In the article, the extent to which problem-based learning (PBL) contributes to the development of students' analytical and conceptual skills in mathematics, physics and English language classes is carried out on the basis of action research, and the results of the research are presented. The purpose of this action research was to contribute to the development of reasoning skills by creating a problem in the classroom. Tasks: implementation of educational goals, use of teaching methods, consideration of individual abilities of students, monitoring of lessons, reflection, re-planning, differentiation. The research was conducted from 2021 until 2023 with the participation of students from grades 9-12, curators, parents, teachers, psychologists. In order to solve practical situations, the student needs to be able to effectively use the previous knowledge and skills formed on the basis of certain laws[1;139]. Therefore, each teacher used practical situations to achieve the expected results. Students, especially with difficulty in analyzing, were considered as experimental and control groups. Innovations of research: implementation of interdisciplinary communication; student's creative work; long-term knowledge retention; 11-12th graders are more inclined to research.

PBL is the principle of differentiation that contributes to the development of students' cognitive and creative abilities. Students search, predict, compare, analyze and conclude while solving situations. Based on research[3], PBL in pedagogy includes three stages: activation of learning, research method, problem-based learning. In 1909 J.Dewey considered PBL as "problem solving" in his book "How I Think". The concept of value is the five stages of reflective thinking, which are: all possible solutions; difficulties in finding a solution; formulation of the problem; the use of assumptions that define observations and data as hypotheses; demonstration of correctness of hypotheses in practice. J.Bruner's concept: the structural role of knowledge in the learning process; the need for the student's readiness to study; development of quick thinking through intuition; the importance of motivation in learning. J.Dewey considers PBL through reflective thinking, and J.Bruner through intuitive thinking. D.Poya, O.Zelts, K.Dunker developed this method and formed foreign pedagogy[3;11-13]. A.M.Matyushkin compiled a model of the problematic situation, presented its conditions and solutions [3;56].

V.Okon considers PBL as a method and pays attention to the stability of knowledge, the development of cognitive interest, and the educational value of it. Taking into account the non-universality of the method, it is intended to be used together with other methods. It is important that it is not immediately after a new topic, but that it leads to the development of the student's cognitive interest in the formation and use of skills[2;69]. M.I.Makhmutov explains:  students' acquisition of new knowledge includes their own, the teacher's explanation, students' reproductive actions, setting tasks, and students' performance[1;299]. H.J.Elaine, K.Goh say that PBL has an impact on the student's long-term retention of knowledge, and the use of it. It is concluded that, compared to traditional teaching, the activity in class increases since they analyze and create[4]. Lerner I.Ya.: having a creative atmosphere in the classroom, PBL requires new and high-quality requirements from the teacher. Therefore, the teacher should master the research situations in their field and master the cognitive methodology[5]. It turns out that this method is effective in activating thinking, and the implementation of PBL organizes a collaborative environment and leads to the planning of teaching strategies accordingly[6]. O.V.Minovskaya clarifies the effectiveness of problem teaching: student's ability to search, analytical thinking skills development; analyze and conclude; acquired knowledge is long-lasting and can be used; confidence is strengthened. K.A.Arapov[6], M.Yu.Soloshchenko[7], R.I.Molofeev[8], S.M.Kaupenbaeva[9], B.M.Utegenova[10], based on the research, reveal the influence, implementation, and effectiveness of PBL in class.

NIS-Programme, which is used in our school, is aimed at the development of critical thinking, the development of functional literacy, in-depth teaching of mathematics and natural sciences, and the formation of trilingual education[11]. Questionnaires were taken from 75 students using Google Forms, conducted conversations with parents, and used reflections of our lessons. The results of the Eysenck test, Gardner's type of intelligence, G.V.Rezapkin's types of thinking and temperament offered by psychologists were effective in the use of differentiation, in the development of tasks and grouping. According to V.Okon PBL in mathematics are: setting a problem, solving it, checking the solution. By using acquired knowledge, checking the correctness of predictions in solving the situation, students can practice the skill of analytical thinking[2;80-85]. A differentiated task was developed for 11th graders to compare the logarithmic function graph using the graph of the exponential function with the graph in Geogebra, and formulate its properties, uses knowledge of angles in space to find angles between lines, lines and planes, and between planes, respectively, through vector and parametric equations. The third stage of solving the problem considered by R.I.Malafeev is the method of checking the forecast, in different ways. There are two main methods: the theoretical concept of prediction; experimental evidence[10;22]: In order to study the problem "The relationship between the potential energy of a spring and its’ use" for the 9 graders, they should first make a hypothesis and perform an experimental test in a group to prove their hypothesis. Innovation: each student in the group presents their ideas, which is effective in providing a theoretical concept of the prediction and determining what equipment is needed. It was evident that for 10 graders PBL is an effective way to enhance language proficiency, including grammatical accuracy, vocabulary development, and pragmatic skills. As Millis[24] suggests PBL can be challenging to implement in the classroom and requires proper preparation. Teachers should consider the proficiency levels, the availability of resources, and the need for scaffolding. It is important to keep in mind that PBL is demanding for the teacher and requires proper planning and preparation. 12th graders make predictions and determine the ways to check their accuracy in performing tasks in physics, provide proofs, conduct experiments, observations, analyze and differentiate the obtained results[8;20]. In this regard, the method of problem-based teaching showed another evidence of its effectiveness in promoting students' academic language learning and development of high-level skills.

The classrooms involved in the study were provided with integrated and traditional lessons. The results of using PBL were higher, than during traditional learning. Through the result of feedback from students "Effectiveness of problem-based learning", it was promoted to increase the learning activity of students, to pay attention to the academic language at its level by searching for information, and creatively increase cognitive interests. Achieving the expected results, we made sure that interdisciplinary connections were implemented, students' confidence increased, and knowledge acquired on the basis of PBL was long remembered. It is clear that the indicator is high during PBL and the tendency of 11-12th-graders to solve the problem when a problemic situation arises. According to the results, we clarify PBL with three conclusions: educational-problematic tasks set by the teacher, which create a problematic situation for students; the use of general methods in learning new knowledge by understanding, accepting and solving the problem; use of appropriate methods in solving specific tasks. In conclusion, we think that using the method of PBL, we have influenced the development of the cognitive interests and activities in class, searching for information individually, in pairs and in groups, predicting, analyzing and drawing conclusions, conducting a small research, and the acquisition of academic language. Disadvantages of the problem-based teaching method: it is not possible to create a problem for all learning objectives; students should have basic knowledge and skills in solving problems; It takes more time to learn new knowledge than other methods. Despite these shortcomings, the PBL method of teaching is firmly established in modern pedagogy. Therefore, we offer the following recommendations: justify the choice of topic or section; systematization of preliminary quality preparation period; development of guidelines; use differentiation during the selection of educational forms.

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