PSY 2C 08: BRAIN, BODY AND
UNIT–I: BRAIN AND BEHAVIOUR
Acalculia is an acquired impairment in which people have difficulty performing simple mathematical tasks,
such as adding, subtracting, multiplying and even simply stating which of two numbers is larger.
TYPES OF ACALCULIA
Henschen introduced the term "acalculia" to refer to the impairments in mathematical abilities in patients
with brain damage (Henschen 1925 ). Berger distinguished 2 different types of acalculia: primary and
secondary acalculia. Secondary acalculia refers to calculation defects resulting from a different cognitive
deficit: memory disorders, attention impairments, language defects, spatial deficits, etc. ( Berger 1926 ).
Gerstmann proposed that acalculia is observed together with agraphia , disorders in right-left orientation,
and finger agnosia , representing the basic brain syndrome usually known as "Gerstmann syndrome"
(Gerstmann 1940 ). Gerstmann syndrome has been associated with left angular gyrus damage (Vallar 2007
). It has been proposed that Gerstmann syndrome represents a disorder in the spatial representation of the
body-scheme and mental rotations occurring after left parietal damage ( Gold et al 1995 ).
Hecaen and colleagues distinguished 3 major types of calculation disorders: (1) alexia and agraphia for
numbers, (2) spatial acalculia, and (3) anarithmetia ( Hecaen et al 1961 ). Alexia and agraphia for numbers
represent calculation disturbances resulting from difficulties in reading and writing quantities. Spatial
acalculia represents a disorder of spatial organization where the rules for setting written digits in their proper
order and position are not followed; spatial neglect and number inversions are frequently found in this
disorder. Anarithmetia corresponds to primary acalculia. It implies a basic defect in computational ability.
Boller and Grafman considered that calculation abilities can be disrupted as a result of: (1) inability to
appreciate the meaning of the number names, (2) visuospatial defects that interfere with the spatial
arrangement of numbers and the mechanical aspects of mathematical operations, (3) inability to recall
mathematical facts and appropriately use them, and (4) defects in mathematical thinking and in
understanding underlying operations ( Boller and Grafman 1985 ).
Ardila and Rosselli have proposed a classification of acalculias (Ardila and Rosselli 2002 ). A basic
distinction between anarithmetia (primary acalculia) and acalculia resulting from other cognitive defects
(secondary acalculias) is included. Secondary acalculias may result from linguistic defects (oral or written),
spatial deficits, and frontal-type disturbances, particularly perseveration , memory, and attention
impairments. However, there is a certain degree of overlap among the acalculia subtypes proposed by Ardila
and Rosselli. Thus, in anarithmetia some spatial deficits can be observed. Spatial acalculia associated with
right hemisphere pathology is also partially an alexic acalculia (eg, some inability to read complex numbers
as a result of left hemineglect can be observed). Even though arithmetical calculation is a rather complex
cognitive activity requiring the participation of many elements, brain damage may result in a relatively
restricted disorder. Rosca reported a patient with preserved arithmetic facts but impaired procedural
knowledge ( Rosca 2009b ). Klessinger and colleagues studied a 56-year-old retired university professor
suffering a vascular lesion in the left middle cerebral artery territory with extensive damage to perisylvian
temporal, parietal, and frontal cortices, resulting in right hemiplegia, severe aphasia, and apraxia of speech.
Regardless of the severe language disturbance and his difficulties with processing both phonological and
orthographic number words, he demonstrated largely intact algebraic fact knowledge, procedures, and
conceptual knowledge; this case illustrates that some aspects of mathematical processing can be preserved
despite severe disruption to the language ability (Klessinger et al 2007 ).
LOCALIZATION OF LESSIONS IN 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.
SIGNS AND SYMPTOMS
Calculation impairments include the inability to perform simple mathematical operations, such as addition,
subtraction, division, and multiplication.
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: 1) understanding that
every number represents a value and immediately registering this value, 2) recognizing a number's value