Types of mathematical procedures

In neuroscience, these are the neural mechanisms that allow our brain to understand and perform mathematical tasks. It is a field of study ranging from the anatomical and functional foundations of numerical thinking and arithmetic calculation, to the disorders that affect these abilities.

Number sense has to do with an ability to determine quantities in the environment, to count elements in space. Experiments in evolutionary psychology and cognitive psychology show that this faculty, at least in its most basic expression, is present in subjects from a very early age. Suggesting that we are born with certain modules prepared for the task of counting, which then become more complex with exposure to learning. Numerical thinking presents common characteristics that depend, in part, on the genetic information of the species:

It proposes that mathematical processing is composed of an input (numerical processing and computational systems), a core of abstract representations with two modules (logographic and phonographic), and an output (product). All this is intervened by a semantic route where the modules are separated.

Primary Mathematical Thinking

Standards in the Educational System – General specifications of the conceptualization and meaning of a national system of educational standards – Basic standards of competencies in the areas – Area of mathematics – five types of mathematical thinking.

The aspects referred to above with respect to the expression being mathematically competent show the variety and richness of this concept for the organization of curricula focused on the development of mathematical competencies in such a way that they involve the different general processes described in the previous section. These processes are closely related to competencies in the broader sense explained above, and even in the restricted sense of “knowing how to do in context”, since being mathematically competent requires being skillful, effective and efficient in the development of each of these general processes, in which each student goes through different levels of competence. In addition to being related to these five processes, being mathematically competent is specifically related to logical thinking and mathematical thinking, which is subdivided into the five types of thinking proposed in the Curricular Guidelines: numerical, spatial, metric or measurement, random or probabilistic, and variational.

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Mathematical thinking

Employed since ancient times for various uses, its application enchanted for centuries great thinkers and philosophers, who, seduced by its depth, considered it a means to obtain an even more human life.

“I believe that the difficulty inherent in the matter adds to the fact that its knowledge is cumulative. It is not the same, for example, as history. You can understand part of world history without knowing the rest; in Mathematics you have to have learned the earlier to learn the later. That is the main problem, because mathematics in itself is not difficult; but for someone who has not been methodical, it gets complicated and creates a psychological situation,” explains Jorge Guier, director of the Department of Pure Mathematics and deputy director of the School of Mathematics at the University of Costa Rica (UCR).

Far from improving, this situation is getting worse; mathematics is not seen as a tool to solve and face problems in everyday life. It seems to be a cultural problem of experts.

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The mastery of knowledge or the development of skills, although necessary, are not enough to advance in the mathematical competence that the Mathematics Program seeks to promote. Other actions are required and that is why five mathematical processes are proposed.

They are conceived as actions or collections of actions that seek to generate higher capacities transversal to all mathematical areas; each process corresponds to a higher capacity. For example: to the process “Communicate” the capacity “communicate”.