METHODS OF COOPERATIVE LEARNING AND THEIR APPLICATION IN THE DEVELOPMENT OF COMPETITIVE THEMES IN TEACHING MATHEMATICS
Authors:   Elementary school ”Žika Popović” Vladimirci, Serbia, Ilić Desa , Rešić Sead ,   Department of Mathematics, Faculty of Sciences, University of Tuzla, Bosnia and Herzegovina
Published: September 2021

Contemporary changes in the whole system of education and training require the teacher to be a person of trust, educator, counselor, friend, organizer, coordinator, associate, innovator, assessor, mentor; in another words, a contemporary and modern person. In the modern school (even more in the future) the role of the teacher is far wider. He needs to be active in school, outside of school, within free activities, as well as cultural and public activities of the school. A good teacher does not resist the influence of a student, because his or her extremely responsible role can be successfully achieved, if they work well with them. To cooperate in this context does not mean that only the teacher listens to the student's suggestions, although that is also very important, but cooperating means accepting the student's proposal, if they are objectively acceptable or explain why a particular proposal cannot be realized. It is not possible to work well and democratically in the classroom if the student's influence is not accepted. If the teacher's behavior and style of work are not necessarily limited to the work and behavior of a student, then there is no interaction, and the teaching process must be an interaction. Changes in the society affect school changes, and changes in school play the most important role in changing the position of the teacher and his role and the style of work in the teaching process. The survival and future of the school is reflected in its educational role. In order for a teacher to be an educator, to fulfill his or her educational role, he/she must love or sympathize with the kids, respect their opinion, encourage them to achieve good results, but also to share with them possible misunderstandings and failures. The success and superiority of teachers as educators depends more on the quality of the relationships established, and less on the knowledge of the subject being taught, even though this component cannot be ignored.Thanks to the good work style, the teacher can achieve better results in the educational process. This does not only apply to the choice of working methods, but the style of work is reflected in the overall individual pedagogical practice of teachers. In the style of work the teacher expresses his / her independence, creativity, initiative, democracy or authoritarianism, lack of competence, irresponsibility. In modern school, children need to play a central role, and the school should become a place where they are exploring, examining, solving problems and to lead them to a deliberate dialogue. Students need to experience the school as a place where the child develops in cognitive, emotional and social sense, and where the child's motivation to work is at a high level. Active teaching (active learning, active school) is an original pedagogical creation based on theoretical settings and practical attempts of transformation of a traditional school into an active school, i.e. a school in which both the student and the teacher have an active role. Thinking about active learning is inspired by the works of Kerenstahner (work school), Laj, Dekrol (school for life and life), Klapard (school by sea), Djuij (pragmatic conception), Montesori, Fereira (active school) Frenoa, Dalton plan, Vinteka-plan, etc. The summary of their research endeavors and theoretical endeavors, aimed at constituting an active school, is the following Piaget's statement, which for active teaching has an absolute programmatic meaning: "In one of the words, the basic principle of active methods should be inspired by the history of science and can be expressed in the following way: Something means self-discovery or reconstruction through re-discovery and it is necessary to adhere to that principle if in the future we want to shape people who will be capable of producing and creating and not just repeating what already exists. " To reach a comprehensive and precise concept of active learning, the activity of children in the learning process is of paramount importance. From the cited Piaget's theoretical point of view, for the active learning, three are very important elements: An important component of activity as an internal (mental) activity is defined: this activity (or at least one of its, important for school learning) is the passage through the intellectual processes through which it came to science when it came to discoveries and finds. So, the student briefly reconstructs these thought processes; The object of thought activities is not only their own immediate experience but also the intellectual content of certain scientific disciplines; The basic goals of school learning through active methods are: a good understanding of what is in science but also the adoption of intellectual arts for productive and creative activities. The traditional school works on pre-defined plans and programs and the goal of the curriculum is to adopt the program. The basic teaching method is the lecture (verbal transfer of knowledge) with the occasional use of teaching resources. The student has a mostly passive role of a listener who has to understand, remember and reproduce the compulsory material. Evaluation, whether verbally or in writing, consists in verifying the measure in which the required degree has been adopted. Learning motives are largely external to nature (appreciation, praise, reward, punishment ...) In a traditional school, the child is looked upon as a pupil, that is to one who should, with understanding, repeat the course more profoundly. An active school is more focused on a young man who is treated as a whole person whose intellectual potentials need to engage more in the teaching process. The active school is based on compulsory education standards based on which the orientation plans and work programs are designed. Such access also implies a part of teaching that is flexible and varies depending on the student's interest. Learning motivation is personal (internal). In teaching, active learning methods are based on work and intellectual engagement of students and research activities. The goal of an active school is not only the adoption of a curriculum, but also the versatile personality development of students. The active school evaluates not only the degree of competence of the knowledge defined by the educational standards, but also the progress of the children in comparison with the initial situation, the motivation and interest of the students for work and activity, the development of the personality and the satisfaction of the student's teaching that is realized.