Elementary mathematics along with literacy constitute the basic learning that children acquire in the first school years. Mathematical knowledge will allow them to function not only at school but in many everyday life situations. Furthermore, it forms the basis for continuing the acquisition of other more complex knowledge, in case of pursuing long-term studies (Defior, 2000).
By the year 2000, only 57% of 13-year-old Spanish children reached a minimum functional level to meet daily demands and function in current society, or in other words, 43% of these children do not possess this ability at its basic instrumental value. Meanwhile, according to DSM V, around 1% of school-aged children suffer from a calculation disorder, which usually becomes apparent in the second or third year of primary school (Defior, 2000).
The difference between mathematics learning difficulties (MLD) and dyscalculia lies in the fact that the latter is based on a specific learning difficulty in mathematics without other associated problems (Defior, 2000).
MLD, understood as mathematical learning difficulties not associated with intellectual disability or a schooling problem, include the following characteristics (Defior, 2000):
– Discrepancy between expected and actual performance.
– Implies a significant alteration in daily life.
– The difficulty is not due to sensory deficits, low intelligence, or schooling problems.
From cognitive psychology, it is recognized that the remedy for the generalized phobia towards mathematics, so frequent among students, and more specifically, the remedy for MLD, does not lie in finding better didactic procedures, but rather should be sought in teaching that corresponds to the understanding of the cognitive processes underlying mathematical thought and execution (Defior, 2000).
Currently, studies indicate that mathematical competence follows a slow and gradual construction process, moving from the concrete and specific to the abstract and general, and that concrete and manipulative activities with objects constitute the foundation of this construction (Defior, 2000).
It is accepted that elementary mathematical ability can be broken down into a series of sub-skills, among which are numeration, calculation, problem-solving, estimation, as well as the concept of measurement and some notions of geometry (Defior, 2000).
Some principles that must be present in the learning and teaching of mathematics are (Defior, 2000):
– The acquisition of mathematical knowledge considered as an active construction process and not a mere absorption by the subject.
– Prior knowledge plays a crucial role in learning, as it forms the basis for the acquisition and understanding of new knowledge.
– Two types of knowledge are distinguished: declarative, which involves knowing what or the knowledge of mathematical concepts, and procedural, which is based on knowing how or the knowledge of algorithms and problem-solving strategies and when to apply them.
– To achieve full mastery of skills, the automation of procedures is essential. Given the processing limitations of human beings, it is necessary to free up cognitive resources in the execution of mathematical operations, such as basic numerical combinations (3+3, 2×2, 8:2) or algorithms.
– To achieve mathematical competence, it is necessary to apply knowledge in a wide variety of contexts.
– Metacognitive aspects of self-monitoring and guiding one’s own activity constitute another group of highly relevant cognitive processes in competent execution.
– The analysis of systematic errors is a valuable procedure for understanding subjects’ thought processes and strategies, since, as Riviére (1990) states: “they are often the only windows through which we can see the minds of students” (p.116). In this sense, it allows the teacher to detect incorrect rules or strategies that originate from flawed procedures, invented to solve new situations for which they have no answer.
– Finally, from cognitive psychology, the human person is not understood only as an active information processor, but emotions, interests, affections, and social relationships also influence their behavior.
The principles that every teacher should take into account as a guide for action for dyscalculia and MLD are (Defior, 2000):
– Focus on stimulating the learning of relationships.
– Focus on helping children see connections and modify their viewpoints.
– Plan teaching taking into account that meaningful learning requires time.
– Stimulate and leverage mathematics invented by the children themselves or informal mathematics.
– Take into account the developmental level and preparation of each individual.
– Utilize children’s natural interest in play.
ISEP offers the Master’s in Intervention in Learning Difficulties for education professionals who wish to pursue a specialization to perform their professional duties in the classroom with greater confidence and effectiveness. Its objective is to provide teachers with the necessary knowledge to investigate the causes that alter normal learning processes and design intervention strategies with the aim of helping each student give their best.