Among the research skills of students, analysis and synthesis, and the weakness of the justification of the method or the answer used in the performance of the assignment when writing papers in natural subjects, are the most common problems. This, in turn, indicates that students experience difficulties in solving problems assigned to high-order thinking skills. In this regard, after considering the theoretical materials on pedagogical methods and tools that develop analysis and synthesis skills, it was planned to study the effectiveness of the "algorithmization" method among high school students according to age characteristics.The problem of this study is based on "The development of analysis and synthesis among students by the method of "algorithmization". The study aims to conduct experimental classes to complete tasks using the "algorithmization" method in mathematics lessons for high school students and to determine how this method influences the development of their analysis and synthesis skills. The study concludes that the method of "algorithmization" affects the systematization of students' thoughts and the development of analysis and synthesis skills.  In order to use the "algorithm" method in the classroom, students learn new material in advance, study various methods related to the mathematical model of the task or problems, take into account all variables, quantities, and parameters, link the stages of solving the problem in a logical sequence. Shaikina and Sapozhnikova (2016) writes that "the involvement of students in the creation of an algorithm is, in turn, a variant of heuristic learning". Shaikina and Sapozhnikova (2016) writes that "the involvement of students in the creation of an algorithm is, in turn, a variant of heuristic learning". Temerbekova (2019) shows a connection between the "algorithm method" and analysis and synthesis (p.214). Blinova and Vasilyeva (2014) state that this method affects the individualization and strengthening of the learning process in accordance with the modern education system.. Pushkareva et al. (2017) reveal the need for the "algorithm" method of high school students for their future professions since "A modern engineer needs to have high potential cognitive abilities, including algorithmic thinking, to solve complex technological and professional problems". In traditional classes, the teacher shows the steps for solving an algorithm or problem and pays attention to the student's correct execution of these algorithm steps. This is called algorithmic learning. A peculiar feature of the method in this study is that the student creates an algorithm for the general situation while performing various tasks. The difference between algorithmic learning and algorithm creation is that the first method encourages students to perform a particular method step by step like a "robot" without thinking. In contrast, the second method aims at the student's creativity. This study, in the form of action research, allowed us to get answers to questions such as "What is the effectiveness of using the "algorithmization" method, which develops the skills of analysis and synthesis, influencing the development of student's skills and abilities, and what are its effective and ineffective sides?" The research hypothesis was that the algorithmic method positively impacted the development of students' analytical and synthesis skills. 

The object of the study is the 12th-grade students who studied in the school in the years 2020 and 2023. The research project employed the study of a series of mathematics lessons within the framework of a qualitative paradigm as a methodology. In a series of lessons, students were offered tasks as experiments: creating algorithms, supplementing algorithms by filling in the missing parts, analyzing created algorithms, and determining an effective template algorithm from them. The results of previous classes and student achievements were considered when planning a series of lessons. This, in turn, has made it possible to adapt the use of the "algorithmization" method to the students' individual abilities. The series of classes included the topics of "the argument and the module of a complex number," "the differential equations," "the geometric interpretation of complex numbers," and "the modeling processes using differential equations." For example, when finding the argument of a complex number, students were tasked with finding different algorithms for different cases, depending on the location of complex numbers in different quarters. The data collection required for the study included systematic observations, interviews, videos, and student test scores. These methods have made it possible to collect a wide range of data for analysis and evaluation. Written tests were taken to determine the levels of analytic and synthetic activity skills of students before and after the experiment. These works were evaluated using criteria and indicators that determine the levels of analytic and synthetic skills [taken from 6th literature source], which made it possible to determine and compare the levels of students' skills. The tasks were designed with a focus on indicators of analytic and synthetic activity skills, i.e., "breaks the whole into parts, creates a connection between the parts of the whole, builds a whole from parts, finds an error and explains its cause."

The first research question is "How effective is "algorithmization" in developing students' analytic and synthetic activity skills? The answer to the question: "Algorithmization" tasks have contributed to developing students' analytic and synthetic activity skills. The results of the control work obtained before and after the experiment show that there was an increase in the indicators of "breaks the whole into parts, creates a connection between the parts of the whole, finds an error and explains its cause," but not the "builds a whole from parts." The student interviews conducted at the end of the learning experience cycle, their written work, and an analysis of lessons in each cycle allowed us to answer the second research question. The benefits of "algorithmization" methods are: - The increase of interest for students who love computer science or programming; - effectively organizes the tasks for "algorithmization" at the stages of generalization and conclusion; - effectively transforms "algorithmization" tasks and differentiates them depending on the abilities and interests of students. Ineffective points: - not all students are interested in the method; - it is impossible to use for any topic and learning objectives; - there are almost no tasks for the "algorithmization" method in mathematical didactic tools; - it takes substantial time in class. The "algorithmization" method affects the systematization of students' thoughts and the development of analytic and synthetic activity skills. Due to the time the "algorithmization" method takes, creative tasks can be provided to the students as a supplement. These findings result from an experiment on 12th-grade NIS students drawn from two classes. The teachers who researched the "algorithmization" method said, "This method has a positive impact on the development of analytic and synthetic activity skills."

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