FROM SELF-ASSESSMENT TO PEER REVIEW: THE DEVELOPMENT OF A COGNITIVE-VERIFICATION APPROACH TO THE EVALUATION OF MATHEMATICAL PROBLEMS IN THE CONTEXT OF GENERATIVE ARTIFICIAL INTELLIGENCE
DOI:
https://doi.org/10.31110/fmo2026.v41i3-05Keywords:
generative artificial intelligence, peer review, assessment validity, metacognitive passivity, cognitive-verification approach, mathematical analysis, distance learning, risk-oriented auditAbstract
Problem statement. Generative artificial intelligence undermines the diagnostic reliability of homework assignments in distance mathematics education: an externally correct result is no longer sufficient evidence of a student’s independent achievement of learning outcomes. The key risk is students’ metacognitive passivity, understood as delegating to technology the analysis of the problem conditions, the choice of method, and the verification of the result. This article extends the author’s cognitive-verification approach by shifting verification activity from individual self-checking to the analysis of another student’s mathematical reasoning through peer review.
Materials and methods. The study is theoretical, with a pilot trial. The theoretical framework is based on Messick’s concept of assessment validity, the notion of metacognitive passivity, and the concept of assessment twins. On this basis, a five-component risk-oriented assessment model was constructed. The pilot involved one academic group of 10 students, one mathematical analysis task, and a qualitative descriptive analysis of the results.
Results. A five-component model was developed: a cognitive-verification solution with checkpoints; structured review of an analogous work according to a rubric; a mandatory author’s response to the review; brief self-reflection; and selective instructor audit of 20–30% of the submitted works. Examples of model implementation for a mathematical analysis course were designed, including the limit of a function of two variables, extrema, and a double integral, as well as three variants of final assessment.
Conclusions. The model shifts the problem from detecting the use of artificial intelligence to ensuring assessment validity by generating several complementary sources of evidence of competence. Selective audit is a more scalable alternative to the comprehensive individual defence of all submitted works. The model is particularly promising for the training of mathematics teachers. Further research should empirically test its impact on metacognitive activity and evaluate the balance between validity gains and resource costs.
Downloads
References
Bennett, R. E. (2011). Formative assessment: A critical review. Assessment in Education: Principles, Policy & Practice, 18(1), 5–25. https://doi.org/10.1080/0969594X.2010.513678
Biton, Y. (2025). Learning mathematics through peer assessment: "How can we assess something that we ourselves don't know how to solve?" EURASIA Journal of Mathematics, Science and Technology Education. https://www.ejmste.com/article/learning-mathematics-through-peer-assessment-how-can-we-assess-something-that-we-ourselves-dont-know-15794
Combrinck, C., & Loubser, N. (2025). Student self-reflection as a tool for managing GenAI use in large class assessment. Discover Education, 4, Article 72. https://link.springer.com/article/10.1007/s44217-025-00461-2
Corbin, T., Bearman, M., Boud, D., & Dawson, P. (2025). The wicked problem of AI and assessment. Assessment & Evaluation in Higher Education. Advance online publication. https://doi.org/10.1080/02602938.2025.2553340
Corbin, T., Dawson, P., & Liu, D. (2025). Talk is cheap: Why structural assessment changes are needed for a time of GenAI. Assessment & Evaluation in Higher Education, 50(7), 1087–1097. https://doi.org/10.1080/02602938.2025.2503964
Dawson, P., Bearman, M., Dollinger, M., & Boud, D. (2024). Validity matters more than cheating. Assessment & Evaluation in Higher Education, 49(7), 1005–1016. https://doi.org/10.1080/02602938.2024.2386662
de-Armas-González, P., Perdomo-Díaz, J., & Sosa-Martín, D. (2023). Peer assessment processes in a problem-solving activity with future teachers. EURASIA Journal of Mathematics, Science and Technology Education, 19(4), Article em2245. https://www.ejmste.com/article/peer-assessment-processes-in-a-problem-solving-activity-with-future-teachers-13057
Fan, Y., Tang, L., Le, H., Shen, K., Tan, S., Zhao, Y., Shen, Y., Li, X., & Gašević, D. (2025). Beware of metacognitive laziness: Effects of generative artificial intelligence on learning motivation, processes, and performance. British Journal of Educational Technology, 56(2), 489–530. https://doi.org/10.1111/bjet.13544
Gao, X., Noroozi, O., Gulikers, J., Biemans, H. J. A., & Banihashem, S. K. (2024). A systematic review of the key components of online peer feedback practices in higher education. Educational Research Review, 42, 100588. https://doi.org/10.1016/j.edurev.2024.100588
Sun, Y., Liao, Y., & Ma, X. (2026). Trusting AI to detect AI? A systematic evaluation of the reliability and robustness of current AIGC detection tools for student academic work. Computers & Education, 249, 105616. https://doi.org/10.1016/j.compedu.2026.105616
Heil, J., & Ifenthaler, D. (2023). Online assessment in higher education: A systematic review. Online Learning, 27(1), 187–218. https://olj.onlinelearningconsortium.org/index.php/olj/article/view/3398
Kerman, N. T., Banihashem, S. K., Karami, M., Er, E., van Ginkel, S., & Noroozi, O. (2024). Online peer feedback in higher education: A synthesis of the literature. Education and Information Technologies, 29(1), 763–813. https://doi.org/10.1007/s10639-023-12273-8
Messick, S. (1989). Validity. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 13–103). American Council on Education.
Messick, S. (1993). Foundations of validity: Meaning and consequences in psychological assessment. ETS Research Report Series, 1993(2), i–18. https://doi.org/10.1002/j.2333-8504.1993.tb01562.x
Perkins, M., Roe, J., Vu, B. H., Postma, D., Hickerson, D., McGaughran, J., & Khuat, H. Q. (2024). Simple techniques to bypass GenAI text detectors: Implications for inclusive education. International Journal of Educational Technology in Higher Education, 21, Article 53. https://doi.org/10.1186/s41239-024-00487-w
Roe, J., Perkins, M., & Giray, L. (2026). Assessment twins: An approach for strengthening assessment validity in the age of generative AI. Journal of Applied Learning & Teaching, 9(2). https://doi.org/10.37074/jalt.2026.9.2.3
Rudolph, J., Tan, S., & Tan, S. (2023). ChatGPT: Bullshit spewer or the end of traditional assessments in higher education? Journal of Applied Learning & Teaching, 6(1), 342–363. https://doi.org/10.37074/jalt.2023.6.1.9
Topping, K. J., Gehringer, E., Khosravi, H., Gudipati, S., Jadhav, K., & Susarla, S. (2025). Enhancing peer assessment with artificial intelligence. International Journal of Educational Technology in Higher Education, 22, Article 3. https://doi.org/10.1186/s41239-024-00501-1
Weber-Wulff, D., Anohina-Naumeca, A., Bjelobaba, S., Foltýnek, T., Guerrero-Dib, J., Popoola, O., Šigut, P., & Waddington, L. (2023). Testing of detection tools for AI-generated text. International Journal for Educational Integrity, 19, Article 26. https://doi.org/10.1007/s40979-023-00146-z
Zhan, Y., Yan, Z., Wan, Z. H., Wang, X., Zeng, Y., Yang, M., & Yang, L. (2023). Effects of online peer assessment on higher-order thinking: A meta-analysis. British Journal of Educational Technology, 54(4), 817–835. https://doi.org/10.1111/bjet.13310
Chkana, Y. (2026). Kohnityvno-veryfikatsiinyi pidkhid do transformatsii domashnikh zavdan z matematychnoho analizu v umovakh vykorystannia shtuchnoho intelektu [A cognitive-verification approach to transforming homework in mathematical analysis in the context of artificial intelligence use]. Fizyko-matematychna osvita – Physical and Mathematical Education, 41(2), 86–93. https://doi.org/10.31110/fmo2026.v41i2-08 (in Ukrainian).
Downloads
Published
Issue
Section
Categories
How to Cite
License
Copyright (c) 2026 Ярослав Чкана
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
- Authors grant the journal a right of the first publication of the work under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0)that allows others freely to use (read, copy and print) submissions, search content and link to published articles, disseminate their full text and use them for any legitimate non-commercial purposes (i.e. educational or scientific) with the mandatory reference to the article’s authors and initial publication in this journal.
- Original published articles cannot be used by users (exept authors) for commercial purposes or distributed by third-party intermediary organizations for a fee.
