; but relatively good performance at finding the number of elements in small sets, comparing numbers written in the Arabic digital code and placing correctly numbers on an analogue number line. The lowest performances of RBD patients were observed for estimation tasks and for placing a number on a scale. Results and their implications for further research are discussed according to the present information processing and anatomofunctional models of calculation and number processing.

Acalculia: Deficits of operational and quantity number knowledge

We describe the standardization of three new tests of knowledge of quantity facts, number operations and multiplication facts. We also report a validation study in which a group of 50 patients with cortical degenerative disorders were tested on these three new tests of number processing. Our results show that the quantity facts and number operations tests are sensitive measures of number processing abilities. Performance on the three new tests and the Graded Difficulty Arithmetic (GDA) test were found to be significantly impaired in the Alzheimer's Disease (AD) group. The frontotemporal dementia (FTD) group was subdivided into those with a semantic dementia (SD) and those with prominent frontal features (Non-SD). The semantic dementia subgroup was more impaired than both the AD patient group and the nonsemantic FTD subgroup on the quantity facts test. A more fine grained analysis reveals several interesting patterns of performance, including a dissociation between impaired performance on the quantity facts and number operations tests and preserved performance on the GDA. The findings attest the value of comparing performance on the GDA and our new tests in delineating the nature of an individual's number processing deficits. Implications for the relation between simple arithmetic fact knowledge and higher level number processing are discussed.

Assessment of Calculation and Number Processing by Adults: Cognitive and Neuropsychological Issues

Calculation and number processing abilities were assessed in normal (n = 138) and traumatic brain-injured (n = 15) Brazilian literature subjects. The study aimed (i) to analyse the effects of demographic factors and to provide tentative norms adjusted for the relevant variables, (ii) to examine the factorial structure of the battery and to evaluate its clinical validity for diagnosis purposes, and (iii) to question the power of current models to account for effects and dissociations found for these groups. Analysis indicated a main effect of education on most subtests and of sex on three, but none for age. Cut-off scores for normality were defined at Percentile 10 with reference to education. The sensitivity of the battery to the presence of arithmetical impairments was considered satisfactory since 11 out of the 15 patients showed pathological scores. A principal component analysis indicated that the different sub-tests were grouped into three factors, which were tentatively interpreted with reference to current information-processing models. The multiple single-case analysis of dissociations in patients' performance suggested some limits with respect to anatomo-functional models of calculation and number processing.

ASSESSMENT OF CALCULATION AND NUMBER PROCESSING BY ADULTS: COGNITIVE AND NEUROPSYCHOLOGICAL ISSUES

Calculation and number processing abilities were assessed in normal (n = 138) and traumatic brain-injured (n = 15) Brazilian literate subjects. The study aimed (i) to analyse the effects of demographic factors and to provide tentative norms adjusted for the relevant variables, (ii) to examine the factorial structure of the battery and to evaluate its clinical validity for diagnosis purposes, and (in) to question the power of current models to account for effects and dissociations found for these groups. Analysis indicated a main effect of education on most subtests and of sex on three, but none for age. Cut-off scores for normality were defined at Percentile 10 with reference to education. The sensitivity of the battery to the presence of arithmetical impairments was considered satisfactory since 11 out of the 15 patients showed pathological scores. A principal component analysis indicated that the different subtests were grouped into three factors, which were tentatively interpreted with reference to current information-processing models. The multiple single-case analysis of dissociations in patients' performance suggested some limits with respect to anatomo-functional models of calculation and number processing.

Calculation and number processing in mild Alzheimer's disease.

Calculation and number processing abilities in 17 patients suffering from a mild form of dementia of Alzheimer's type (DAT) were studied by means of a standardized multitask assessment battery, the EC301 (Deloche et al., 1994). Patients were selected from a larger sample by using a specific visuo-perceptive task to control the confounding effects of deficits in analysing digit serial order. Language and memory skills were evaluated by means of standardized testing procedures. The EC301 overall score showed impaired performance in 12 cases. Calculation and number processing scores were highly correlated with Mini-Mental State Examination and language performance. However, multiple single-case analyses indicated heterogeneous patterns of preserved/impaired abilities with respect to the three cognitive areas under investigation (calculation, memory, and language) and to the different components of the calculation and number processing system.

Number Processing in Pure Alexia: The Effect of Hemispheric Asymmetries and Task Demands

Abstract The relative sparing of arabic numerals, in patients who fail to read words or even letters, is a classical feature of pure alexia originally observed by Dejerine (Comptes Rendus des Seances de la Societé de Biologie 1892; 4: 61–90). We report a study of number processing abilities in two patients suffering from typical pure alexia. Our main finding was that number identification performance varied considerably with task demands. Both patients could name pairs of digits, when they were engaged in a simple naming task or for the purpose of magnitude comparison. In contrast, they frequently misidentified the very same digits when treating them as the components of multidigit numerals, or as the operands of addition problems. With two-digit numerals, a similar dissociation was shown between excellent comparison and severely impaired reading aloud. Finally, the variation of performance with task demands was shown not to prevail with spelled-out numerals. These findings confirm that some patients with pure alexia are able to process up to a semantic level symbolic stimuli that they cannot read aloud. We speculate that both hemispheres possess effective digit identification abilities, which are differentially called on depending on the task.

Number processing in pure alexia: The effect of hemispheric asymmetries and task demands

Abstract The relative sparing of arabic numerals, in patients who fail to read words or even letters, is a classical feature of pure alexia originally observed by Dejerine (Comptes Rendus des Seances de la Societe de Biologie 1892; 4: 61–90). We report a study of number processing abilities in two patients suffering from typical pure alexia. Our main finding was that number identification performance varied considerably with task demands. Both patients could name pairs of digits, when they were engaged in a simple naming task or for the purpose of magnitude comparison. In contrast, they frequently misidentified the very same digits when treating them as the components of multidigit numerals, or as the operands of addition problems. With two-digit numerals, a similar dissociation was shown between excellent comparison and severely impaired reading aloud. Finally, the variation of performance with task demands was shown not to prevail with spelled-out numerals. These findings confirm that some patients with...

Diagnostik von Störungen im Umgang mit Zahlen (Akalkulie)

Disturbances in numeric skills (acalculia) often occur in adults following CNS damage. We present an examination procedure which assesses number-processing abilities as well as basic skills in calculation. Results of an investigation based on a unselected sample of brain-damaged adults (N = 52) show that numeric skills can be impaired in a variety of different ways. With our acalculia examination procedure it is possible to distinguish secondary forms of acalculia, which can only occur in combination with other neuropsychological disturbances, and primary acalculia, which cannot be explained as resulting from accompanying disturbances.