“Numerical cognition is a subdiscipline of cognitive science that studies the neural, developmental and behavioral bases of the use of numbers and the learning of mathematics. It is a multidisciplinary field in which cognitive psychology, development psychology, linguistics and neuroscience participate.”
Numerical cognition is fundamental for our daily activities, it starts early in the infantile development and improves significantly with the appearance of the symbolization thanks to the acquisition of the language and to the beginning of the learning in the classroom. In schooling children learn a wide range of mathematical tools and one of the first and most important is to associate a quantity -four apples- (analog system) with its symbol, a word (four) or a written number (4) (system symbolic). Transcoding between the analog and digital systems is the fundamental substrate of much later mathematical knowledge and the basis for the incorporation by the student of more sophisticated numerical tools.
A curious aspect is that animals also have that approximate sense of quantity, which is called numerosity. If a rat, for example, is trained to press a lever 8 or 16 times, with which it gets a food reward, it is seen that the number of times it is pressed follows a normal distribution with a peak around 8. or 16, the predefined amount. If the rats are hungry, they press the lever faster, but the number of pressures is the same. The numbers also serve to evaluate situations. A research group (McComb et al., 1994) issued a number of roars through a loudspeaker in the African savannah, near a group of lionesses. If you heard three roars and a lioness was alone, it would go away. On the other hand, if he was with four other lionesses, with four sisters, they would approach and explore, indicating that they had an estimated criterion of “when they were outnumbered”.
Numerosity is different from mathematical ability. Numbersity only refers to quantities. The capacity to distinguish the numerosidad varies enormously from person to person, there are those who are closer to reality than others. There are some savants, some of whom have autism, who can see a mountain of matches and know instantly how many there are.
Our brain has a “map” to perceive quantities, numbers. Use it to appreciate, at a glance, how many fish are in a stream or how many fruits in a tree. We knew that our brain includes topographic maps for the primary senses such as sight, hearing or touch, but now we know that there is also a map of numerosity, something that allows a more effective communication between neurons that are dedicated to doing similar tasks.
Studies in monkeys had shown that some neurons in the parietal cortex are activated when animals see a specific number of objects. Ben Harvey of the University of Utrecht and his collaborators worked with volunteers who put them in a functional MRI scanner while showing them patterns of points that varied over time. First they put a point over and over again, then two points repeatedly, then three … What they saw is that the posterior parietal cortex responded in an organized way, small groups of points were represented in one area, while large groups in other. In a way, the brain acted like an abacus, placing numbers in a space. The brain region dedicated to small numbers was wider than that of large numbers, which may explain why the number sense becomes less precise as the number of items increases.
Does numerical learning and the transcoding system produce brain changes?
It is an important question because other topics such as reading and writing do. The answer is yes, flatly, but it is a complex process to measure for the following reason.
Brain maturation progresses in two superimposed levels: on the one hand, a genetic program that follows stage after stage in an orderly and successive way, coded in the genes. On the other, a series of environmental influences that modulate this program and generate changes, sometimes subtle, in others enormously striking. The genetic program generates an explosion of neurons that are then progressively eliminated, in a brutal topping, leaving only those that have established functional connections. It is therefore a non-linear process, with a sudden increase in the number of neurons and a subsequent decrease, and which also continues to show changes at more advanced ages.
Thus, the gray matter shows a loss of density over time, which is related to synaptic pruning during adolescence and early youth. On the other hand, the synaptic plasticity of the brain is evident in early childhood itself and the result of learning programs, such as those that occur in the home and in the classroom, generate an increase in gray matter. It is a specific process and, for example, numerical training produces more important changes in the regions involved in those tasks and in groups specialized in these functions, such as, for example, mathematics students.
Next question and it is not banal is the children who have better numerical learning, have more marked brain changes than those of their peers in which that mathematical domain is lower? The answer is also yes. Lubin and his group (2013) have used a technique called voxel-based morphometry, which allows to measure and study the anatomical differences between different brains in a non-invasive way. They applied this technique in 22 children of ten years of age, who differed in their ability to transcode between the analog and digital systems. The main results were that children with lower numerical ability had a smaller volume of gray matter in the parietal cortex (particularly in the left intraparietal sulcus and bilateral angular gyration) and in the occipito-temporal area. It is known that these regions participate in the transcoding process between the analog and symbolic systems.
What about children who have dyscalculia, the difficulty in learning the principles of calculus caused by a brain problem that hinders the use of the symbolic system?
Magnetic resonance study of children with dyscalculia and controls shows that the former present less gray matter, especially in the parietal and frontal cortical regions, such as the left parietal groove and the middle and lower frontal turns. Those children with dyscalculia who have a deficit in the “sense of numbers” (for example, difficulties in understanding a quantity) present a smaller amount of gray matter in bilateral parietal areas compared to control children. As in the rest of the studies, it is difficult to know whether the smaller gray matter in the “numerical areas” prevents them from performing well or, if it is the other way around, and the little taste for mathematics, the little time spent calculating and other related disciplines generate in a certain way an atrophy of the regions involved in the handling of numbers.
Uniting research in neuroscience with education is a fundamental process to understand how children learn. Neuroimaging techniques allow us to see the brain changes associated with learning and seem a way to achieve a better quality of education and a pedagogy more adapted to the reality, including biological reality, of our children. We can have measurable references, for example, to see if a therapeutic strategy or a specific pedagogical approach is improving the density and extension of the brain areas involved, allowing anatomical evidence to be added to the results of tests and exams. On the other hand, we are still not able to produce direct applications for the classroom, an increasingly clear demand from teachers and teachers and that is sometimes covered by proposals without scientific basis.