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Acalculia is an acquired Disability in which people have difficulty performing simple mathematical tasks, such as adding, subtracting, multiplying, and even simply stating which of two is larger. Acalculia is distinguished from dyscalculia in that acalculia is acquired late in life due to neurological injury such as a stroke, while dyscalculia is a specific developmental disorder first observed during the acquisition of mathematical knowledge. The name comes from the Greek language a- meaning "not" and Latin calculare, which means "to count".
As calculation involves the integration of several cognitive skills, it is understood that an individual with acalculia (or calculation difficulties) is deficient in any of the following four realms:
Young schoolchildren are presented with mathematical concepts in a cumulative manner. Advancement requires the grasping of fundamental concepts before progressing to more difficult and involved concepts. There is a natural variation in the speed with which young schoolchildren grasp mathematical concepts, and those that have extreme difficulty retaining the foundations of mathematical concepts (such as global quantification or numerosity perception) are considered to have developmental dyscalculia.
Studies of patients with lesions to the parietal lobe have demonstrated that lesions to the angular gyrus tend to lead to greater impairments in memorized mathematical facts, such as multiplication tables, with relatively unimpaired subtraction abilities. Conversely, patients with lesions in the region of the intraparietal sulcus tend to have greater deficits in subtraction, with preserved multiplication abilities.Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33(2), 219-250 These double dissociations lend support to the idea that different regions of the parietal cortex are involved in different aspects of numerical processing.
A basic examination of numerical abilities in brain-damaged patients should include both verbal and non-verbal aspects of number processing. The following tests are suggested:
There are several ways in which rehabilitation of acalculia is carried out. Tsvetkova proposes using the "number reconstruction" method. It is started by incorporating certain "visual elements (e.g., completing eight, starting from the number 3), looking for certain elements within a number (e.g., looking for the number 1 in the number 4), and finally, performing a verbal analysis of the similarities and differences that can be observed between numbers".Tsvetkova, L. S. (1996). Acalculia: Aproximacion neuropsicologica al analisis de la alteracion y la rehabilitacion del calculo. In: Ostrosky, F., Ardila, A., and Dochy, R. (eds.), Rehabilitacion neuropsicologica, Planeta, Mexico, pp. 114–131. At the same time that these number reconstruction technique is used, spatial orientation exercises, comprehension of the right-to-left relationship, and visual analysis of geometrical objects and forms should be developed.
In a more basic form, the method used was rote practice: the retrieval of simple arithmetical facts through drillGirelli L, Delazer M, Semenza C, Denes G. The representation of arithmetical facts: evidence from two rehabilitation studies. Cortex 1996; 32: 49-66. or through conceptual training,Domahs F, Bartha, L., Delazer, M. Rehabilitation of arithmetic abilities: Different intervention strategies for multiplication. Brain and Language 2003; 87: 165-166. or the creation of strategies for solving concrete problems.Fasotti L, Bremer JJCB, Eling PATM. Influence of improved test encoding on arithmetical word problem solving after frontal lobe damage. Neuropsychological rehabilitation 1992a; 2: 3-20.
Sohlberg and Mateer have said that "treatment should then include exercises that permit spatial analysis and visual motor ability training." Rehabilitation tasks are implemented following a program that progressively increases difficulty, beginning with simple movements designed for reaching for or indicating objects following by copying figures in two dimensions, and concluding with the construction of three-dimensional figures.Sohlberg, M. M., and Mateer, C. A. (1989). Introduction to Cognitive Rehabilitation: Theory and Practice, Guilford Press, New York.
In a case study, Rosselli and Ardila describe the rehabilitation of a 58-year-old woman with spatial alexia, agraphia, and acalculia associated to a vascular injury in the right hemisphere."The rehabilitation was based on the rehabilitation of unilateral spatial neglect and associated spatial difficulties." (Rosselli and Ardila 1996). The patient could adequately perform oral calculations but was completely incapable of performing written arithmetical operations with numbers composed of two or more digits. In a special test of written arithmetical operations (addition, subtraction, multiplication, and division), and initial score of 0/20 was obtained. She was observed to have mixed up the arithmetical procedures and inadequately oriented the columns in mathematical problems.
The rehabilitation techniques implemented included the following:
Individuals with acalculia generally live normal lives, unless there are other disabilities or traumatic injuries present that prevent normal living. Details from a case study published in 2003 described the condition of a 55-year-old woman living with acalculia. "In addition to writing and calculation deficits, both spelling and reading had declined. Lapses of memory occurred occasionally. Despite these deficits, daily living activities remained intact". Another case study published in 1990 described the condition and management of a former female accountant who had "suffered a small circumscribed left parietal subdural hematoma in an auto accident." She was able to speak, read, and write normally, but she was unable to perform simple addition past the number ten. The case study reports that the patient also demonstrated "severe finger agnosia, and in fact the finger agnosia appeared to be directly related to her inability to perform calculations." The patient was somewhat able to manage her acalculia by visiting a therapist who worked with her specifically on finger recognition tasks, especially on finger calculations. This therapy raised her mathematical ability to a high school level after she received treatment for a number of months.Joseph, Rhawn. Neuropsychology, Neuropsychiatry, and Behavioral Neurology. New York: Plenum, 1990. Print.
Henschen's research was consistent with Lewandowsky's and Stadelmann's finding. From his research, he was also able to propose that certain areas of the brain played particular roles involved in the understanding and execution of calculation. These areas include the third frontal convolution (pronunciation of numbers), the angular gyrus and the fissure interparietalis (reading of numbers), and the angular gyrus again for the writing of numbers.
Shortly after Henshen's advances, Berger in 1926 distinguished between primary and secondary acalculia. Primary acalculia is a "pure" condition in which an individual can neither comprehend mathematical concepts nor perform mathematical operations. Secondary acalculia is a loss of calculation abilities that stems from other cognitive difficulties, such as memory. It has been questioned whether primary acalculia can exist independently of other cognitive impairments.
In 1936, Lindquist proposed that lesions of different areas of the brain can cause different calculation defects, and that there are therefore several variations of acalculia.
In 1940, Gerstmann claimed that acalculia is associated with aspects of Gerstmann syndrome, which include right-left confusion, agraphia, and digital agnosia.
In 1983, Boller and Grafman further concluded that calculation difficulties can also arise from various shortcomings, such as the inability to assign value to the name of a number.
Little research has been done on acalculia, despite the fact the calculation is considered an essential, upper-level cognitive skill. However, calculation skills are assessed in neuropsychological exams such as the mini-mental state examination (MMSE). There exist no norms for acalculia against which a person can be compared to assess his/her level of cognitive impairment with regards to calculation abilities.
Epidemiology
"Gerstmann syndrome and similar posterior parietal symptom combinations (like acalculia) are usually the result of focal cerebrovascular disease in a posterior branch of the left middle cerebral artery or a broader zone infarct, usually involving the angular gyrus or subjacent white matter (Brodmann area 39). In rare cases, traumatic brain injury of an expanding neoplasm in this same region can cause all or elements (acalculia is one of four elements) of the symptoms of this syndrome".
History
The term acalculia was coined by Salomon Eberhard Henschen in 1925; it refers to the decrease in cognitive capacity for calculation that results from damage to the brain. Earlier, in 1908, researchers Max Lewandowsky and Stadelmann published the first report of an individual with calculation impairment due to brain damage. The individual had trouble performing calculations on paper and mentally. Further, he had difficulty recognizing arithmetic symbols. The report was key in that it established calculation disorders as separate from language disorders, as the two were formerly associated.
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