融入AI的高中三角函数数学建模教学活动的设计

Design of AI-Integrated Trigonometric Function Mathematical Modeling Teaching Activities in Senior High Schools

摘要: 本文以《普通高中数学课程标准(2017年版2025年修订)》及数字化赋能教育发展相关政策为依据，针对高中数学建模教学活动中数学核心素养培养的现实需求，构建融入AI的高中数学建模教学活动框架。以“大连港潮汐模型构建”为案例，围绕“潮汐规律建模与船舶靠离泊时段优化”核心问题进行教学设计，引导学生整合三角函数、数据处理等数学知识，借助DeepSeek、GeoGebra AI等工具贯穿数学建模全流程，通过分层任务设计与可视化探究实现认知进阶。研究表明，该模式能有效破解传统建模教学中复杂计算门槛高、偏差归因难等问题，促进学生数学核心素养的内化，显著提升其建模能力、AI工具应用能力与实践创新素养，为高中数学建模教学与信息技术的深度融合提供了可借鉴的实践范式。

Abstract: Based on the “Curriculum Standards for General High School Mathematics (2017 Edition, Revised in 2025)” and relevant policies on digitalization-empowered educational development, this paper addresses the practical demand for cultivating core mathematical competencies in senior high school mathematical modeling teaching activities and constructs an AI-integrated teaching activity framework for senior high school mathematical modeling. Taking “the Construction of Dalian Port Tidal Model” as a case study, it designs teaching activities around the core problem of “tidal pattern modeling and optimization of ship berthing/unberthing time windows”, guiding students to integrate mathematical knowledge such as trigonometric functions and data processing, and apply AI tools, including DeepSeek and GeoGebra AI, throughout the entire mathematical modeling process. Cognitive progression is achieved through hierarchical task design and visual inquiry. The research findings indicate that this model can effectively overcome the bottlenecks of traditional modeling teaching, such as the high threshold of complex calculations and the difficulty in attributing model deviations. It facilitates the internalization of students’ core mathematical competencies, significantly enhances their modeling capabilities, AI tool application skills, and practical innovation literacy, and provides a replicable practical paradigm for the in-depth integration of information technology into senior high school mathematical modeling teaching.