How to Optimize Students’ Study Achievements Under Multiple Influences A Quantitative Discussion Based On Mathematical Modeling

When many students struggle to find optimal learning strategies, this paper investigates how various factors—through changes during exams and their impacts during regular study—ultimately influence academic performance. We quantitatively incorporate the effects of everyday learning efficiency (referencing Hattie's 2008 "Visible Learning" to some extent), the impact of study duration, the average weighted influence of other events, and the factors determining exam performance, ultimately deriving a formula that illustrates their interplay. This enables us to explore how individuals can optimize their learning strategies. Additionally, we introduce random Gaussian noise into the formula to balance the chaotic effects on the system. The resulting model offers an extensible and integrable framework, transforming student learning from being purely data-driven to actual learning process, thereby enhancing the robustness of the model. Its modular design allows researchers to refine and fit the model incrementally based on theory, extract compensatory terms within the formula, and thus strengthen both interpretability and future rigor. Unlike direct weighted calculations, this study is the first to conduct a quantitative analysis with a strong emphasis on interpretability. Although limited by scale so that we cannot do large-scale data collection, the model’s inclusion of environmental variables provides micro-level insights into how external factors affect learning and generate optimized rankings, while AI-based multimodal perception offers valuable references for intelligent optimization of learning environments.