MICRO-DECOMPOSITION OF LEARNING CONTENT AS A STRATEGY FOR PREPARING STUDENTS FOR THE EXTERNAL INDEPENDENT EVALUATION (ZNO) IN MATHEMATICS
DOI:
https://doi.org/10.54662/veresen.2.2026.02Keywords:
cognitive load, mathematical education, micro-decomposition, educational losses, preparation for external independent assessment (EIA)Abstract
This paper substantiates micro-decomposition of learning content as a strategic didactic approach for preparing students for ZNO and NMT examinations in mathematics, specifically addressing the systemic educational losses caused by the pandemic and the war. Based on a comprehensive analysis of national and international research (2022–2026), it identifies trends in declining proficiency and highlights the challenges of traditional methods that lead to cognitive overload due to excessive theoretical volume. The article advocates for adaptive learning to facilitate personalized environments and the effective recovery of structural gaps in knowledge. The theoretical foundations integrate cognitive load theory, microlearning, and mastery learning concepts. The proposed 'Chunk-Objective' model partitions complex topics into elementary, measurable 'micro-skills,' enabling students to internalize material without exceeding their cognitive limits. This strategy is particularly effective for mathematics, which demands higher working memory resources for processing abstract symbols and logical transitions. The model integrates diagnostic screening, adaptive instruction, and formative evaluation into a unified five-stage didactic system: diagnostics, decomposition, micro-learning, correction, and integration. Practical implementation is detailed through its successful testing in the in-service teacher training system at the Mykolaiv Regional Institute and various student initiatives such as 'Express Mathematics.' The results demonstrate that forming automated cognitive units enhances student performance in high-stakes testing by fostering motivation, autonomy, and the ability to solve multi-component problems. This approach effectively localizes specific learning deficits and constructs resilient competencies required for further success in higher education.
References
Bloom, B. S. (1984). The 2 sigma problem: The search for methods of group instruction as effective as one-to-one tutoring. Educational Researcher, 13(6), 4–16. https://doi.org/10.3102/0013189X013006004 (eng).
Bychko, H., Vakulenko, T., Lisova, T., Mazorchuk, M. & et al. (2023). Natsionalnyi zvit za rezultatamy mizhnarodnoho doslidzhennia yakosti osvity PISA-2022 [National report on PISA-2022 results]. Kyiv: Ukrainskyi tsentr otsiniuvannia yakosti osvity (ukr).
Buchem, I., & Hamelmann, H. (2010). Microlearning: A strategy for ongoing professional development. eLearning Papers, 21 (eng).
Glaser, R., & Bassok, M. (1989). Learning theory and the study of instruction (Technical Report No. 11). Pittsburgh: University of Pittsburgh (eng).
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. London: Routledge. DOI: https://doi.org/10.4324/9780203181522 (eng).
Hug, T. (2020). Microlearning: A strategy for ongoing professional development. In Emerging technologies and pedagogies in the curriculum. Springer. https://doi.org/10.1007/978-981-15-0618-5_7 (eng).
Jin, H., Yan, D., & Krajcik, J. (Eds.). (2024). Handbook of research on science learning progressions. Routledge. DOI: https://doi.org/10.4324/9781003170785 (eng).
Leong, K., Sung, A., Au, D., & Blanchard, C. (2021). A review of the trend of microlearning. Journal of Work-Applied Management, 13(1), 88–102. https://doi.org/10.1108/JWAM-10-2020-0044 (eng).
Mao, X., Dai, Y., Liu, Y., Jiang, Y., & Zhang, Y. (2025). Optimizing cognitive load in digital mathematics textbooks. Journal of Educational Technology and Innovation, 7(3), 44–59 (eng).
Matematyka u tsyfrovomu suspilstvi [Mathematics in digital society]. (n.d.). Retrieved from: https://math.moippo.mk.ua/знодпа/експрес-математика-2025 (ukr).
OECD. (2023). PISA 2022 results (Volume I–II): Country notes: Ukrainian regions. Retrieved from https://www.oecd.org/en/publications/pisa-2022-results-volume-i-and-ii-country-notes_ed6fbcc5-en/ukrainian-regions-18-of-27_78043794-en.html (eng).
OECD. (2023). Recovering lost learning opportunities in Ukraine: Key education policy strategies. Retrieved from: https://www.oecd.org/content/dam/oecd/en/publications/reports/2023/04/recovering-lost-arningle-opportunities-in-ukraine-key-education-policy-strategies_0790a596/c10085eb-en.pdf (eng).
Pohromska, H. S., Makhrovska, N. A., & Rohozhynska, E. K. (2023). Stratehiia pidhotovky vypusknykiv do skladannia ispytiv (DPA, ZNO, NMT) z matematyky v umovakh dystantsiinoho navchannia [Strategy of preparing graduates for mathematics exams (DPA, ZNO, NMT) under distance learning conditions]. Veresen, 1(96), 152–163 (ukr).
Profspilky pratsivnykiv osvity i nauky Ukrainy. (2023). Onovlennia «Vyvchaiu – ne chekayu»: novi uroky ta polipshenyi funktsional [Update «Learning – no waiting»: new lessons and improved functionality]. Retrieved from: https://pon.org.ua/novyny/10795-onovlennia-vyvchau-ne-chekau-novi-uroky-v-zastosunku-ta-polipshenyi-funkcional.html (ukr).
Şahina Z. G. & Kırmızıgül H. G. (2026). Reflections from the mathematics lesson with microlearning: A different educational experience in the digital age. (2026). Journal of Learning and Teaching in Digital Age, 11(1), 28–40 (eng).
Topuzov, O. M., & Zasiekina, T. M. (2022). Problemy ta perspektyvy rozvytku shkilnoi pryrodnycho-matematychnoi osvity v umovakh reformuvannia zahalnoi serednoi osvity [Problems and prospects of development of school science and mathematics education]. Ukrainskyi pedahohichnyi zhurnal, 2, 5–12 (ukr).
Troian, I. (2023). Microlearning, zavdannia, poviazani z realnym zhyttiam, ta spiralnyi pidkhid: yak stvoriuiut suchasni pidruchnyky dlia 5–6 klasiv [Microlearning, real-life tasks and spiral approach in textbooks]. NUSH. Smart osvita. Retrieved from: https://nus.org.ua/2023/01/11/microlearning-zavdannya-pov-yazani-z-realnym-zhyttyam-ta-spiralnyj-pidhid-yak-stvoryuyut-suchasni-pidruchnyky-dlya-5-6-klasiv/ (ukr).
Ukrainskyi tsentr otsiniuvannia yakosti osvity. (2025). ZZMIApO-2024: uspishnist uchnivstva z matematyky ta chytannia [ZZMYAPO-2024: Students’ achievement in mathematics and reading]. Kyiv. Retrieved from: https://testportal.gov.ua/zzmyapo-2024-uspishnist-uchnivstva-v-galuzyah-matematyky-ta-chytannya/ (ukr).
UNESCO. (2024). Monitoring SDG 4 2024/5: Global education monitoring report. Retrieved from: https://www.unesco.org/reports/gem-report/en/2024-monitoringsdg4 (ukr).
World Bank. (2024). Ukraine third rapid damage and needs assessment (RDNA3), February 2022 – December 2023. Retrieved from: https://documents1.worldbank.org/curated/en/099021324115085807/pdf/P1801741bea12c012189ca16d95d8c2556a.pdf (eng).
Van Maanen, L., Zhang, Y., De Schryver, M., & Liefooghe, B. (2024). The curve of learning with and without instructions. Journal of Cognition, 7(1), 48. DOI: https://doi.org/10.5334/joc.373 (eng).
Van Nooijen, C. C. A., de Koning, B. B., Bramer, W. M. & et al. (2024). A cognitive load theory approach to understanding expert scaffolding of visual problem-solving tasks: A scoping review. Educational Psychology Review, 36, Article 12. (eng).
Zhang, Y., Li, H., & Clark, J. D. (2020). Experimental simulation of mathematical learning process based on «chunk-objective». Applied Mathematics and Nonlinear Sciences, 5(2), 425–434 (eng).

