Planet of Thinking

Плюси та мінуси української математичної освіти. Прямий ефір з Ольгою Гісь,
автором курсу з розвитку продуктивного мислення учнів початкової школи.

In the Era of highly developed technologies, when knowledge requires constant renewal and updating, the question how to educate school children in order to prepare them for such a rapid tempo of life, becomes extremely important.


If we explain to children everything in details and do not allow them to seek the truth themselves, we can at best develop the so-called reproductive thinking. Now a days much attention is paid to the reproductive character of modern education (problem 1). General educational programs are targeted at the acquisition of a certain amount of knowledge and its reproduction. Children get “ready” knowledge and therefore lose independent and creative approach to learning. However, it is much more important to teach children to think and to learn than to provide them with certain knowledge. The attention of educationalists and psychologists is now getting focussed on searching new and more effective forms of learning, which can enhance children’s creativity and develop the so-called productive thinking (the ability to produce ideas). It has been amply shown that productive thinking develops when children solve unusual tasks, and when they look for new approaches and independently explore the surrounding world.


Logical thinking is characterised by the ability to analyse, to evaluate, and to sort information. But this is not enough for productive thinking. Current school programs are mostly concentrating on the development of logical thinking and do not pay enough attention to children’s creative thinking. It is necessary to develop the skills to produce new ideas, to think originally and courageously, to see a problem holistically in order to think creatively. It is quite likely that the harmonious development of a person requires the integration of both types of thinking, and this is problem 2, which needs to be addressed.


To find the solutions to these problems, national programs for the development of children’s productive thinking and appropriate abilities are being elaborated in some developed countries. Very interesting investigations were carried out in USA, Singapore, Finland, and Japan. New educational technologies are based on the latest research in the field of cognitive psychology, in particular, heuristics, which reveals subtle mechanisms of the cognitive activity of humans. We can also mention here the theory of “trials and errors” elaborated by American psychologist-behaviourist E. Thorndike, and the idea of productive thinking and principle of integrity of perception formulated by well-known gestalt psychologists M. Wertheimer, F. Keller, K. Koffka, and J. Levine. A tangible contribution has been made by gestalt psychologist K. Duncker who put forward the idea of functional fixation of human thinking on the properties of an object or a situation.


An interesting idea has been expressed by Scandinavian psychologist L. Sekey who has shown that the process of productive thinking consists in revealing hidden, latent properties of objects. The Test of Remote Associations (RAT) suggested by American psychologist S. Mednick is most widespread in the investigations of creativity as a type of thinking. American scholars J. Guilford and E. Torrance are also considered to be leading researchers in the field of investigation of creative thinking. The characteristics of creativity, based on J. Guilford’s research, are most widely used in practice. These characteristics include such parameters as easiness, flexibility, originality and accuracy of thinking, and also imagination. Based on the tests proposed by Prof. E. Torrance, the following four generalised indicators of cognitive activity are calculated: speed, flexibility, originality, and degree of detailed elaboration. Also of interest are the investigations of American scholars M. Wollach and N. Kogan who modified and improved research of their great predecessors. The problems of intellect were also considered by H. Y Eysenck and H. Steinberg. D. Wechler’s test on the level of intellect, which introduces the notion of intellect as a structural transformation, became world famous. The ideas of the founder of the brainstorming method, Alex Osborn, are also being successfully implemented. There is an idea of lateral thinking (structured creativity), a term coined by Edward de Bono, the leading proponent  of the deliberate teaching of thinking in schools.


These and other fruitful ideas laid the foundations of my research in the field of new educational technologies. I dedicated more than 10 years of my research and pedagogical activity to the following problem: how to teach children to think and to be creative? Nowadays at school thinking skills are formed rather spontaneously and there exists no subject that would straightforwardly teach children to think both logically and creatively. It is known that basic thinking structures are already formed by 10-12 years, and that is why it is necessary to start developing creative and cognitive abilities of children as early as possible, since their late formation becomes less effective. Taking this into account, I developed and implemented a teaching program on logic and non-standard thinking for pupils of elementary school. This is an integrated course, elaborated at the interface of logic, mathematics, and psychology.


The program is oriented at the development of the main aspects of cognitive activity and aims at stimulating children’s thinking, teaching basic operations of thinking, developing quick-wittedness, spatial imagination, memory, and attention. It takes into account the development of basic aspects of thinking on both verbal and non-verbal levels. The tasks: to form children’s ability to analyse and synthesise, generalise and concretise, abstract and transfer, classify, compare and single out most essential, think by analogy, see differences and regularities, find cause and effect relationships, and also to develop the skills to think by association and to search for non-standard approaches to solving problems. The program preserves the principle of spirality and cyclic recurrence.

The important feature of the program is its orientation at the achievements of modern psychology. The course aims not only at the diagnostics of a certain level of intellect but rather at the development of cognitive abilities of pupils. Many tasks prepare pupils for tests, which, as generally known, are actively used in many developed countries of the world (GRE General, etc.).

This course has been implemented as an experimental subject at Lviv first-level school “Dzhereltse” for 9 years. It is also taught at other schools of Lviv, Kyiv and other cities of Ukraine. By 2007, more than 600 children only at “Dzhereltse” school had taken this course.


My experience has been generalized in five textbooks on the development of logical and creative thinking for pupils of 1-4 grades. The program and textbooks were supported by the Ministry of Education and Science of Ukraine. These books have won a number of top awards in international publishing fora in various nominations.


In 1999, the Psychology Department of the National University of Lviv conducted a comparative test of the cognitive development level of the children from the experimental school (where the subject “thinking” had been taught for 2 years) and an ordinary school (called a Control one), where such a subject was not implemented. The result of the test showed that the logical thinking of children from the experimental school was twice as developed as that of the children from the Control school.

It is evident that the creative heuristic thinking of the children of this age group can be developed most successfully, since its indicators appeared to be 4.5 times higher than those of the children from the Control school. Based on the results obtained, the cross co-relational analysis according to Pearson was conducted and co-relational sets were built that demonstrated an interconnection between different types of thinking. It was brought out that teaching “thinking”, increases the integration of different types of thinking and promotes their interdependence and mutual influence.

Home  |  News  |  Підписка на новини  |  About the author  |  Where to buy  |  Site map  |  Support

All rights reserved.

© "Planet of Thinking"