Dissociating Arabic Numeral Reading and Basic Calculation: A Case Study

This study is about JS, a patient who suffered from anomia, phonological dyslexia and severe writing problems following a left hemispheric stroke. He showed good arabic numeral comprehension as evidenced in number-comparison tasks, but impairment in transcoding arabic numerals into verbal numbers and verbal numbers into arabic numerals. Although JS had several operand reading errors, the four arithmetic operations were not affected. In calculations with arabic numerals, he produced the correct results both in oral and written responses. For instance, when presented with the multiplication “7×3”, JS read the operation as “four times five”, but provided the correct response orally “twenty one” and written “21”. This behavior goes against those hypotheses which posit that multiplication facts are verbally-based, and those which establish the same route for verbal number production in calculation and arabic numeral reading.     

Code-dependent pathways for number transcoding: evidence from a case of selective impairment in written verbal numeral to arabic transcoding

This article presents a brain-damaged patient (RR) suffering from cognitive deficits following neurological insults, who showed a selective impairment in number transcoding. Except for written verbal numeral to arabic transcoding, his ability to transcode numerals, including writing arabic numerals to dictation, is largely preserved. Other number processing skills, including numeral recognition, numeral comprehension, and calculation, were unimpaired. Semantic and asemantic models of number processing cannot easily account for the patient's performance and it is suggested that the number transcoding system should include different code-dependent pathways for arabic transcoding from spoken verbal numerals and from written verbal numerals. Since the errors produced in the impaired transcoding rely upon the syntactical structure of numeral stimuli, it is also proposed that transcoding code-dependent pathways should reflect the structure of the verbal numeral system, especially the difference between sum and product relationships.     

"Progressive acalculia": a variety of focal degenerative atrophy affecting number processing

A 72-year-old man experienced increasing difficulties in calculating and processing numbers. He made many syntactic errors when he read and wrote numbers, both in arabic and number-word forms. Transcoding between arabic numerals and number-words was severely impaired. His calculation abilities were grossly impaired. He could not perform even simple multiplications, but additions and subtractions were preserved. He was unable to recite multiplication tables or the alphabet. In contrast, numerosity judgment, magnitude comparisons,and semantic evaluation of numbers were intact. The patient's deficit could be summarized as an Impairment in all tasks involving numbers in a verbal format, corresponding to the so-called "verbal anarithmetia'." It was noteworthy that verification of operations, including multiplications, was accurately performed. For example, the patient could not solve a multiplication like 8 x 9, but could estimate that 9 x 2=1 1 was closer to the exact result than 9 X 2=17, or could state that 8 x 2=16 was exact even though, at the same time, he expressed verbally the terms of the corresponding addition "eight plus two is ten." Other cognitive deficits were detected by neuropsychological tests which demonstrated mainly anomic aphasia, dysorthographic agraphia without alexia, impairment of short term and episodic memory, digital agnosia. However, the patient could not be considered to have demon-eti due to preserved self-sufficiency, except for tasks requiring calculation abilities. During the two years of follow-up, the impairment in processing numbers and calculation remained predominant over other deficits. Cerebral MRI showed an atrophy of the left temporal and parietal lobes, and SPECT study showed a reduction of regional cerebral blood flow of the left hemisphere. This original clinical presentation of a cerebral degenerative disease could be described as "primary progressive acalculia" whatever the underlying primary pathological process.     

Language and calculation within the parietal lobe: a combined cognitive, anatomical and fMRI study

We report the case of a patient (ATH) who suffered from aphasia, deep dyslexia, and acalculia, following a lesion in her left perisylvian area. She showed a severe impairment in all tasks involving numbers in a verbal format, such as reading aloud, writing to dictation, or responding verbally to questions of numerical knowledge. In contrast, her ability to manipulate non-verbal representations of numbers, i.e., Arabic numerals and quantities, was comparatively well preserved, as evidenced for instance in number comparison or number bisection tasks. This dissociated impairment of verbal and non-verbal numerical abilities entailed a differential impairment of the four arithmetic operations. ATH performed much better with subtraction and addition, that can be solved on the basis of quantity manipulation, than with multiplication and division problems, that are commonly solved by retrieving stored verbal sequences. The brain lesion affected the classical language areas, but spared a subset of the left inferior parietal lobule that was active during calculation tasks, as demonstrated with functional MRI. Finally, the relative preservation of subtraction versus multiplication may be related to the fact that subtraction activated the intact right parietal lobe, while multiplication activated predominantly left-sided areas.     

A clinical study of the number processing system: decimal size effects on reading numbers in patients with left parieto-occipital gliomas

An increasing number of studies are focusing on the anatomo-functional organisation of number processing and some cognitive models have been recently developed. Nevertheless, relationships between areas implicated in number processing, and language areas and circuits remain unclear. Recently, Dehaene and Cohen, in their "triple-code model of number processing", (Dehaene and Cohen, 1995) distinguished two alternative number representation and processing systems: one depending on verbal processes, the other representing a quantity manipulation. According to this model, the retrieval of "arithmetical facts" (AF), learned by rote at school and memorised in a verbal form (such as the multiplication table or simple addition problems) can be considered as a verbal automatism; conversely, subtraction problems, which require mental manipulation of the quantities, represent an abstract, semantic elaboration: "Actual Calculation" (AC). The anatomical correlate of the retrieval of AF (depending on automatic verbal associations) seems to correspond to the left-hemispheric perisylvian areas, while impairment of the actual calculation (AC) depends on the intraparietal region, particularly in the left dominant hemisphere. The present study describes the neuropsychological assessment of three patients, tested after surgery for left parieto-occipital tumors. Two of them were affected by an anaplasic glioma, the third by a low-grade glioma. The cognitive evaluation included: words of Rey, numeral (directed and reversed) span, reading of "simple" numbers (from 1 to 10) and of "complex" numbers (many decimals), writing (dictation) and reading a standard text, finger denomination and right-left distinction. All patients showed language disturbances, dysgraphia and severe dyslexia. In reading numbers, we identified two types of errors: lexical and syntactic. "Lexical errors" consisted in a wrong choice among words in the number's lexicon. For instance, all patients made errors in reading "complex" numbers composed by many decimals, switching single numbers but respecting the decimal size and the structure of the whole number (such as 69107 instead of 68107). On the other hand, only one patient committed syntactic errors, misunderstanding the decimal size and the structure of the number. We considered lexical errors as verbal errors, and syntactic errors as semantic errors, affecting the notion of quantity. We tried to explain verbal disturbances as well as lexical errors as a consequence of lesion of the left-hemispheric perisylvian areas, while syntactic errors as a consequence of impairment of the intraparietal region.     

Cerebral networks for number processing: Evidence from a case of posterior callosal lesion

Abstract

We report a study of number processing in a patient with a lesion selectively destroying the posterior half of her corpus callosum. This case provided an opportunity to study the cerebral distribution of numerical abilities across hemispheres, and their interhemispheric communication pathways. Tasks of interhemispheric same-different judgement with digits and sets of dots showed that exact digit identity could not be transferred between hemispheres, but that some approximate magnitude information could. With arabic numerals presented in the left visual field, reading aloud and arithmetic were severely impaired. In contrast, larger-smaller magnitude comparison was spared. With right-visual-field stimuli, the patient's performance was essentially normal in reading aloud, arithmetic and number comparison. These findings lend support to the hypothesis that both hemispheres are capable of identifying arabic digits, and of accessing and comparing the corresponding magnitudes. However, the verbal abilities which underlie overt naming and arithmetic computations are available only to the left hemisphere.     

Treating number transcoding difficulties in a chronic aphasic patient

Background : Number transcoding comprises the ability to read and write Arabic numerals and number words. Although number transcoding and counting are frequently impaired in aphasic patients, little attention has been given to the development of specific treatment methods and the evaluation of their efficiency. We report the treatment of the chronic aphasic patient PK who had severe difficulties in reading Arabic numerals. Number words could only be produced with an automatic counting strategy, always beginning with one. Aims : The therapy study was aimed at examining whether PK's numeral transcoding abilities could be improved by an intensive remediation programme that comprised tasks in which Arabic numerals had to be transcoded into number words. Methods & Procedures : Treatment consisted of specific training blocks of gradually increasing complexity. Therapy started with reading one-digit Arabic numerals, followed by teens, decades, and two- to five-digit numerals, which were divided into different subgroups according to complexity. Outcomes & Results : After an 8-week therapy period significant improvement in the processing of one- to five-digit numbers was observed. PK was able to read 49.4% of the Arabic numerals as compared to 2.2% before treatment. Performance was influenced significantly by number length and number word structure. Transcoding abilities improved remarkably for two- and three-digit numbers containing a zero or ending with two zeros. Stability of the treatment effects was assessed in a follow-up study 6 months after termination of the treatment programme. PK was still able to read 48.3% of the Arabic numerals successfully. Conclusions : In a single-case study of patient PK, suffering from chronic severe aphasia that was also characterised by severe transcoding and calculation impairments it could be demonstrated that these transcoding problems could be remedied to a substantial degree when employing a carefully graded intensive retraining programme for Arabic number naming.     

Language Disorder in a Child with Early Left Thalamic Lesion

The present paper describes two patients, AB and FS, whose deficit in transcoding verbal to Arabic numerals was greatly affected by the format of the input. Despite intact comprehension of written verbal numerals and otherwise intact production of Arabic numerals they both transcode inefficiently the former into the latter. Yet, their ability to write the same Arabic numerals on dictation was fully preserved. Moreover, in both patients’ performance, a systematic error pattern emerged reflecting the influence of the lexico-syntactic structure of the input numerals in the transcoding processes. Current models of number transcoding may not easily account for this pattern of dissociation without postulating different code-dependent pathways for verbal to Arabic transcoding. Within a more parsimonious approach, it is tentatively suggested that spoken and written verbal codes activate with different efficiency the same transcoding algorithm.     

Writing and rewriting arabic numerals: dissociated processing pathways?

The present paper describes two patients, AB and FS, whose deficit in transcoding verbal to Arabic numerals was greatly affected by the format of the input. Despite intact comprehension of written verbal numerals and otherwise intact production of Arabic numerals they both transcode inefficiently the former into the latter. Yet, their ability to write the same Arabic numerals on dictation was fully preserved. Moreover, in both patients' performance, a systematic error pattern emerged reflecting the influence of the lexico-syntactic structure of the input numerals in the transcoding processes. Current models of number transcoding may not easily account for this pattern of dissociation without postulating different code-dependent pathways for verbal to Arabic transcoding. Within a more parsimonious approach, it is tentatively suggested that spoken and written verbal codes activate with different efficiency the same transcoding algorithm.     

The role of the temporal lobe semantic system in number knowledge: evidence from late-stage semantic dementia

Previous reports have demonstrated that many aspects of number knowledge remain unimpaired in semantic dementia, despite severe comprehension problems in other domains. It is argued that this advantage for numbers arises because the disease spares the parietal lobe magnitude system thought to be critical for number processing. Models of numerical cognition that favour a separation between verbal and magnitude representations of number might, however, predict a restricted impairment of the verbal number code in this condition. We obtained support for this hypothesis in a patient with late-stage semantic dementia. She was impaired at a variety of tasks tapping the verbal number code; for example, reading and writing Arabic numerals, naming and word-picture matching with dot pictures, reading aloud number words, digit span and magnitude comparison/serial ordering tasks with number words. In contrast, she demonstrated good understanding of the magnitude and serial order of numbers when tested with Arabic numerals and non-symbolic representations. These findings suggest that although the magnitude meaning of numbers is isolated from the temporal lobe semantic system, the anterior infero-temporal lobe may play a critical role in binding English number words to their non-symbolic magnitude meaning.     

Attention deficits and schizophrenia. Multidisciplinary approaches and the Stroop's test]

Since McGhie & Chapman's (1961) pioneering work, there have been continual attempts to clarify the link between attentional disturbances observable in schizophrenics and their schizophrenic symptoms. Venables (1964, 1977) claims that this diminution is a consequence of a badly controlled arousal, resulting in an inadequate filtering at the level of sensory input. Although the notion of a faulty sensory filter is simple and intellectually satisfying, this idea rapidly met with articulate opposition. Broadbent himself, in 1971, revised his model to take into account the way in which semantic aspects influence selective attention, and proposed the existence of a second stage of information processing, coming after the sensory filter. It became increasingly clear that progress in understanding selective attention would depend upon more centrally-directed approaches. In 1935, Stroop developed an ingenious way of studying selective attention. In his task, an "automatic", overlearned task (reading short words aloud) is put into conflict with a slightly more difficult task (colour-naming): the subject has to name the colour of the ink in which a word is printed, but the word itself is the name of a different colour. For instance, when the word "blue" is written in red ink, the correct response is "red". Typically, subjects find it difficult to inhibit the reading response, and take significantly more time to name a colour that forms an incompatible word than take to name the colour of a row of letters "x". This increased reaction time for the incompatible condition is attributed to an "interference" caused by the verbal information contained in the double stimulus.(ABSTRACT TRUNCATED AT 250 WORDS)     

Cognitive neuropsychological models of adult calculation and number processing: the role of the surface format of numbers

Several brain-damaged patients showed a series of performance dissociations related to the surface format of numbers. These findings provide empirical evidence against two crucial assumptions of the calculation and number processing model proposed by McCloskey, Caramazza and Basili (36) and widely accepted within the current literature on developmental dyscalculia. First, the unique syntactical system for verbal numbers can fractionate into two syntactic components, one for spoken verbal and one for written verbal numbers, respectively. Second, access to simple number facts (multiplication tables) seems to rely on format-specific routes and not on the access to supposedly unique abstract representations. The data can also hardly be interpreted within the theoretical framework of the "triple-code" information processing model of Dehaene (16) and of its anatomical implementation by Dehaene and Cohen (19). Taken together, these results favour a cognitive architecture of the numerical system with a variety of format-specific processes and multiple representations proposed by Campbell and Clark (8) which remain to be fully specified.     

The neural origin of the priming distance effect: Distance‐dependent recovery of parietal activation using symbolic magnitudes

Numerical magnitudes are known to be processed in areas around the intraparietal sulci of the brain. We used an fMRI‐adaptation paradigm to investigate how they are actually coded at the neural level. In a number identification task, we manipulated the numerical distance between prime and target numbers (same, close, and far pairs) and their symbolic notation (Arabic and verbal numerals). We show that bilateral parietal activations present a distance‐dependent recovery of activation positively correlated with the distance between primes and targets: the larger the prime‐target distance, the higher the recovery of activation. Importantly, this effect is only present for trials where an Arabic numeral precedes a verbal numeral and not the reverse. Together, these findings reveal the neural origin of the behavioral priming distance effect and demonstrate that the relative importance of the semantic and nonsemantic pathways in a dual‐route model of number processing is modulated by symbolic notation. Hum Brain Mapp, 2010. © 2009 Wiley‐Liss, Inc.     

Number representation deficit: a bilingual case of failure to access written verbal numeral representations

This study reports the case of a Greek–German bilingual patient (S.V.) with specific deficit in Arabic number production from written German number words. S.V. was able to successfully complete the reverse task, i.e. to convert Arabic numerals into written or oral German number words. She also showed preserved ability to produce both German and Greek numbers and to accurately make oral magnitude judgments in both languages. However, when transcoding two-digit numbers from German written numerals to Arabic numbers she consistently reversed the digits. A series of in-house tasks were used to test her general abilities of number processing, i.e. number synesthesia and calculation. Moreover, a number magnitude comparison task was developed specifically for pairs of numbers with reverse digits and we found that out of pairs of numbers with reverse digits with magnitude less than 100, there exist 19 pair combinations for which distance and relative distance are not concordant. The results suggest that S.V.’s performance was significantly worse as the absolute distance between the numbers in the number pairs increased. These investigations are discussed in analogy with a grammatical rule problem related to absolute and relative distance effects.     

Neuroelectric correlates of a neuropsychological model of word decoding and semantic processing in reading disabled children

The purpose of this study was to distinguish the characteristics and components of event related potentials (ERPs) correlated with word decoding and semantic processing in a subgroup of children with specific reading disabilities related to visual processing deficiencies. The results were compared with those obtained from a group of normal readers previously studied (Ostrosky et al. in press). Visual ERPs were recorded to four stimuli: three physically different but with the same semantic content: a frequently used noun written in capitals (COCHE), the same noun in handwriting, the pictorial representation of the noun (drawing), and a neutral stimulus consisting of a checkerboard. Four derivations were used: occipital (O1-O2) and parietal (P3-P4) with reference to linked mastoids. Data were analyzed using multivariate procedures. A Principal Component Analysis with Varimax rotation of the solution was applied. In the normal readers, we found some components in the occipital derivations which identified the words presented in different styles of handwriting and others which seemed to identify these words with the pictorial representation (and not with the neutral stimuli). The first "verbal" components were situated around the 156-256 ms latency range and the second "semantic" components were observed at over 380 ms. In the disabled readers, there was no "verbal" or "semantic" recognition grouping of these physically different stimuli. As opposed to the normal readers, interhemispheric responses were symmetrical. At the left parietal leads in the normal readers, the morphology of the verbal stimuli (capitals and handwriting) were very similar throughout the sweep and both were very different from the nonverbal stimuli. At 376 ms the four stimuli elicited a prominent negative peak in which the verbal stimuli elicited significantly higher amplitude than the nonverbal stimuli. In the disabled group, the morphologies of the four stimuli were very similar and no significant differences were observed. The results are discussed in accordance with a hypothetical model of the neural bases underlying reading. The model takes into account the complexity of the reading process and the various cognitive skills required for its adequate performance, and emphasizes a complex, dynamic interplay between occipital, parietal and temporal areas.     

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.     

Cognitive neuropsychological models of adult calculation and number processing: the role of the surface format of numbers

Several brain-damaged patients showed a series of performance dissociations related to the surface format of numbers. These findings provide empirical evidence against two crucial assumptions of the calculation and number processing model proposed by McCloskey, Caramazza and Basili (36) and widely accepted within the current literature on developmental dyscalculia. First, the unique syntactical system for verbal numbers can fractionate into two syntactic components, one for spoken verbal and one for written verbal numbers, respectively. Second, access to simple number facts (multiplication tables) seems to rely on format-specific routes and not on the access to supposedly unique abstract representations. The data can also hardly be interpreted within the theoretical framework of the “triple-code” information processing model of Dehaene (16) and of its anatomical implementation by Dehaene and Cohen (19). Taken together, these results favour a cognitive architecture of the numerical system with a variety of format-specific processes and multiple representations proposed by Campbell and Clark (8) which remain to be fully specified.     

Differential effects of covert and overt training of the syntactical component of verbal number processing and generalisations to other tasks: A single-case study

Abstract

We report on the significant beneficial outcomes of two contrasted experimental rehabilitation techniques for grammaticality judgements operating on numbers in written word forms (verbal numbers).

The information processing approach provided the theoretical framework for designing training programmes. The verbal primitives were classified into lexical categories (units, teens, decades, and hundreds). A set of lexico-syntactical rules was stated in terms of well-formed or illegal sequences of categories. Grammaticality judgement was simulated by a left-to-right parser performing the lexical categorization of verbal number primitives and operating with the relevant acceptance/rejection syntactical rules.

In Therapy I, neither rules nor lexical categorization were taught to the patient, who was just presented with many verbal numbers in a grammaticality judgement task on a video screen. Automatic feedback to the patient qualified only the nature of his responses (correct or errors). In Therapy II, the patient was taught the rules and the lexical categories they operated upon.

The two rehabilitation methods were successively administered and each induced different but significant improvement in grammaticality judgements not only on trained items but also on comparable undrilled items. Intratask learning transfer was enhanced by training with a large variety of items sharing the same underlying lexicosyntactical structure, which proved more efficient than mere repetition of exercises on the very same items. Intertask learning transfers were obtained in other number processing situations like writing verbal numbers from Arabic forms (or the reverse), magnitude comparisons, and numerical size estimation of verbal numbers.     

Poor anchoring limits dyslexics' perceptual, memory, and reading skills

The basic deficits underlying the severe and persistent reading difficulties in dyslexia are still highly debated. One of the major topics of debate is whether these deficits are language specific, or affect both verbal and non-verbal stimuli. Recently, Ahissar and colleagues proposed the "anchoring-deficit hypothesis" (Ahissar, Lubin, Putter-Katz, & Banai, 2006), which suggests that dyslexics have a general difficulty in automatic extraction of stimulus regularities from auditory inputs. This hypothesis explained a broad range of dyslexics' verbal and non-verbal difficulties. However, it was not directly tested in the context of reading and verbal memory, which poses the main stumbling blocks to dyslexics. Here we assessed the abilities of adult dyslexics to efficiently benefit from ("anchor to") regularities embedded in repeated tones, orally presented syllables, and written words. We also compared dyslexics' performance to that of individuals with attention disorder (ADHD), but no reading disability. We found an anchoring effect in all groups: all gained from stimulus repetition. However, in line with the anchoring-deficit hypothesis, controls and ADHD participants showed a significantly larger anchoring effect in all tasks. This study is the first that directly shows that the same domain-general deficit, poor anchoring, characterizes dyslexics' performance in perceptual, working memory and reading tasks.