Abstract
<jats:p>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.</jats:p>