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The Euler operator on the space of Lie elements in free Novikov algebra
(SDU University, 2026) Yersaliyeva A.
This thesis is devoted to the study of special subspaces in the free Novikov algebra, namely the spaces of multilinear Lie and symmetric elements. The main aim of the work is to investigate the intersection of these subspaces and to study conditions for recognizing Lie elements in the free Novikov algebra. The first main result concerns the spaces Ln and Tn. Here Ln denotes the space of multilinear Lie elements constructed by means of the commutator [a, b] = a · b − b · a, while Tn denotes the space of multilinear symmetric, or Tortken, elements constructed by means of the symmetrized product a ◦ b = a · b + b · a. Using the differential realization of the free Novikov algebra and the null Lagrangian criterion in terms of the Euler operator, we prove that for degrees n ≤ 7 this intersection is trivial: Ln ∩ Tn = {0}. The case n = 3 is treated explicitly, while the cases n = 4, 5, 6, 7 are verified by computer computations. The second part of the thesis is devoted to the problem of constructing a criterion for Lie elements. We consider an operator associated with replacing the Novikov product by the Lie commutator and then expressing the result in a basis of the corresponding multilinear component. In small degrees, polynomial conditions satisfied by the elements of Ln are obtained. These computations provide the first steps toward a possible criterion for Lie elements in the free Novikov algebra.
Olympiad Preparation as a Factor in Physics Teachers’ Development
(SDU University, 2026) Makhsutbekova A.
Global declines in physics enrollment and shortages of qualified teachers raise serious concerns for physics education quality. While Olympiad programs are mainly seen as boosting student achievement, their role in teacher professional growth remains underexplored. This study examines how Physics Olympiad (PO) preparation affects in-service teachers' content knowledge (TCK), instructional practices, and student achievement. Using a quantitative design, data were collected from 23 Bilim Innovation Schools in Kazakhstan through three sources: Teacher Assessment Tests (TAT), Olympiad Preparation Activities (OPA) across six subdomains, and multi-level Olympiad results. Twenty-three teachers were grouped by performance and analyzed using ANOVA and LSD post hoc tests in SPSS. Teachers fully engaged in Olympiad lesson delivery, planning, and event organization showed significant TCK gains, though effects on student achievement were less consistent. Active participation — particularly in exams and events — was linked to stronger pedagogical competence. These results suggest Olympiad preparation functions as embedded, practicebased professional development, benefiting both teachers and learning environments, and offer evidence for national STEM policy and sustainable teacher development models.
Forecasting educational services in Kazakhstan using time series analysis methods: analysis of the growth in the number of children attending schools and universities
(SDU University, 2026) Turapbay A.
This dissertation develops a reproducible regional forecasting framework for demand indicators for education in Kazakhstan up to 2030. The study considers school enrolment, university enrolment, preschool capacity, technical and vocational education, population dynamics, birth rates and migration inflow at the level of individual administrative regions identified by KATO codes. The key research problem is to make forward-looking quantitative estimates for planning educational infrastructure, but demographic and migration processes vary greatly in the twenty regions of Kazakhstan. The methodology uses four families of forecasting models: Holt's linear trend, damped Holt trend, automatic non-seasonal ARIMA with orders selected by the corrected Akaike Information Criterion and ARIMAX dynamic regression models using lagged birth counts and migration inflow as exogenous demographic covariates. Model selection is performed for each region-indicator pair using three-year holdout cross-validation with mean absolute percentage error as evaluation metric. The empirical results confirm that there is not a single model dominating all regions and indicators. Damped exponential smoothing is effective for stable trend indicators, with ARIMAX specifications being more accurate in areas where predictive demographic covariates exist. Six-year lagged birth counts provide statistically significant leading indicators for school enrolment in several regions and migration in-flow helps explain urban enrolment pressure. The aggregate national forecasts indicate continued growth in total school enrolment and demand for preschool. There is strong regional heterogeneity in the rates of change. The scientific contribution ofthis work is a region-level comparative forecasting pipeline that includes the official demographic and educational statistics of Kazakhstan, uses uniform standards of model evaluation, and generates visual and tabular outputs for planning purposes. The practical contribution is a set of regional forecast grids, model aсcuracy heatmaps, demographic pipeline analyses and summary tables that can directly support school construction, teacher recruitment and higher education capacity allocation decisions.
Creating the Integrative STEM Lesson Unit Plan for 11th Grade Students
(SDU University, 2026) Adilzhan A.
This study investigates the development, implementation, and evaluation of an integrative STEM lesson unit plan for 11th grade chemistry students across three secondary schools in Almaty, Kazakhstan a private school, a state school, and a specialized school. The study addresses three research questions concerning the development of an effective STEM unit plan, its impact on academic performance, and the challenges associated with its integration. Grounded in constructivism, the Zone of Proximal Development, inquiry-based learning, and the 5E Instructional Model, the research employed a mixed-methods design combining a quasi-experimental pre-test and post-test with semi-structured online interviews. A total of 117 students participated in the pedagogical experiment, and 15 chemistry teachers were interviewed. Research instruments were validated by five experts using Kendall's W analysis (W = 0.82 and W = 0.79, both p < .05). Paired samples t-tests confirmed statistically significant improvement in all six groups (p < .05). ANCOVA revealed significant advantages for the experimental group at the state school (F(1) = 9.34, p = .004) and the specialized school (F(1) = 9.14, p = .004). Qualitative findings indicated positive impacts on student engagement, motivation, and 21st-century skill development, while four systemic barriers were identified: infrastructural limitations, curriculum rigidity, inadequate teacher preparation, and student resistance. The study concludes that integrative STEM education has genuine and statistically demonstrable potential to enhance chemistry learning in Kazakhstan, and that successful implementation requires sustained investment in teacher professional development, school infrastructure, and curriculum reform.
Implementation of STEM Projects to Foster Research Competencies in High School Chemistry classes
(SDU University, 2026) Kailarbek A.
The incorporation of STEM (Science, Technology, Engineering, and Mathematics) projects in high school chemistry classes is the most effective way to create research competencies among students. These projects, which are the fusion of science and technology, engineering, and mathematics, give students chances to bring the theoretical knowledge they have learned to real-life situations. The approach is about enhancing different skills such as the development of hypothesis, data gathering, experimental design, and critical analysis of results which are the necessary skills needed for students in the academic and professional fields in the sciences. Through collaborative and problem-based learning activities, that not only deepen their understanding of chemistry but also develop essential life skills such as teamwork, communication, and critical thinking. STEM projects foster active engagement where students can take on the roles of researchers to apply the scientific method to investigate phenomena, test theories, and interpret results. This process creates a more dynamic and inquiry-based learning atmosphere that is on par with the needs of modern scientific research. Additionally, students acquire practical experience with equipment found in laboratories, data analysis tools, and scientific software that they will use later in life. They would learn how to deal with setbacks and reach a positive outcome during the progress of their experiments. Chemistry teachers can employ the STEM integrated approach to arm the students with necessary skills for their future academic learning in the fields of science and engineering. The paper suggests that STEM projects are not only capable of improving the results of students in a course but that they also will furnish them with the challenges and demands of future careers in science.