There has been less research into the nature and causes of mathematical difficulties in comparison to some other disorders like reading or coordination disorders. Like in another cases, we have an example of a specific difficulty in acquiring a critical educational skill. The typical developmental pattern for mathematical skills is very complex and hard to understand. We call “dyscalculia” to the impairment of calculation and “acalculia” to the inability to perform calculation (both of them are typical in adult neurology after some damage in the brain).
The Diagnostic and Statistical Manual of Mental Disorders (DSM-IV, APA) defines mathematics disorders as “the mathematical ability measured by individually administrated standardized tests is substantially below that expected, taking in account the chronological age, measure of intelligence and age-appropriate education”.

The typical development of number skills

How do mathematical skills typically develop? The skills involved in arithmetic are complex and diverse. We use different standardized test, for example the Wechler Objective Number Dimensions Test, the British Ability Scales or instrumental abilities test like PROLEC-R, EVALÚA, BANHEVAR (in Spanish) and other scales like DN: CAS (Cognitive Assessment System).
It was proved in the last decade that some primitive numerical abilities are possessed by animals and preverbal human infants (Dehaene, 1997). It is possible to train a chimpanzee to select a physically matching stimulus – to choose half-full glass of liquid matching another glass. Can be that cause of the evolution? Who knows.

The same has been proved with infants. In some experiment held in 1992, Wynn demonstrated how a baby with just 5 months old can notice when we take off a toy. About the surface area and density, children can discriminate between 8-16 dots but no 16-24 dots. So evidence suggests that some basic numerical skills exist in the absence of language. In my opinion this skill is imprecise and basic. It is possible that the humans need more complex verbal skills in order to create “a number sense”. It is possible that humans have a kind of “magnitude system” with which we can judge correctly about the magnitude of numbers. If we have to choose between two pair of digits which one is larger, it results more difficult if the difference between both is short.

The symbolic distance effect shows that we compare the physical size of objects – we access to analogue representations. We have a mental number line represented in our mind, where numbers are arranged from left to right. (Maybe that is the reason why children with laterality problems struggle with mathematics). There is now some evidence that children with mathematics disorder have also problems with non verbal representation of numerical magnitudes.

How we learn to count?

Gelman and Gallistel (1978) defend that humans need to know some principles in order to know how to count. These principles depend of some innate constraints that guide the correct development of effective counting. The principles are the one to one principle, the stable order principle (we need a fixer order 1,2,3…) the cardinality, the abstraction and the order irrelevance principle (the order in which objects are counted has not effect in the outcome).
Even the simplest example of arithmetic (add 2 digits) involves multiple procedures or strategies that a child might use. With the time such computational strategies generate knowledge in long time memory. Some difficulties in older children can result a cause of a lack in basic procedures at an earlier stage. However it is true that exist some genetic influences on mathematic disorder and brain mechanisms involved in arithmetic performance.
In other article we will discuss about the cognitive bases of difficulties in children with mathematics disorder.

Today I have assessed the cognitive processes of a 7 years old girl with high IQ.. I couldn’t avoid to ask her – How did you come up with this conclusion? it made me think about mathematical cognition and how much I learn interacting with people each day.

The mind never stops to amaze me