Complex mental addition and multiplication rely more on visuospatial than verbal processing

Conference Theme: Mind, Technology, and SocietyRecent imaging studies have found that in simple arithmetic processing, addition calculation is lateralized to the right hemisphere, whereas multiplication to the left. Here we aimed to investigate the cognitive mechanism underlying complicated arithmetic processing in addition and multiplication with a dual task paradigm. Participants were asked to complete a calculation task (addition or multiplication) and a letter judgment task (rhyme or shape judgment) simultaneously. We found that participants’ performance in solving addition and multiplication problems was interfered more by the simultaneous shape judgment task than the rhyme judgment task. This effect suggested that both complicated addition and multiplication calculations relied more on right-lateralized visuospatial than left-lateralized phonological/verbal processing. The shift from left- to more right-lateralized processing in complicated multiplication suggests that participants may have adopted a visuospatial strategy to approximate numerosity when the calculation involved large numbers. These results suggest that the cognitive mechanism involved in arithmetic processing depends on both the operation and the context.postprin

Dissociation of subtraction and multiplication in the right parietal cortex: Evidence from intraoperative cortical electrostimulation

Previous research has consistently shown that the left parietal cortex is critical for numerical processing, but the role of the right parietal lobe has been much less clear. This study used the intraoperative cortical electrical stimulation approach to investigate neural dissociation in the right parietal cortex for subtraction and multiplication. Results showed that multiplication (as well as picture naming) was not affected by the cortical electrical stimulation on all the targeted sites of the right parietal cortex as well as those of the right temporal cortex. In contrast, stimulation at three right parietal sites (two sites in the right inferior parietal lobule and one in the right angular gyrus) impaired performance on simple subtraction problems. This study provided the first evidence from an intraoperative cortical electrical stimulation study to show the dissociation of arithmetic operations in the right parietal cortex. This dissociation between subtraction and multiplication suggests that the right parietal cortex plays a more significant role in quantity processing (subtraction) than in verbal processing (multiplication) in numerical processing

Priming effects of arithmetic signs in 10‐ to 15‐year‐old children

International audienceIn this research, 10- to 12- and 13- to 15-year-old children were presented with very simple addition and multiplication problems involving operands from 1 to 4. Critically, the arithmetic sign was presented before the operands in half of the trials, whereas it was presented at the same time as the operands in the other half. Our results indicate that presenting the 'x' sign before the operands of a multiplication problem does not speed up the solving process, irrespective of the age of children. In contrast, presenting the '+' sign before the operands of an addition problem facilitates the solving process, but only in 13 to 15-year-old children. Such priming effects of the arithmetic sign have been previously interpreted as the result of a pre-activation of an automated counting procedure, which can be applied as soon as the operands are presented. Therefore, our results echo previous conclusions of the literature that simple additions but not multiplications can be solved by fast counting procedures. More importantly, we show here that these procedures are possibly convoked automatically by children after the age of 13 years. At a more theoretical level, our results do not support the theory that simple additions are solved through retrieval of the answers from long-term memory by experts. Rather, the development of expertise for mental addition would consist in an acceleration of procedures until automatization

Neuropsychologia 41 (2003) 1942--1958

Numerical abilities are thought to rest on the integration of two distinct systems, a verbal system of number words and a non-symbolic representation of approximate quantities. This view has lead to the classification of acalculias into two broad categories depending on whether the deficit affects the verbal or the quantity system. Here, we test the association of deficits predicted by this theory, and particularly the presence or absence of impairments in non-symbolic quantity processing. We describe two acalculic patients, one with a focal lesion of the left parietal lobe and Gerstmann's syndrome and another with semantic dementia with predominantly left temporal hypometabolism. As predicted by a quantity deficit, the first patient was more impaired in subtraction than in multiplication, showed a severe slowness in approximation, and exhibited associated impairments in subitizing and numerical comparison tasks, both with Arabic digits and with arrays of dots. As predicted by a verbal deficit, the second patient was more impaired in multiplication than in subtraction, had intact approximation abilities, and showed preserved processing of non-symbolic numerosities

Dissociation of Exact and Approximate Calculation in Severe Global Aphasia

We report a 68-year-old patient with severe global aphasia secondary to a large left hemisphere infarction including the parietal lobe. In addition to language and neuroradiological evaluation, the patient was given specifically designed arithmetic and clock tasks requiring either exact calculation or approximate calculation. Despite severe language impairment, the patient showed relatively well-preserved abilities for numerical comprehension and arithmetic operations. Further analyses using specifically designed arithmetic and clock tasks demonstrated a clear dissociation of the patient’s abilities between impaired exact calculation and well-preserved approximate calculation. The results support the notion that numerical and arithmetic abilities are heterogeneous in that rote verbal arithmetic facts and quantitative numerical knowledge can be separable. Implications of the present findings for neural correlates of numerical and arithmetic processing suggest that the right hemisphere plays a crucial role in approximate calculation

The application of rules in morphology, syntax and number processing: a case of selective deficit of procedural or executive mechanisms?: Deficit of procedural or executive mechanisms

International audienceDeclarative memory is a long-term store for facts, concepts and words. Procedural memory subserves the learning and control of sensorimotor and cognitive skills, including the mental grammar. In this study, we report a single-case study of a mild aphasic patient who showed procedural deficits in the presence of preserved declarative memory abilities. We administered several experiments to explore rule application in morphology, syntax and number processing. Results partly support the differentiation between declarative and procedural memory. Moreover, the patient's performance varied according to the domain in which rules were to be applied, which underlines the need for more fine-grained distinctions in cognition between procedural rules

Numeracy Skills in Patients With Degenerative Disorders and Focal Brain Lesions: A Neuropsychological Investigation

Objective: To characterize the numerical profile of patients with acquired brain disorders. Method: We investigated numeracy skills in 76 participants—40 healthy controls and 36 patients with neurodegenerative disorders (Alzheimer dementia, frontotemporal dementia, semantic dementia, progressive aphasia) and with focal brain lesions affecting parietal, frontal, and temporal areas as in herpes simplex encephalitis (HSE). All patients were tested with the same comprehensive battery of paper-and-pencil and computerized tasks assessing numerical abilities and calculation. Degenerative and HSE patients also performed nonnumerical semantic tasks. Results: Our results, based on nonparametric group statistics as well as on the analysis of individual patients, and all highly significant, show that: (a) all patients, including those with parietal lesions—a key brain area for numeracy processing—had intact processing of number quantity; (b) patients with impaired semantic knowledge had much better preserved numerical knowledge; and (c) most patients showed impaired calculation skills, with the exception of most semantic dementia and HSE patients. Conclusion: Our results allow us, for the first time, to characterize the numeracy skills in patients with a variety of neurological conditions and to suggest that the pattern of numerical performance can vary considerably across different neurological populations. Moreover, the selective sparing of calculation skills in most semantic dementia and HSE suggest that numerical abilities are an independent component of the semantic system. Finally, our data suggest that, besides the parietal areas, other brain regions might be critical to the understanding and processing of numerical concepts