Aiming at the pain points in the teaching of "Monotonicity and Extrema of Functions" in Applied Advanced Mathematics, such as "difficulty in understanding abstract concepts, difficulty in breaking through key and difficult points, and low student participation", this paper proposes an integrated teaching model of "Artificial Intelligence + Traditional Culture". Taking GeoGebra software as the core AI tool, it visually demonstrates the correlation between the positive/negative nature of derivatives and the monotonicity of functions; and integrates the poetic artistic conception of Su Shi's "Inscription on the Wall of West Forest Temple" and the image of Lushan Mountain's terrain to materialize the abstract concept of extrema. Each peak, though not necessarily the highest across the entire range, stands as the local maximum in its vicinity; similarly, each valley, while not the lowest overall, serves as the local minimum nearby.This paper constructs a teaching closed loop of "artistic conception introduction—visual exploration—precision breakthrough—personalized consolidation". Practice shows that this model can effectively reduce students' cognitive load, improve classroom interaction and teaching effect, and provide a replicable teaching reform plan for Applied Advanced Mathematics teachers.
Wang Tong (2026) studied this question.