Calculation deficits are a common early indication of Alzheimer disease (AD) (Martin et al., 2003).

Calculation skills include a number of different competencies, such as the retrieval of arithmetic facts, and knowledge and execution of arithmetic procedures. The functional independence of these particular abilities as well as the multiple mechanisms that mediate each of them is evidence of dementia. As stated by a study of Kulason et al. (2016), brain imaging studies pointed out that simple arithmetic operations activate the frontal cortex of the temporal and parietal association cortices (Kawashima et al, 2005, & Uchida and Kawashima, 2008). Solving arithmetic problems is also achieved by many cognitive processes, for example, recognition of visually presented numbers, arithmetic operations, and control of hand movements and the bilateral prefrontal cortices are activated even when solving very simple and easy problems (Earnst et al., 2001).

According to the first systematic report of calculation disorders in dementia by Grafman et al. (1989), acalculia or acquired dyscalculia is the loss of the ability to perform calculation tasks deriving from a cerebral pathology (Girelli & Delazer 2001). Acalculia has been defined as an acquired disturbance in computational ability. The developmental defect in the acquisition of numerical abilities, on the other hand, is usually referred to as developmental dyscalculia (DD) or dyscalculia (Ardila et al., 2002).

The first detailed report of people suffering from calculation disturbances was published by Lewandowsky and Stadelmann in 1908.

Henschen (1925) proposed the term acalculia (akalkulia). He defined acalculia as the impairment in computational skills resulting from brain injury. He proposed an anatomical substrate for arithmetical operations, different from but close to the anatomical substrate for language and musical ability for patients with calculation disturbances without evident language impairments. The third frontal convolution was suggested to represent the center for the pronunciation of numbers. The angular gyrus and the fissure interparietalis were proposed as the brain areas participating in number reading, and the angular gyrus was regarded as the brain structure responsible for writing numbers.

Berger (1926) introduced the distinction between primary and secondary acalculia. Primary or “pure” acalculia resulted from the loss of numerical concepts and to the inability to understand or execute basic arithmetical operations. Secondary acalculia corresponds to the defect in calculation derived from other cognitive deficits (e.g., memory, language, etc.). Also, calculation disturbances could be associated with and dependent upon other cognitive defects, such as aphasia, alexia, and agraphia.

Boller and Grafman (1983) claim that calculation abilities can be negatively affected as a result of different types of defects. They believe that calculation skills can be changed as a result of inability to appreciate the significance of the names of numbers, visual–spatial defects that interfere with the spatial organization of the numbers and the mechanical aspects of the operations, inability to remember mathematical facts and to appropriately use them, and defects in mathematical thought and in the comprehension of the underlying operations.

The calculation ability represents a multifactor skill, including verbal and spatial memory, body knowledge, and executive function abilities (Ardila et al., 2002). However, many investigations indicate its independence from other cognitive functions (e.g., language, memory) and its internal structure, including multiple independent components (Girelli & Delazer, 2001).

In general, acalculia is in a strange position amid the cognitive disturbances met in cases of brain pathology. Thus, there is a general agreement that calculation ability represents an extremely important type of cognition, and calculation abilities are tested in virtually any psychological and neuropsychological assessment (Ardila et al., 2002). Calculation abilities are included when testing for general intelligence (e.g., WAIS-III; Wechsler, 1997) and in most neuropsychological assessment procedures worldwide. Moreover, they are frequently included in the Mini-Mental State Examination (MMSE) (Folstein et al., 1975) and other brief neuropsychological assessment procedures (e.g., Neuropsi; Ostrosky et al., 1997).

Why is it important at the functional level?

Calculation deficits can occur early in the course of Alzheimer disease and can have substantial consequences for everyday functioning (Marson et al., 2000). Simple arithmetic operations activate the three association cortices, including the dorsolateral prefrontal cortex, of the bilateral hemispheres of humans (Girelli & Delazer, 2001). Also, many results suggest that complex computations may tax cognitive systems, such as working memory, in normal cognitive aging as well as in dementia (Martin et al, 2003).

Group studies have mainly emphasized the role of executive function deficits and limited cognitive resources in determining numerical disorders in dementia. Follow-up studies, on the other hand, have allowed the tracing of the orderly dissolution of numerical abilities in dementia, providing insight into their underlying functional organization (Girelli & Delazer, 2001).

Furthermore, calculation is important at a functional level for the daily financial capacity, which is already significantly damaged in mild AD, according to Marson et al. (2000). Recent aging research has suggested the special character of financial capacity as a higher order capacity. People with mild AD demonstrate deficits in more complex financial abilities and impairment in most financial activities. People with moderate AD present severe impairment of all financial abilities and activities. Financial capacity consists of a broad range of conceptual, pragmatic, and judgmental abilities important to the independent functioning of older adults. Financial capacity has been found to be an “advanced” activity of daily life (along with using the telephone and eating), conceptually and statistically separate from “household” activities of daily life (ie, meal preparation, shopping, and light and heavy housework) and “basic” activities of daily life (ie, bathing, dressing, walking, and toileting).

Moreover, the loss of financial capacity has important consequences for patients with dementia and their families. There are also, economic and psychological consequences. People with dementia often have difficulties paying bills and handling basic financial tasks, and they are at risk for making decisions that endanger possesions needed for their own long-term care or intended for testamentary distribution to family members. The media are filled with reports of older adults victimized in consumer fraud and other scams. Finally, loss of financial capacity is associated with important legal issues of competency.

According to the Earnst et al. (2001), working memory may be strongly connected with financial abilities, since many financial tasks require temporary storage and manipulation of numerical and other data. For example, basic monetary skills, checkbook management, bank statement management, and bill payment.


Alterations in this dimension in patients with Alzheimer’s Dementia.

There is evidence that performance in addition and multiplication problems was systematically lower in people with AD and was found to correlate with the severity of the disease (Marterer et al, 1996).

People with AD demonstrate deficiencies in both written and oral arithmetic skills. The extent of the calculation deficits in AD may correlate with dementia severity, and cortical regions associated with calculation abilities indicate degeneration. Calculation abilities in AD may deteriorate in a hierarchical manner, beginning with more complex arithmetic skills and spreading over eventually to more basic operations, although atypical preservation of arithmetic skills has also been noted (Martin et al., 2003).

The findings of Martins study in 2003, support the view that dyscalculia occurs early in AD and progresses. Regarding written arithmetic abilities, people with mild AD had some significantly problems on the more complex single- and multiple-digit multiplication and multiple-digit division problems. In contrast, people with moderate AD showed global impairment on all written arithmetic problems except single-digit addition, and performed inferior to people with mild AD on all problems except single-digit addition and multiple-digit division.

Errors of operation substitution, arithmetic facts carrying and position were observed in the general population of the elderly, while errors of perseveration and borrowing were more frequently observed in AD patients. These results indicate that a wide range of calculation skills, such as arithmetic fact knowledge, progressively deteriorates in AD. There is evidence that, deterioration of procedural arithmetic operations in AD is both hierarchical (by operation) and a function of disease severity (Martin et al., 2003).

The patients at an early stage of the disease had particular difficulties in performing complex calculation procedures as compared to the retrieval of arithmetic facts. The investigation of numerical disorders associated to dementia has mainly concerned numerical transcoding and calculation abilities (Girelli & Delazer, 2001). In line with another study with simple arithmetic, an interesting dissociation between severely impaired multiplication, moderately impaired addition, and significantly better preserved subtraction was observed (Pesenti et al., 1994).

Concluding, various and highly specific numerical disorders emerge in AD. At an early stage, deficits may be limited either to transcoding abilities or to calculation abilities. In both cases they may involve very selective mechanisms or subcomponents. Although, at the general level, the multiple difficulties showed by AD patients may be quantitatively and qualitatively similar to the numerical disorders determined by cerebral focal lesions, few typical error patterns may differentially identify dyscalculia in dementia. The numerical deficits should be considered among the early signs of AD (Girelli & Delazer, 2001).


Serious games appropriate for this dimension.

The serious games recommended to train this dimension are the following:

In addition, Math Research, which is an application forundertaking various arithmetic questions to complete various tasks.


  • Ardila, A., Rosselli, M. Acalculia and Dyscalculia (2002). Neuropsychology. Review, Vol. 12, No. 4, pp 179–231.
  • Berger, H. (1926). UberRechenstorungerbeiHerderkraunkunger des Grosshirns. Arch. Psychiatr. Nervenkr. 78: 236-263.
  • Boller, F., and Grafman, J. (1983). Acalculia: Historical development and current significance. BrainCogn. 2: 205-223.
  • Earnst, K., Wadley, V., Aldridge,  T.  Loss of financial ability in Alzheimer’s disease: the role of working memory.  Aging Neuropsychol Cogn.2001;8:109-119.
  • Folstein MF, Folstein S, Mchugh PR (1975) Mini Mental State: a practical method for grading the cognitive state of patients for the clinician. J Psychiat Res 121:189–198.
  • Girelli, L. & Delazer, M. Numerical abilities in dementia (2001), Aphasiology, 15:7, 681-694 .
  • Grafman, J., Kampen, D., Rosemberg, J., Salazar, A.M., &Boller, F. (1989). The progressive breakdown of number processing and calculation ability: A case study. Cortex, 25, 121–133.
  • Henschen, S. E. (1925). Clinical and anatomical contributions on brain pathology. Arch. Neurol. Psychiatry 13: 226-249.
  • Kawashima R, Okita K, Yamazaki R, Tajima N, Yoshida H, Taira M, et al. Reading aloud and arithmetic calculation improve frontal function of people with dementia. J Gerontol A BiolSci Med Sci. 2005;60(3):380–4. doi: 10.1093/gerona/60.3.380.
  • Kulason, K., Nouchi, R., Hoshikawa, Y.,   Noda, M.,  Okada, Y., and Kawashima, R. (2016). The beneficial effects of cognitive training with simple calculation and reading aloud in an elderly postsurgical population: study protocol for a randomized controlled trial. Bio med. 17: 334.
  • Marson, DC., Sawrie, SM., Snyder, S., McInturff, B., Stalvey, T., Boothe, A., Aldridge, T., Chatterjee, A., Harrell, LE. Assessing financial capacity in patients with Alzheimer’s disease: a conceptual model and prototype instrument.  Arch Neurol.2000;57:877-884.
  • Marterer, A., Danielczyk, W., Simanyi, M., & Fischer, P. (1996). Calculation abilities in dementia of Alzheimer’s type and in vascular dementia. Archives of Gerontology Geriatrics, 23(2), 189–197.
  • Martin, RC., Annis, SM., Darling, LZ., Wadley, V., Harrell, L., Marson, DC. (2003). Loss of calculation abilities in patients with mild and moderate Alzheimer disease. Archivesof Neurology.;60(11):1585-9.
  • Ostrosky, F., Ardila, A., and Rosselli, M. (1997). Neuropsi: Evaluación Neuropsicológica Breve en Español, Bayer, Mexico, DF.
  • Pesenti, M., Seron, X., & Van der Linden, M. (1994). Selective impairment as evidence for mental organisation of arithmetical facts: BB, a case of preserved subtraction? Cortex, 30, 661–671.
  •  Uchida, S. & Kawashima, R. Reading and solving arithmetic problems improves cognitive functions of normal aged people: a randomized controlled study.  Age (Dordr) 2008;30(1):21–9. doi: 10.1007/s11357-007-9044-x.
  • Wechsler, D. (1997). WAIS-III: Administration and Scoring Manual, The Psychological Corporation, San Antonio, TX.