Historical Notes

  • Henschen coined the term ‘akalkulia’ in 1919, describing disturbances in calculation associated with brain damage. However, the idea of brain related calculation deficits had been around for nearly a century by then.
  • Gall and Spurzheim in 1808 postulated the idea of a ‘calculation center’ in the brain. When phrenology fell into disfavor, this idea disappeared for nearly a century
  • Stadelman in 1908 published the first detailed report of a calculation disorder resulting from focal brain damage. The patient also had a right homonymous hemianopsia.
  • Hans Berger (1926) described primary and secondary acalculia. Primary acalculia referred to a disturbance in performing calculations specifically, whereas secondary acalculia (the more common of the two), referred to problems with calculations due to more general disturbances in memory, language, attention, etc.

Hecaen’s (1961) Classifications

Hecaen (1961) proposed the first classification scheme for acalculias based on the presumed mechanism of the disorder.

  1. Acalculia associated with alexia and agraphia for numbers. Previously referred to as ‘aphasic acalculia’ (Benson and Weir, 1972)
    1. Associated Features: aphasia (84%), verbal alexia (79%), ideational and ideomotor apraxia (36.5%), constructional deficits (68%), somatognosia (26%)
    2. This type is most often associated with left hemisphere disease.
    3. McCloskey and Caramazza (1987) later subclassified “number processing skills” based on lexical and syntactic systems: Lexical processing involves the ability to read or write individual numbers and syntactic processing involves the ability to combine numbers into the correct form and quantity.
  2. Acalculia of the Spatial Type: Impaired spatial organization results in calculation problems due to misalignment of numbers, reversals of digits, inversions (e.g., 9 for 6) and reversal errors (e.g., 12 is 21). Actual calculation is largely preserved.
    1. Generally associated with more general visual-constructive impairment
    2. Right hemisphere is implicated: This type is ‘rare in patients with lesions confined to the left hemisphere’
  3. Anarithmetria: Deficits in performing the calculation itself. This is consistent with Berger’s ‘Primary Acalculia’
    1. Associated deficits: aphasia (62.5%), visuoconstructive deficits (61%), general cognitive deterioration (50%), verbal alexia (39%), directional confusion (37%), visual field defects (54.5%), oculomotor disturbance (33%), sensory impairment (37%)
    2. Left sided and bilateral brain disease predominate these cases.

Localization of lesions in the Acalculias

  • Inability to read or write numbers strongly suggests left parietal lesion, but does not rule out involvement of the right hemisphere.
  • Alexia for arithmetical signs with preserved reading of numbers and otherwise intact visual recognition is often associated with focal left hemisphere lesions in the parietal or temporal-occipital regions.
  • There is a strong association between left hemisphere lesions and anarithmetria. However, there are cases with right parietal disease that present with anarithmetria. Haecen found that focal lesions in the dominant temporal or occipital lobe were sufficient to cause anarithmetria. Anarithmetria does not appear to be caused by right hemisphere lesion unless the parietal lobe is involved.
  • The spatial type of acalculia suggests a post-rolandic lesion of the right hemisphere, but does not exclude the possibility of bilateral disease.

Gertsmann’s Syndrome

Gerstmann’s Syndrome (agraphia, finger agnosia, left/right disorientation, acalculia) is not associated with any specific type of acalculia. Gerstmann claimed that this syndrome was characterized by an anarithmetria, but others have found that the spatial type and alexia/agraphia for numbers also occur.


Benton (1963) proposed guidelines for assessing number operations. These should be done both orally and in written format:

  1. appreciation of number values/greater than-less than. e.g., which is greater? 23 or 31?
  2. Appreciation of values in written format. Point to the larger number.
  3. reading numbers aloud
  4. pointing to written numbers named by examiner
  5. writing numbers to dictation
  6. copying numbers
  7. counting aloud
  8. estimating numbers of items in a series of continuous vs discontinuous dots
  9. oral arithmetic
  10. written arithmetic
  11. arithmetical reasoning (WAIS Arithmetic subtest)
  12. Immediate memory for calculation problems.

Additionally, one should qualitatively look for specific error types:

  1. substitution of one operation for another (2+3=6 [multiplying instead of adding])
  2. counting for calculation (4+7=8)
  3. perseveration of last digit presented (5×4=24)
  4. giving a reversal of number presented as answer (13+6=31)
  5. Impaired immediate retention of components of problems.