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The neuropsychology of mathematical cognition.
Cognitive estimation is a mental ability applied to solve numerical problems when precise facts are unknown, unavailable or impractical to calculate. It has been associated with several underlying cognitive components, most often with executive functions and semantic memory. Little is known about the neural correlates of cognitive estimation. To address this issue, the present cross-sectional study applied lesion-symptom mapping in a group of 55 patients with left hemineglect due to right-hemisphere stroke. Previous evidence suggests a high prevalence of cognitive estimation impairment in these patients, as they might show a general bias towards large magnitudes. Compared to 55 age- and gender-matched healthy controls, the patient group demonstrated impaired cognitive estimation. However, the expected large magnitude bias was not found. Lesion-symptom mapping related their general estimation impairment predominantly to brain damage in the right anterior temporal lobe. Also critically involved were the right uncinate fasciculus, the anterior commissure, and the right inferior frontal gyrus. The main findings of the present study emphasise the role of semantic memory in cognitive estimation, with reference to a growing body of neuroscientific literature postulating a transmodal hub for semantic cognition situated in the bilateral anterior temporal lobe. That such semantic hub function may also apply to numerical knowledge is not undisputed. We here propose a critical contribution of the right anterior temporal lobe to at least one aspect of number processing, i.e. the knowledge about real-world numerical magnitudes.
Acalculia is an acquired disorder in calculation abilities, usually associated with left posterior parietal damage. Two types of acalculic disorders are usually distinguished: (1) primary acalculia or anarithmetia, where the patient presents a loss of numerical concepts (difficulties are observed both in oral and written calculations), and (2) secondary acalculia due to a different disturbance in cognition and affecting mathematical abilities. Secondary acalculias are associated with aphasia, alexia, agraphia, executive function disorders, or visuospatial difficulties. This paper is a proposal for clinical intervention to rehabilitation of acquired primary and secondary acalculias.
The role of the left hemisphere in calculation has been unequivocally demonstrated in numerous studies in the last decades. The right hemisphere, on the other hand, had been traditionally considered subsidiary to the left hemisphere functions, although its role was less clearly defined. Recent clinical studies as well as investigations conducted with other methodologies (e.g. neuroimaging, transcranial magnetic stimulation and direct cortical electro-stimulation) leave several unanswered questions about the contribution of the right hemisphere in calculation. In particular, novel clinical studies show that right hemisphere acalculia encompasses a wide variety of symptoms, affecting even simple calculation, which cannot be easily attributed to spatial disorders or to a generic difficulty effect as previously believed. The studies reported here also show how the right hemisphere has its own specific role and that only a bilateral orchestration between the respective functions of each hemisphere guarantees, in fact, precise calculation. Vis-à-vis these data, the traditional wisdom that attributes to the right hemisphere a role mostly confined to spatial aspects of calculation needs to be significantly reshaped. The question for the future is whether it is possible to precisely define the specific contribution of the right hemisphere in several aspects of calculation while highlighting the nature of the cross-talk between the two hemispheres.
This article is part of a discussion meeting issue ‘The origins of numerical abilities’.
Children use numbers every day and typically receive formal mathematical training from an early age, as it is a main subject in school curricula. Despite an increase in children neuroimaging studies, a comprehensive neuropsychological model of mathematical functions in children is lacking. Using quantitative meta-analyses of functional magnetic resonance imaging (fMRI) studies, we identify concordant brain areas across articles that adhere to a set of selection criteria (e.g., whole-brain analysis, coordinate reports) and report brain activity to tasks that involve processing symbolic and non-symbolic numbers with and without formal mathematical operations, which we called respectively number tasks and calculation tasks. We present data on children 14 years and younger, who solved these tasks. Results show activity in parietal (e.g., inferior parietal lobule and precuneus) and frontal (e.g., superior and medial frontal gyri) cortices, core areas related to mental-arithmetic, as well as brain regions such as the insula and claustrum, which are not typically discussed as part of mathematical problem solving models. We propose a topographical atlas of mathematical processes in children, discuss findings within a developmental constructivist theoretical model, and suggest practical methodological considerations for future studies.
Objectives:
Recent findings suggest that mental arithmetic involves shifting attention on a mental continuum in which numbers would be ordered from left to right, from small to large numbers, with addition and subtraction causing rightward or leftward shifts, respectively. Neuropsychological data showing that brain-damaged patients with left neglect experience difficulties in solving subtraction but not addition problems support this hypothesis. However, the reverse dissociation is needed to establish the causal role of spatial attention in mental arithmetic.
Method:
R.H., a 65-year-old left-brain-damaged patient exhibiting right unilateral visuospatial and representational neglect, was tested with various numerical tasks including numerical comparison, arithmetic problem-solving, and numerical interval bisection.
Results:
In numerical comparison, R.H. showed a selective response latency increase when judging numbers larger than the references whereas his performance was normal for numbers smaller than the references. In the arithmetic task, R.H. was impaired in solving addition but not subtraction problems. In contrast, performance in number bisection shows a deviation toward larger numbers.
Conclusion:
These results establish a double dissociation between subtraction and addition solving in patients with left versus right neglect and demonstrate clear evidence that attentional mechanisms are crucial for mental arithmetic. We suggest that attention shifts are involved whenever a number is represented relative to another on a mental continuum, be it during numerical comparison or arithmetic problem-solving. R.H.'s performance in numerical interval bisection indicates that this task involves processes that are distinct from those involved in number comparison and mental arithmetic. (PsycINFO Database Record
Previous studies that investigated the association of numbers and space in humans came to contradictory conclusions about the spatial character of the mental number magnitude representation and about how it may be influenced by unilateral spatial neglect. The present study aimed to disentangle the debated influence of perceptual vs. representational aspects via explicit mapping of numbers onto space by applying the number line estimation paradigm with vertical orientation of stimulus lines. Thirty-five acute right-brain damaged stroke patients (6 with neglect) were asked to place two-digit numbers on vertically oriented lines with 0 marked at the bottom and 100 at the top. In contrast to the expected, nearly linear mapping in the control patient group, patients with spatial neglect overestimated the position of numbers in the lower middle range. The results corroborate spatial characteristics of the number magnitude representation. In neglect patients, this representation seems to be biased towards the ipsilesional side, independent of the physical orientation of the task stimuli.
The present study aimed at exploring basic number and calculation abilities in right-hemisphere damaged patients (RHD), focusing primarily on one-digit orally presented tasks, which do not require explicit visuo-spatial abilities. Twenty-four non mentally-deteriorated RHD patients [12 with clinical neglect (RHDN+), 12 without clinical neglect (RHDN−)], and 12 healthy controls were included in the study. Participants were administered an ad hoc numerical battery assessing abilities such as counting, number magnitude comparison, writing and reading Arabic numerals and mental calculation, among others. Significant differences emerged among healthy controls and both the RHDN+ group and the RHDN− group, suggesting that the mathematical impairment of RHD patients does not necessarily correspond to the presence of left-neglect. A detailed analysis of the sub-tests of the battery evidenced expected differences among RHDN+ patients, RHDN− patients, and controls in writing and reading Arabic numerals. Crucially, differences between RHDN+ patients and controls were also found in tasks such as mental subtraction and mental multiplication, which do not require written visuo-spatial abilities. The present findings thus suggest that unilateral right hemisphere lesions may produce specific representational deficits that affect simple mental calculation, and not only the spatial arrangement of multi-digit written numbers as previously thought.
The aim of this study was to build an instrument, the numerical activities of daily living (NADL), designed to identify the specific impairments in numerical functions that may cause problems in everyday life. These impairments go beyond what can be inferred from the available scales evaluating activities of daily living in general, and are not adequately captured by measures of the general deterioration of cognitive functions as assessed by standard clinical instruments like the MMSE and MoCA. We assessed a control group (n = 148) and a patient group affected by a wide variety of neurological conditions (n = 175), with NADL along with IADL, MMSE, and MoCA. The NADL battery was found to have satisfactory construct validity and reliability, across a wide age range. This enabled us to calculate appropriate criteria for impairment that took into account age and education. It was found that neurological patients tended to overestimate their abilities as compared to the judgment made by their caregivers, assessed with objective tests of numerical abilities.
The number bisection tasks, whereby participants estimate the midpoint of a given number interval, is frequently used to explore the idea that numbers are spatially represented within the brain across a 'mental number line'. Some neuropsychological research supports the argument that number bisection is a spatial task, recruiting parietal brain regions, whereas other data suggest that number bisection is dissociable from spatial processing and is instead dependent on working memory in the prefrontal cortices. This study explored the anatomical correlates of deficits in the number bisection task, using voxel-based morphometry in a sample of 25 neuropsychological patients with both left and right hemisphere damage. Interestingly, impairments in number bisection were strongly associated with grey matter lesions in the left hemisphere including both frontal and prefrontal cortices, extending to inferior parietal cortex. Similar prefrontal and frontal grey matter areas were found to be associated with increased leftward deviations (underestimations of the midpoint), whereas no suprathreshold clusters were observed for rightward deviations from the midpoint. Analysis of white matter integrity revealed that lesions in the tracts connecting the parietal and frontal cortices (i.e. the superior longitudinal fasciculus) were highly associated with leftward deviation impairments in number bisection. The data suggest that there is a common parieto-frontal number processing network underlying performances on number bisection, with larger numbers represented on the left side.
This article describes a patient (S. A. M.), suffering from a progressive neurological degenerative condition of unknown origin, who showed a severe difficulty in number transcoding tasks. S. A. M. could recognize and understand arabic numerals and written number names, but he could neither read them aloud nor write them. However, he had a well maintained ability to perform oral and written calculations. The striking pattern of performance observed in S. A. M. suggests that deficits affecting the ability to produce arabic or verbal numerals can be specific to particular task demands. This observation cannot be easily accommodated by current models of numerical processing. A new multiroute model for numerical processing is proposed to account for S. A. M's pattern of performance. This model adds asemantic transcoding pathways to the semantic processing mechanisms proposed by the M. McCloskey model. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Converging evidence suggests that visuospatial attention plays a pivotal role in numerical processing, especially when the task involves the manipulation of numerical magnitudes. Visuospatial neglect impairs contralesional attentional orienting not only in perceptual but also in numerical space. Indeed, patients with left neglect show a bias toward larger numbers when mentally bisecting a numerical interval, as if they were neglecting its leftmost part. In contrast, their performance in parity judgments is unbiased, suggesting a dissociation between explicit and implicit processing of numerical magnitude. Here we further investigate the consequences of these visuospatial attention impairments on numerical processing and their interaction with task demands. Patients with right hemisphere damage, with and without left neglect, were administered both a number comparison and a parity judgment task that had identical stimuli and response requirements. Neglect patients’ performance was normal in the parity task, when processing of numerical magnitude was implicit, whereas they showed characteristic biases in the number comparison task, when access to numerical magnitude was explicit. Compared to patients without neglect, they showed an asymmetric distance effect, with slowing of the number immediately smaller than (i.e., to the left of) the reference and a stronger SNARC effect, particularly for large numbers. The latter might index an exaggerated effect of number-space compatibility after ipsilesional (i.e., rightward) orienting in number space. Thus, the effect of neglect on the explicit processing of numerical magnitude can be understood in terms of both a failure to orient to smaller (i.e., contralesional) magnitudes and a difficulty to disengage from larger (i.e., ipsilesional) magnitudes on the number line, which resembles the disrupted pattern of attention orienting in visual space.
Spatial reasoning has a relevant role in mathematics and helps daily computational activities. It is widely assumed that in cultures with left-to-right reading, numbers are organized along the mental equivalent of a ruler, the mental number line, with small magnitudes located to the left of larger ones. Patients with right brain damage can disregard smaller numbers while mentally setting the midpoint of number intervals. This has been interpreted as a sign of spatial neglect for numbers on the left side of the mental number line and taken as a strong argument for the intrinsic left-to-right organization of the mental number line. Here, we put forward the understanding of this cognitive disability by discovering that patients with right brain damage disregard smaller numbers both when these are mapped on the left side of the mental number line and on the right side of an imagined clock face. This shows that the right hemisphere supports the representation of small numerical magnitudes independently from their mapping on the left or the right side of a spatial-mental layout. In addition, the study of the anatomical correlates through voxel-based lesion-symptom mapping and the mapping of lesion peaks on the diffusion tensor imaging-based reconstruction of white matter pathways showed that the rightward bias in the imagined clock-face was correlated with lesions of high-level middle temporal visual areas that code stimuli in object-centred spatial coordinates, i.e. stimuli that, like a clock face, have an inherent left and right side. In contrast, bias towards higher numbers on the mental number line was linked to white matter damage in the frontal component of the parietal-frontal number network. These anatomical findings show that the human brain does not represent the mental number line as an object with an inherent left and right side. We conclude that the bias towards higher numbers in the mental bisection of number intervals does not depend on left side spatial, imagery or object-centred neglect and that it rather depends on disruption of an abstract non-spatial representation of small numerical magnitudes.
Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) – a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus – on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG’s performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the “indifference zone” that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space.
Acalculia is the inability to process numbers and perform calculations. It may be acquired after a brain lesion or derive from congenital defects of the nervous system. This chapter reviews the contribution of neuropsychology to the understanding of acalculia, reflecting the highly modular organization of math and numbers in the brain. The main aspects of number processing and calculation are considered, including number transcoding, signs, facts, rules, procedures and conceptual knowledge, along with their anatomical underpinnings. The relation of acalculia with aphasia and spatial disorders is discussed. Developmental dyscalculia is briefly described.
Our ability to calculate implies more than the sole retrieval of the correct solution. Essential processes for simple calculation are related to the spreading of activation through arithmetic memory networks. There is behavioral and electrophysiological evidence for these mechanisms. Their brain location is, however, still uncertain. Here, we measured magnetoencephalographic brain activity during the verification of simple multiplication problems. Following the operands, the solutions to verify could be preactivated correct solutions, preactivated table-related incorrect solutions, or unrelated incorrect solutions. Brain source estimation, based on these event-related fields, revealed 3 main brain networks involved in simple calculation: 1) bilateral inferior frontal areas mainly activated in response to correct, matching solutions; 2) a left-lateralized frontoparietal network activated in response to incorrect table-related solutions; and (3) a strikingly similar frontoparietal network in the opposite hemisphere activated in response to unrelated solutions. Directional functional connectivity analyses revealed a bidirectional causal loop between left parietal and frontal areas for table-related solutions, with frontal areas explaining the resolution of arithmetic competition behaviorally. Hence, this study isolated at least 3 neurofunctional networks orchestrated between hemispheres during calculation.
How our intuitive understanding of numbers is deeply rooted in our biology, traceable through both evolution and development.
Humans' understanding of numbers is intuitive. Infants are able to estimate and calculate even before they learn the words for numbers. How have we come to possess this talent for numbers? In A Brain for Numbers, Andreas Nieder explains how our brains process numbers. He reports that numerical competency is deeply rooted in our biological ancestry; it can be traced through both the evolution of our species and the development of our individual minds. It is not, as it has been traditionally explained, based on our ability to use language. We owe our symbolic mathematical skills to the nonsymbolic numerical abilities that we inherited from our ancestors. The principles of mathematics, Nieder tells us, are reflections of the innate dispositions wired into the brain.
Nieder explores how the workings of the brain give rise to numerical competence, tracing flair for numbers to dedicated “number neurons” in the brain. Drawing on a range of methods including brain imaging techniques, behavioral experiments, and twin studies, he outlines a new, integrated understanding of the talent for numbers. Along the way, he compares the numerical capabilities of humans and animals, and discusses the benefits animals reap from such a capability. He shows how the neurobiological roots of the brain's nonverbal quantification capacity are the evolutionary foundation of more elaborate numerical skills. He discusses how number signs and symbols are represented in the brain; calculation capability and the “neuromythology” of mathematical genius; the “start-up tools” for counting and developmental of dyscalculia (a number disorder analogous to the reading disorder dyslexia); and how the brain processes the abstract concept of zero.
We developed a new visual search test to assess signs of left visual peripersonal neglect. Five right-hemisphere-damaged patients, 10 healthy controls, and 10 orthopedic controls were administered the test in four conditions: easy task (no distractors)/time-limited (45’’), easy task (no distractors)/time-unlimited, difficult task (distractors)/time-limited (45’’), difficult task (distractors)/time-unlimited. With respect to controls, most RHDP showed signs of left visual peripersonal neglect in the time-limited condition, but not in the time-unlimited condition, particularly on the difficult task. We suggest that the presence of appropriate time limits, in difficult visual search tasks, could considerably improve the diagnosis of left visual peripersonal neglect.
Financial capacity is the ability to manage one's own finances according to self-interests. Failure in financial decisions and lack of independence when dealing with money can affect people's quality of life and are associated with neuropsychological deficits or clinical conditions such as mild cognitive impairment or Alzheimer's disease. Despite the importance of evaluating financial capacity in the assessment of patients with neuropsychological and psychiatric disorders, only a few tools have been developed. In the present article, the authors introduce the Numerical Activities of Daily Living - Financial (NADL-F) test, a new test to assess financial capacity in clinical populations. The NADL-F is relatively short, yet it encompasses the most common activities involving financial capacities. The NADL-F proved to have satisfactory psychometric properties and overall good validity for measuring financial abilities. Associations with performance on basic neuropsychological tests were investigated, in particular focusing on mathematical abilities as cognitive correlates of financial capacity. Results indicate that the NADL-F could be a useful tool to guide treatments for the enhancement of financial capacities. By sharing all materials and procedures, the authors hope to promote the development of further versions of the NADL-F in different languages, taking into account the necessary adjustments related to different socio-cultural contexts.
Processing numbers induces shifts of spatial attention in probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. This has been interpreted as supporting the concept of a mental number line with number magnitudes ranging from left to right, from small to large numbers. Recently, the investigation of this spatial-numerical link has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems might induce attentional displacements, rightward or leftward respectively. At the neurofunctional level, the activations elicited by the resolution of additions have been shown to resemble those induced by rightward eye movements. However, the possible behavioural counterpart of these activations has not yet been observed. Here we investigated overt attentional shifts with a target detection task primed by addition and subtraction problems (2-digit ± 1-digit operands) in participants whose gaze orientation was recorded during the presentation of the problems and while calculating. No evidence of early overt attentional shifts was observed while participants were hearing the first operand, the operator or the second operand, but they shifted their gaze towards the right during the solving step of addition. These results show that gaze shifts related to arithmetic problem solving are elicited during the solving procedure, and suggest that their functional role is to access, from the first operand, the representation of the result.
Arithmetical deficits in right-hemisphere damaged patients have been traditionally considered secondary to visuo-spatial impairments, although the exact relationship between the two deficits has rarely been assessed. The present study implemented a voxelwise lesion analysis among 30 right-hemisphere damaged patients and a controlled, matched-sample, cross-sectional analysis with 35 cognitively normal controls regressing three composite cognitive measures on standardized numerical measures. The results showed that patients and controls significantly differ in Number comprehension, Transcoding, and Written operations, particularly subtractions and multiplications. The percentage of patients performing below the cutoffs ranged between 27% and 47% across these tasks. Spatial errors were associated with extensive lesions in fronto-temporo-parietal regions -frequently leading to neglect-whereas pure arithmetical errors appeared related to more confined lesions in the right angular gyrus and its proximity. Stepwise regression models consistently revealed that spatial errors were primarily predicted by composite measures of visuo-spatial attention/neglect and representational abilities. Conversely, specific errors of arithmetic nature linked to representational abilities only. Crucially, the proportion of arithmetical errors (ranging from 65% to 100% across tasks) was higher than that of spatial ones. These findings thus suggest that unilateral right hemisphere lesions can directly affect core numerical/arithmetical processes, and that right-hemisphere acalculia is not only ascribable to visuo-spatial deficits as traditionally thought.
Transcoding numerals containing zero is more problematic than transcoding numbers formed by non-zero digits. However, it is currently unknown whether this is due to zeros requiring brain areas other than those traditionally associated with number representation. Here we hypothesize that transcoding zeros entails visuo-spatial and integrative processes typically associated with the right hemisphere. The investigation involved 22 right-brain-damaged patients and 20 healthy controls who completed tests of reading and writing Arabic numbers. As expected, the most significant deficit among patients involved a failure to cope with zeros. Moreover, a voxel-based lesion–symptom mapping analysis showed that the most common zero-errors were maximally associated to the right insula which was previously related to sensorimotor integration, attention, and response selection, yet for the first time linked to transcoding processes. Error categories involving other digits corresponded to the so-called Neglect errors, which however, constituted only about 10% of the total reading and 3% of the writing mistakes made by the patients. We argue that damage to the right hemisphere impairs the mechanism of parsing, and the ability to set-up empty-slot structures required for processing zeros in complex numbers; moreover, we suggest that the brain areas located in proximity to the right insula play a role in the integration of the information resulting from the temporary application of transcoding procedures.
This book provides an overview of attentional impairments in brain-damaged patients from both clinical and neuroscientific perspectives, and aims to offer a comprehensive, succinct treatment of these topics useful to both clinicians and scholars. A main focus of the book concerns left visual neglect, a dramatic but often overlooked consequence of right hemisphere damage, usually of vascular origin, but also resulting from other causes such as neurodegenerative conditions. The study of neglect offers a key to understand the brain's functioning at the level of large-scale networks, and not only based on discrete anatomical structures. Patients are often unaware of their deficits (anosognosia), and often obstinately deny being hemiplegic. Diagnosis is important because neglect predicts poor functional outcome in stroke. Moreover, effective rehabilitation strategies are available, and there are promising possibilities for pharmacological treatments. Attention Disorders After Right Brain Damage is aimed at clinical neurologists, medics in physical medicine and rehabilitation, clinical psychologists and neuropsychologists. It will also be useful for graduate students and medical students who wish to understand the topic of attention systems and improve their knowledge of the neurocognitive mechanisms of attentional deficits. In addition, clinical researchers in neuropsychology and cognitive neuroscience will find in this book an up to date overview of current research dealing with the attention systems of the human brain.
Number-processing may be altered following brain injury and might affect the everyday life of patients. We developed the first ecological tool to assess number-processing disorders in brain-injured patients, the Ecological Assessment Battery for Numbers (EABN; in French, the BENQ). The aim of the present study was to standardize and validate this new tool.
Standardization included 126 healthy controls equally distributed by age, sex and sociocultural level. First, 17 patients were evaluated by the EABN; then scores for a subgroup of 10 were compared with those from a French analytical calculation test, the Évaluation Clinique des Aptitudes Numériques (ECAN). The concordance between the EABN and the ECAN was analyzed to determine construct validity. Discrimination indexes were calculated to assess the sensitivity of the subtests.
Standardization highlighted a major effect of sociocultural level. In total, 9 of 17 patients had a pathological EABN score, with difficulties in telling time, making appointments and reading numerical data. The results of both the EABN and ECAN tests were concordant (Kendall's w=0.97). Finally, the discriminatory power was good, particularly for going to the movies, cheque-writing and following a recipe: scores were>0.4.
The EABN is a new tool to assess number-processing disorders in adults. This tool has been standardized and has good psychometric properties for patients with brain injury.
Copyright © 2015 Elsevier Masson SAS. All rights reserved.
We studied the effects of optokinetic stimulation (OKS; leftward, rightward, control) on the visuo-perceptual and number space, in the same sample, during line bisection and mental number interval bisection tasks. To this end, we tested six patients with right-hemisphere damage and neglect, six patients with right-hemisphere damage but without neglect, and six neurologically healthy participants. In patients with neglect, we found a strong effect of leftward OKS on line bisection, but not on mental number interval bisection. We suggest that OKS influences the number space only under specific conditions.
Recent behavioural and brain imaging studies have provided evidence for rightward and leftward attention shifts while solving addition and subtraction problems respectively, suggesting that mental arithmetic makes use of mechanisms akin to those underlying spatial attention. However, this hypothesis mainly relies on correlative data and the causal relevance of spatial attention for mental arithmetic remains unclear. In order to test whether the mechanisms underlying spatial attention are necessary to perform arithmetic operations, we compared the performance of right brain-lesioned patients, with and without left unilateral neglect, and healthy controls in addition and subtraction of two-digit numbers. We predicted that patients with left unilateral neglect would be selectively impaired in the subtraction task while being unimpaired in the addition task. The results showed that neglect patients made more errors than the two other groups to subtract large numbers, whereas they were still able to solve large addition problems matched for difficulty and magnitude of the answer. This finding demonstrates a causal relationship between the ability to attend the left side of space and the solving of large subtraction problems. A plausible account is that attention shifts help localizing the position of the answer on a spatial continuum while subtracting large numbers.
Traditional developmental models describe a series of sequenced stages and interpret developmental disorders in terms of arrested development. Two different cases of developmental dyscalculia are described which cannot both be explained against the same stage model of the development of arithmetical skill. In both cases accurate number processing skills have developed. SW has also acquired accurate number facts and tables but has selective difficulty with the procedures of calculation. HM shows the reverse pattern with normal mastery of calculation procedures but selective difficulty in the mastery of arithmetical tables. The arithmetical modules involved in tables and procedures develop in a semi-independent fashion, neither being an essential precursor of the other. This study demonstrates that there are individual differences in the developmental dyscalculias consistent with individual differences in the developmental pathways to the adult calculation system. It also-demonstrates that the developmental dyscalculias are anala-gous to the acquired dyscalculias.
A case study of developmental dyscalculia is presented in which there is impairment of number processing. When reading and writing arabic numbers the syntactic component of the number is processed accurately but lexical processing results in incorrect digit selection. When reading arabic numbers the allocation of lexical items into syntactic frames is particularly poor for digits in the units position. Lexical allocation is unaffected by stimulus length. Despite poor short term memory, word reading is not impaired except for the reading of numeral words for which there is a category specific deficit. Reading errors to numeral words are more frequent than to arabic numbers but the nature of the errors is comparable. This reading deficit coexists with good phonological reading skills. The results are discussed in relation to models derived from studies of the acquired dyscalculias.
Examines dyscalculic disorders in children based on a framework developed in research on adult pathology, to determine whether or not the various sub-components hypothesized in the adult models are dissociable in children, thereby supporting a modular view of development. A selective disorder of components of the number processing system is discussed in which numerical syntactic skills are intact but lexical skills are impaired. In other cases where number processing is intact but there are impairments in the calculation system, no systematic connection can be found between the acquisition of arithmetical facts and mastery of procedural knowledge. There are children whose procedural knowledge of arithmetic has been adversely affected but whose declarative knowledge of arithmetic has not, and other children for whom opposite dissociation exists. Data suggest an arithmetical development model wherein each sub-component has its own developmental capacities. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Two left-neglect patients were asked (i) to bisect a 15 cm line, (ii) to bisect the empty space between the endpoints of a 15 cm virtual line, and (iii) to set the endpoints of a 15 cm virtual line, given its midpoint. With one patient, the subjective midpoint of the virtual line was found to be displaced leftwards with respect to the subjective midpoint of the real line, whereas with the other it was found to be displaced rightwards. However, in condition (iii) both patients significantly underestimated the distance from the centre of the rightmost point of the virtual line while relatively overestimating that from the centre to the left endpoint. This latter result challenges current accounts of unilateral neglect.
This article discusses cognitive neuropsychological research on acquired dyscalculia (i.e., impaired numerical processing resulting from brain damage), surveying issues of current interest, and illustrating the ways in which analyses of acquired deficits can contribute to an understanding of normal processing. I first review the logic whereby inferences concerning normal cognition are drawn from patterns of impaired performance. I then consider research exploring the general functional architecture of the cognitive numerical processing mechanisms, and finally turn to studies aimed at probing the internal structure and functioning of individual processing components.
This article describes a theory-based approach to assessment of acquired dyscalculia. A model of the normal cognitive number-processing/calculation system is presented, and methods are discussed for characterizing number-processing/calculation deficits in terms of functional damage to the mechanisms specified in the model.
A well educated right-handed woman developed severe and stable alexia and agraphia following a circumscribed surgical lesion in the left premotor cortex. The lesion was located in Brodmann's field 6, above Broca's area, in the region traditionally referred to as Exner's area. The alexia and agraphia occurred in a pure form, that is, in the setting of otherwise normal cognitive and neurological function. She was not aphasic or hemiparetic and her visual perception, intellect, memory, oral spelling and drawing were normal. The patterns of impairment of reading and writing closely paralleled one another. Reading of single words and letters was severely impaired, and she was entirely unable to read sentences. She was virtually unable to write recognizable letters, could write no words, and her writing attempts were severely distorted spatially. By contrast, she could easily read all numbers and nonverbal symbols, and she was equally able to write numbers and perform written calculations without difficulty. These striking dissociations provide further evidence of the domain specificity of cognitive/neural representations. They also point to the possible role of premotor cortices in the coactivation of precise sequences of motor and sensory activity patterns involved in reading and writing.
In the first part of this paper, 45 French (left-to-right readers) and 30 Israeli (right-to-left readers) normal dextrals were given half a line and requested to construct the missing other with the same length (either the left one or the right one). Using this line extension task, a significant effect of reading habits on the performance was found, with no significant bias for Israeli subjects, and a significant underconstruction when building the left half from the right one for French subjects. In the second part, two patients with opposite reading habits (one French, one Israeli) suffering from left unilateral neglect were submitted to the same protocol. Both patients were found to under-construct the right half of the line from the left given half, and to over-construct the left half from the right given one, hence reproducing the well-known line bisection bias. Results are discussed with regard to enhancement and activation hypotheses, and current theories of the neglect syndrome.
A patient is described with a specific deficit for arithmetical procedures. Unlike in previously described cases, where the observed problems could be attributed to the systematic application of disturbed algorithms, this patient's difficulty seems to stem from an inability to monitor the sequence of operations that calculation procedures specify. Criteria are provided for distinguishing impairments in written calculation due to the application of defective knowledge of the procedures from those determined by lack of monitoring. The role of monitoring and control processes in different calculation components is also discussed.