Understanding dyscalculia

DEVELOPMENTAL dyscalculia (DD) is a learning disorder that affects a person’s ability to manipulate quantities. This deficiency is manifested in subjects such as mathematics or wherever number-related skills are required.

It is estimated that it affects between three-six per cent of people (boys and girls) and symptoms usually appear in childhood and often results in people developing an aversion to mathematics from a tender age well into adulthood. They may even display psychological trauma such as fear, anxiety, anger, and even depression when confronted with tasks that involve the manipulation of numbers.

In the Handbook of Mathematical Cognition, Butterworth, B (2005) states that mathematical cognition involves a variety of complex mental activities, such as identification of relevant quantities, encoding or transcribing those quantities into an internal representation, mental comparisons, and calculations.

Working memory encompasses those mechanisms or processes that are involved in the control, regulation and active maintenance of task-relevant information in the service of complex cognition, forming the basis for mathematical intelligence.

The eyes perceive the mathematical task and send the components back to the brain for processing. Short-term memory systems now hold the specifics of the task while it is worked upon. The language locus of the brain then translates the symbols in the problem by connecting with prior knowledge, while long-term memory is activated to solve the problem. The brain then translates the number symbols into an understanding that it represents specific quantities that can be manipulated in a logical manner.

People may have challenges with one or more of these steps, which results in them having difficulties with mathematics. These can be observed in primary school when children display problems counting on fingers with small numbers, especially at an age where that may seem unnecessary.

They may also have challenges identifying small quantities of items just by looking at or performing simple calculations from memory, such as memorising multiplication tables. They may be unable to recognise the same mathematical problem when the order of the numbers or symbols change, understanding word problems or more advanced symbols, or organising numbers by scale.

At the secondary level, symptoms may include the inability to count backward, solve word problems, break down problems into multiple steps to solve them, measure items and quantities, use money to pay for items, and understand and convert fractions.

While the root cause of DD is unknown, there is evidence it may be hereditary. It is known that people with this condition are more likely to have certain differences in some areas of the brain.

These differences may seem to indicate less development and fewer connections between brain cells in those areas. It may also be associated with other learning conditions, such as attention-deficit hyperactivity disorder (ADHD), dyslexia, sensory processing disorders, and autism spectrum disorders. People with DD also have a higher risk of mental health disorders.

According to Price, GA and Ansari, D (2013), writing in Numeracy (Open Access Journals), experts have been able to distinguish between primary and secondary DD where the former is the result of impaired development of brain mechanisms for processing numerical magnitude information, while the latter refers to mathematical deficits arising from external factors, such as poor teaching, low socio-economic status, behavioural attention problems, or domain-general cognitive deficits.

According to the British Dyslexia Association, because mathematics is a hierarchical subject where topics are revisited at a more complex level, if early concepts have not been mastered it impacts later learning. In early learning, children should not just be taught the digit symbol and the name, but also how to form an internal visual representation of that number, which is to see the number as a dice pattern or numicon title.

This will help to establish a good understanding of the relationship between the name of the number, the symbol and its magnitude or size. Children then need to develop number flexibility and know how numbers are made up, for example 6 can be 4+2, 3x2, 5+1, 7-1. That is equivalent to being able to match letters to sounds in learning to read. Thereafter all concepts need to be modelled using concrete materials.

The main cause of failure in mathematics is when symbols have no meaning and children are taught in a procedural way, not understanding what they are doing and therefore not being able to remember the procedure or have the confidence to look for diverse ways to solve the problems. We also need to be careful to use mathematical terms correctly and ensure that their meaning is understood.