生成式AI支持直观想象素养发展的教学实践——以函数$y=Asin\left(\omega x+\phi \right)$的图像为例

Teaching Practice of Generative AI Supporting the Development of Intuitive Imagination Literacy—A Case Study of the Graph of the Function $y=Asin\left(\omega x+\phi \right)$

摘要: 围绕高中数学函数$y=Asin\left(\omega x+\phi \right)$ 的图像教学，探讨生成式AI促进学生直观想象素养发展的实践路径。研究以46名高一学生为对象，采用前后测、课堂观察和访谈相结合的方法，借助DeepSeek生成动态图像、关键点轨迹、周期标注和位移对比图，引导学生在观察、比较与解释中建构参数和图像变换的对应关系。结果显示，学生在七个考查维度上的后测正确率均高于前测，其中平移量判断正确率由32.6%提高至73.9%，由图析式能力由41.3%提高至76.1%，数学解释能力由34.8%提高至71.7%。研究表明，生成式AI能够有效支持学生形成动态表象和数形联系。

Abstract: This study investigates a practical pathway through which generative AI supports the development of students’ intuitive imagination literacy in the teaching of the graph of the high school mathematics function $y=Asin\left(\omega x+\phi \right)$ . A total of 46 Grade 10 students participated in the study. Using a combination of pre- and post-tests, classroom observation, and interviews, the study employed DeepSeek to generate dynamic graphs, key point trajectories, period annotations, and displacement comparison diagrams, guiding students to construct the correspondence between parameters and graph transformations through observation, comparison, and explanation. The results show that students’ post-test accuracy was higher than their pre-test accuracy across all seven assessment dimensions. Specifically, the accuracy of displacement judgment increased from 32.6% to 73.9%, graph-to-formula analysis from 41.3% to 76.1%, and mathematical explanation from 34.8% to 71.7%. These findings suggest that generative AI can effectively support students in forming dynamic mental representations and establishing connections between algebraic expressions and graphical transformations.