Dyscalculia & the Development of Mathematical Ability

Introduction:

Dyscalculia, or mathematical learning disability, is a specific learning disability, which affects around 6% of the population. Individuals with dyscalculia are not less intelligent than other individuals, but struggle to learn mathematics despite having an adequate learning environment at home and at school. Dyscalculia is assumed to be due to a difference in brain function. Dyscalculia affects individuals over their life span. Children with dyscalculia fall behind early in primary school, and may develop anxiety or a strong dislike of mathematics. In their senior phase of schooling they are likely to struggle to pass mathematics and sciences courses and find their career options very limited. In adult life, they may earn less, and have difficulties managing their everyday finances. This can definitely impact on them as functioning individuals. Knowledge of mathematics is an important aspect for both individuals and for society as a whole. Low numeracy and low literacy skills can cause daily difficulties and aggravation for the affected individual. This can become a handicap or disability, for life. It is a disadvantage to a person carrying out a normal livelihood through employability, and this in turn will reduce lifetime earnings. This will ultimately lead to an unhappy, frustrated individual and this can then lead to depression. Societal norms impose that, improvement in Mathematics and Science performance and achievement has been associated with an increase in gross domestic product (Butterworth et al., 2011). Mathematics is a complex subject involving language, space and quantity. Even simple and straightforward numerical calculations such as arithmetic or counting, involve transcoding between spoken number words and Arabic numerals, relating these to semantic representations of set size (if 1 is added to 2, the result should be 3), and understanding the relations between set size and counting order. Mathematical disorders can affect attention skills, perceptual skills and linguistic skills. Furthermore, certain deficits in mathematical skills, including following sequences of mathematical steps, counting of objects, or learning multiplication tables, may arise. This results in a conceptual difference between “primary dyscalculia”, in which the deficit is a specific inherent abnormality, and cases in which dyscalculia is “secondary” to other cognitive impairments including attention deficits or visual perceptual spatial deficit (Rosenberger, 1989).

Historical background

Phrenological maps from the 19th century included “calculation” and “size” as two of the brain faculties – the first as an aptitude for the understanding of numbers and the second as an aptitude for judgment of proportion and space (Temple, 2006). It seems therefore, that it was understood that at least some mathematical ability was determined in the brain from birth (Temple, 1990). Early reference to dyscalculia was by (Menschen, 1920), (Berger, 1926) and (Gerstmann, 1940). Luria, (1946) noted the fact that dyscalculia is common in cases of diffuse higher cortical function impairment. Developmental dyscalculia (DD) was noted later by (Kinsbourne & Warrington, 1963). Cohn, (1968) was the first to introduce the name “developmental dyscalculia.” These researchers understood that dyscalculia arises from abnormalities of cognitive processes and is the result of a biological dysfunction, and that this entity is reserved to cases in which the deficit is specific and the rest of cognition is completely preserved. Some of the early knowledge of the neural basis of arithmetic skills come from the patients described by Menschen in the 1920’s and the observations by Gerstmann on the effects of damage to the angular gyrus in the parietal lobe of the brain, on calculations. (Menschen, 1920) wrote, “The calculation ability is a highly composite cerebral function that results from the collaboration of various posterior areas of the left hemisphere”. Gerstmann and others found that left parietal damage causes deficits in calculation, and damage to the left angular gyrus disturbs the neural representation of fingers, causes right – left confusion, and agraphia (a tetrad known as Gerstmann syndrome). Disturbances in the ability to perform calculation tasks, known as acalculia or acquired dyscalculia was observed and determined through observations of patients that acquired brain disease or brain damage (i.e. brain tumours or strokes). A structural lesion to parietal areas in infants, leading to severe arithmetic deficits, is seen in children born prematurely. Decrease in parietal grey matter density in these premature babies is associated with lower math performance at the age of 15 years (Isaacs, Edmonds, Lucas, & Gadian, 2001). It has been more of a challenge to determine that a developmental defect in the acquisition of numerical ability, known as developmental dyscalculia (DD) exists and is the outcome of brain dysfunction for this ability. However, as is the case with reading disabilities, cumulative genetic, neurobiological, and epidemiological data indicate that DD arises from abnormalities of cognitive processes and is the expressions of a biological brain dysfunction (Kucian et al., 2006).

Development and mathematical skills

The development of knowledge and mathematical skill consists of early numerical skills that are intrinsic and inherent and exist without learning and more complex skills that are attained and learned. Young infants and animals process biologically determined, domain specific number concept and numerosity including relational concepts such as more, less and the ability to arrange objects according to size, as well as simple counting skills. Studies in animals of a behavioural nature reveal number perception, discrimination and elementary calculation abilities in chimpanzees, proving that a sense of numerosity even exists in animals (Kawai & Matsuzawa, 2000). Basic numerical skills are probably innate and develop in infants without formalized schooling. In the first week of life, infants seem to discriminate visual arrays on the basis of numerosity. Precursors to the acquisition of formal mathematical skills are developed in preschool years of children. Number concept refers to relationships such as more, less and the ability to arrange objects according to size. Development can be seen in terms of an increasingly enhanced and sophisticated understanding of numerosity and its implications, and an increasing skill in manipulating numerosities. The impairment in the ability to learn arithmetic - dyscalculia – is, in many cases, a weakened area or deficit in the child’s concept of numerosity (Butterworth, 2005). Toddlers can add and subtract numbers up to three. At 3 to 4 years they can count up to four items, and by 5 years, up to 15 items. Four-year-old children can use fingers to aid adding. Five-year-old children can add small numbers and are able to count out sums. Eight year olds can recognise arithmetic symbols, and perform + & - exercises, and division is acquired at 9 to 12 years of age.