What types of mathematical thinking exist?
of the Mathematician - the queen of sciences, perhaps, the most exact and caustic science from all which the mankind has on hand. But also here not everything is so simple, apparently, scientists - psychologists came to an interesting conclusion. In the general structure of thinking, according to I. Ya. Kaplunovich`s proposal, it is possible to allocate five crossed substructures - types of mathematical thinking. The dominating type also defines cogitative activity of the person in different practical cases.
Topological thinking. This type appears at the person in the very first turn, approximately in 2 - 3 years. He is responsible for integrity and coherence of logical operations. They are inclined to make continuous transformations with object. In approach to business such principles dominate: it is continuous or broken off, inside or outside, whole or parts. People - topologists do not like to act at random and from a bay - a barakhta. They need to begin always action with the beginning, to grasp a consequence thread, without passing any detail, scrupulously, without hurrying, to bring to the end result. In life topologists are very accurate, live measuredly, on a certain cycle. Quite often they are very conservative, badly get used to innovations. Their main shortcoming: rare meticulousness and sluggishness.
Serial thinking. It is formed in a brain almost at once after topological and is responsible for exact following of logical operations. “ Poryadkovtsam “ unlike topologists, association of operations in a single whole is not important; they love a strict linear order, from initial to final. In activity by it the form and the extent of objects (more or less), their ratio (more to the right, more to the left, above, below), the direction of the movement is important (on or against, up or down). People with such type of thinking seek to follow accurately an order, in any actions try to develop algorithm which depends on some one objective principle. In everyday life absolute poryadkovets are pedantic, seldom depart from the standard rules and always accurately follow instructions.
Metric thinking. This structure rukovodstvut in the person quantitative inquiries. Metrista in business consider as the most important exact mathematical value - figures, figures and once again figures. Always and in everything they try to reduce to concrete sizes and constantly operate with such parameters as width, height, range, the price, quantity, time etc. of Metrista do not love figurativeness and a community - it is difficult to them to present some abstract size which is not expressed by definiteness; they always clearly imagine what will leave as a result of work how many it is necessary to spend and how many you will receive from it. Such people are careful and provident, uncertainty frightens them - until the person finds out thoroughly all details and nuances - will not begin to act.
Algebraic thinking. People with the dominating thinking of this type are born schemers and designers. They constantly seek for representation of object through structural perception. That is, constantly sort and collect a subject, try to build different combinations from parts. Approach the solution of any tasks with a chaotic spirit - begin with that place which is pleasant to them, then jump somewhere in the middle, passing the intermediate stages, and anew come back to the beginning, previously having investigated part which has to finish process. Such people something is difficult to force to do by rules and within. In life they are most often absent-minded, often are late, are inclined to simplify a situation. They see a subject at the same time and entirely and each its part that allows them to find quickly only necessary in this situation.
Projective thinking. the Most difficult of all five. That at whom the structure of this type prevails is inclined to consider a subject from the different points of view, under different corners. He is interested in all options of application of a subject in the theory and in practice. Such person thinks unconventionally, surprises the decisions surrounding with diversity, apparently, of a banal problem. “ Proyektivist “ to seek to find optimum application of any phenomenon, concerns him not characteristics, but degree of applicability and usefulness. In life these people have extraordinary intelligence, love everywhere and in everything to look for benefit, these are excellent ideological leaders who can instantly assess a situation and turn it to the necessary course. The biggest lack of proyektivist is that, considering a subject as not static structure, they forget about absolute characteristics and considerable details.
Certainly, in each person there are at different quantities all these types of thinking. By the way, at most of people the serial thinking is main, prepotent - all this is explained by what at school of all 10 years is trained on this system. Dominants defines many aspects cogitative and, respectively, practical activities. And not only in a mathematics field. Even how the person weeds beds, places objects in the room, puts on, it is possible to isolate information on the prevailing structure though there is a set of simple tests which allow to define it. For example, it is enough to ask the person to describe the room. The Metrist will begin to list quantity of chairs, room dimensions; the topographer will list on groups, at first about chairs, chairs, sofas, and already then about the tape recorder, the computer, phone; the algebraist will just pour out on paper all the thoughts, in any order, jumping from place to place; poryadkovets will pay special attention to an arrangement of objects relatively each other, to their forms and the sizes; and at proyektivist will get the biggest job on volume - he will try to paint application of the most important things of its apartment.
Scientists found out that people with identical types of thinking last to each other as it is difficult to them to understand “ mathematically others “ people. Watch yourself and develop in yourself all types of thinking! Have a good time!