Beauty of Number-Shapes and Course Creativity: Teaching Model with Core Math Thinking Infiltration

数形之美与课堂创意：以数学思想渗透为核心的教学模式

[Background]With the deepening reform of the new college entrance examination,it is increasingly important to explore the artistic traits of“the beauty of number-shape combination” in analytic geometry and build a math teaching model integrating artistic perception and focusing on mathematical thinking infiltration. [Objective] To explore its construction path: to guide teachers to integrate artistic perception for students ’ mathematical thinking enhancement, inject artistic creativity into math classes, and offer references for “mathematical aesthetics”-related practices. [Method]Taking high school analytic geometry as the subject,it sorts out “the beauty of number-shape combination” elements in 5-year new college entrance exam analytic geometry questions;via tests,interviews and questionnaires,it surveys Luoyang/Jiyuan(Henan)students on their perception of this beauty and analytic geometry mastery,then refines a better model with cases. [Results]Teachers should hierarchically infiltrate mathematical thinking based on curve beauty,symmetry and other artistic traits for students of different levels;guide students from “perceiving graphic beauty” to “understanding mathematical beauty” in different stages,and master flexible application of mathematical thinking. [Conclusion]The model(with “the beauty of number-shape combination” as artistic link and mathematical thinking as core)needs two-way empowerment:improving teachers' professional abilities and students' dual development of math literacy+artistic perception.Teachers' mathematical thinking cognition,infiltration teaching ability and artistic material integration ability are three key supports,offering a practical paradigm for teaching reconstruction.

【背景】随着新高考的深入改革，挖掘解析几何中“数形之美”的艺术特质，构建融合艺术感知、以数学思想渗透为核心的数学教学模式日益重要。 【目的】探究以融合“数形之美”与数学思想渗透为核心的数学教学模式构建路径。指导教师融合艺术感知培养学生加强数学思想；为数学课堂注入艺术创意，并为“数学美学”相关的教学实践提供参考。 【方法】以高中解析几何作为研究对象，一方面梳理近5 年的新高考数学中解析几何试题中“数形之美”的元素；另一方面通过现场测试、访谈以及问卷调查的形式对河南洛阳、济源高中生对“数形之美”的感知程度及解析几何掌握情况，结合教学案例提炼出更加完善的教学模式。 【结果】教师应针对不同程度的学生对结合曲线美、对称美等艺术特质分层渗透数学思想；在不同学习阶段，引导学生从“感知图形美”到“理解数学美”，同步掌握数学思想的灵活应用。 【结论】以“数形之美”为艺术纽带、数学思想为核心的高中数学教学模式，需实现“教师专业能力提升”与“学生数学素养+艺术感知双发展”的双向赋能；且教师的“数学思想认知水平”、“渗透教学能力”及“艺术素材整合能力”是模式有效运转的三大关键支撑，为重塑教学构建提供实践范式。