T.L. Melekhina1, A.Yu. Vladova2

1, 2 Financial University under the Government of the Russian Federation (Moscow, Russia)
1 tmelehina@fa.ru, 2 ayvladova@fa.ru

In modern higher education, especially in the field of economics and finance, the formation of a holistic set of analytical and quantitative competencies among students is of particular importance. The effectiveness of this process largely depends on the continuity of training courses, when the knowledge and skills acquired at the initial stages serve as a solid foundation for mastering more complex, applied disciplines.

The presented research, carried out on the basis of the Financial University, is devoted to a critical assessment of such continuity within the block of mathematical and analytical disciplines. An analysis of the academic performance of a large cohort of students (2,000 people) for the 2023–2025 academic years allows us to obtain objective data for improving the educational process. The study is based on a comprehensive statistical analysis of data on students' academic performance. The focus is on the courses "Mathematics" and "Digital Mathematics" (first year of study), "Computer Workshop" (2023–2024) and "Data Analysis" (second year, 2024–2025). The methodological apparatus of the work includes: Descriptive statistics and visualization: The construction of histograms and scatter plots for the primary analysis of the distribution of scores and visual assessment of the links between disciplines. Correlation analysis: The use of Pearson and Spearman coefficients to quantify the strength and direction of the relationship between the results of different courses. Testing statistical hypotheses: Using nonparametric criteria such as Kolmogorov-Smirnov to compare distributions and the Wilcoxon (Mann-Whitney) U-test to identify differences in average exam scores. This multi-level approach allows not only to state the facts, but also to assess their statistical significance.

The analysis revealed a number of important and ambiguous patterns. The presence of selective continuity: A moderate positive correlation was found between the final scores in the basic course "Mathematics" and the subsequent "Data Analysis". This indicates that the general academic discipline and diligence of students shown throughout the course are a significant success factor in mastering more complex material.

Weak correlation of exam results: At the same time, exam scores in the same disciplines show only a weak correlation. This paradox suggests that the final score, which includes current work, homework, and projects, better reflects the accumulated competencies than a one-time exam. Statistically significant difference in difficulty: The Wilcoxon test confirmed that the average exam scores for courses differ statistically significantly. This may indicate a higher level of exam difficulty in some disciplines compared to others.

Problems of motivation and perception: In addition to statistics, the study revealed substantive problems. Students often do not see a clear logical and practical connection between the courses studied sequentially. This leads to a decrease in internal motivation and a formal attitude towards the study of "basic" disciplines, which ultimately negatively affects the preparation for applied modules.

Based on the results obtained, the authors formulate specific proposals for optimizing the educational process. Strengthening program continuity: Developing coordinated work programs where subsequent course lecturers explicitly refer to specific topics and skills acquired earlier. Support system: Creation of mechanisms for timely identification and additional support of students who showed poor results at the initial stage in order to prevent their "lagging behind" in the future. Improvement of teaching and assessment methods: Revision of the exam format towards a more practice-oriented approach, as well as the introduction of end-to-end projects into the educational process that clearly demonstrate the relationship between mathematics and data analysis methods. Overall, the study provides a compelling basis for a data-driven approach to modernizing educational programs aimed at improving the quality of training for future financiers and analysts.

Melekhina T.L., Vladova A.Yu. Educational trajectories under the control of statistics: identification of trends and patterns. Neurocomputers. 2025. V. 27. № 6. P. 96−106. DOI: 10.18127/j19997493-202506-10 (in Russian).

1. Kolesnik N.V. Obrazovatel`ny`e traektorii rossijskoj e`lity`: regional`naya proekciya. Mir Rossii. 2019. T. 28. № 4. S. 30–48. DOI: 10.17323/1811-038X-2019-28-4-30-48.
2. Val`ko D. V., Filippova A.M., Bunina M., Kozlova M., Vasilevskaia M., Rud D. Educational and Career Trajectories in Russia: Introducing a New Source and Datasets with a High Granularity. Research Data Journal for the Humanities and Social Sciences. 2024. P. 1–14. doi: 10.1163/24523666-bja10046.
3. Yacevich O.E., Speranskaya N.I., Omelaenko N.V., Yudashkina V.V., Shabatura L.N. Realizaciya individual`ny`x obrazovatel`ny`x traektorij v vy`sshix uchebny`x zavedeniyax.  Vy`sshee obrazovanie v Rossii. 2024. № 5. P. 150–168. doi: 10.31992/0869-3617-2024-33-5-150-168.
4. Dinecz D.A., Mixajlova N.S. Vozmozhnosti individualizacii obrazovatel`noj traektorii dlya licz, imeyushhix srednee professional`noe obrazovanie, pri prodolzhenii obucheniya v vuze. Texnik transporta: obrazovanie i praktika. 2023. Vy`p. 4. № 3. S. 266–272. doi: 10.46684/2687-1033.2023.3.266-272.
5. Lindenbaum T., Belyaev A., Grebenyuk E., Kramarov S.O., Xramov V. The method of identifying a person in formation of an educational trajectory. Lecture notes in networks and systems. 2023. P. 1323–1332. doi: 10.1007/978-3-031-21219-2_148.
6. Maheshwari A., Malhotra A., Hada B.S., Ranka M., Basha S.A. Comparative analysis of machine learning models in predicting academic outcomes: Insights and implications for educational data analytics. International Conference on Smart Systems for applications in Electrical Sciences. 2024. P. 1–7. doi: 10.1109/icsses62373.2024.10561260.
7. Khamzatova E.A., Akieva Z.M., Shakhdullaeva K.D. Assessing the quality of education using big data and analytics. Ekonomika I Upravlenie Problemy Resheniya. 2024. V. 11/14. № 152. P. 183–188. doi: 10.36871/ek.up.p.r.2024.11.14.023.
8. Saeedi S., Božanić D., Safa R. Strategic analytics for predicting students’ academic performance using cluster analysis and bayesian networks. Education Science and Management. 2024. V. 2. № 4. P. 197–214. doi: 10.56578/esm020402.
9. Vladova A.Yu. Formirovanie gruppovoj i individual`noj traektorij uspevaemosti po danny`m e-learning platform. Upravlenie bol`shimi sistemami. 2024. Vy`p. 111. S. 179–196. doi: 10.25728/ubs.2024.111.7.
10. Vladova A.Yu., Borchyk K.M. Predictive analytics of student performance: Multi-method and code. Journal of Research and Advances in Mathematics Education. 2024. V. 9(4). P. 190–204. doi: 10.23917/jramathedu.v9i4.4643
11. Melexina T.L., Pozdeeva S.N. Upravlenie znaniyami v universitete kak metod e`ffektivnogo ispol`zovaniya resursov. Baikal Research Journal. 2025. T. 16. № 1. S. 241–250. DOI: 10.17150/2411-6262.2025.16(1).
12. Melexina T.L., Kochetkov A.A. Cifrovy`e texnologii kak faktor povy`sheniya e`ffektivnosti obucheniya v vy`sshej shkole. Problemy` teorii i praktiki upravleniya. 2025. № 7. S. 91–102.
13. Melexina T.L., Vladova A.Yu. Xeshirovanie dlya obezlichivaniya danny`x obrazovatel`noj platformy`: prakticheskie resheniya v MSExcel. Innovacii i investicii. 2025. № 10. S. 277–279.
14. Melexina T.L., Vladova A.Yu. Analitika obrazovatel`ny`x traektorij v sisteme menedzhmenta kachestva. Problemy` teorii i praktiki upravleniya. 2025. № 9. S. 172–183.
15. Vladova A.Y. Educational analytics in the learning management system: From visualization to forecasting. 18th International Conference on Management of Large-Scale System Development (MLSD). 2025. P. 1–4. doi: 10.1109/MLSD65526.2025.11220633.