Continuity in Teaching the Course Algebra and the Beginning of Analysis: Adaptation of Students to New Conditions

Without continuity in education, it is impossible to ensure a high level of academic achievement of students and prepare students for learning at the next stage of education. The continuity of school and higher education is one of the most difficult and still unresolved problems of general education. The urgency of this research lies in addressing the critical gap in continuity between school and higher education, as the lack of a seamless transition in teaching algebra and the beginning of analysis significantly hampers students' academic success and adaptability to university-level education. Recent studies show that the low level of training of school graduates in mathematics causes difficulties in adapting them to subjects in pedagogical universities. The purpose of this work is to develop the concept of continuity in the teaching of algebra and the beginning of analysis in secondary and higher educational institutions and to verify the conditions for its implementation. In the course of the study, a systematic analysis of scientific papers based on the PRISMA method was carried out and a questionnaire method was obtained among students. The results of the impact value analysis of 10 studies (N = 105) published from 2010 to 2024 showed that continuity in learning contributed to the average overall impact value (Es = 2.27, 95% CI [2.015–2.35], p < 0.001) compared to other learning methods. Also, an assessment of the effectiveness of continuity-based learning on the algebra and the beginning of analysis course was carried out based on the results of knowledge surveys. This experiment was conducted in accordance with the academic calendar of the 2022-2023 academic year on the basis of 2 universities and 2 secondary schools in Almaty, Kazakhstan. A total of 86 students who participated in the experiment were divided into control and experimental groups. The conditions for the effective implementation of continuity in higher and secondary education have shown that in experimental groups, students have a high rate of adaptation (Temp = 2.315 > 1.96). The scientific novelty of the research is that it solves the problem of continuity in teaching algebra on a fundamentally new basis - in the context of the "school - pedagogical university" system. The results of the study can be used by teachers of mathematical disciplines at a pedagogical university and teachers of mathematics in secondary schools, which will improve both the quality of knowledge of students in grades 10 and 11 of secondary schools and students of a pedagogical university.