On the morning of May 13, 2025, Professor Wang Xiaoqin, doctoral supervisor from the School of Mathematical Sciences at East China Normal University, was invited to our college to deliver a special lecture titled "Preliminary Exploration of the Application of Ancient Chinese Mathematical Thinking in High School Mathematics Teaching." The lecture was hosted by Professor Gu Jiling from Nanjing Normal University, with participation from all students in the 2024 cohort of the Subject Teaching (Mathematics) program.

The lecture focused on four types of thinking from traditional Chinese mathematics: "seeking common ground while preserving differences," "different forms with equal quantities," "accumulating small amounts to achieve greatness," and "categorizing and grouping." These concepts demonstrated extensive applications in high school mathematics. The presentation fully illustrated how utilizing Chinese computational thinking can not only solve various algebraic, geometric, trigonometric, and analytic geometry problems, but also unify the conceptual methods scattered across different fields and topics in today's mathematics curriculum. This showcase highlighted the captivating charm of excellent traditional Chinese mathematical culture, the tremendous value of Chinese computational materials, and outstanding examples of applying ancient wisdom to modern contexts while innovating through adaptation.

At the beginning of the lecture, Professor Wang Xiaoqin introduced the academic background of mathematics history education research and used the question "How to promote HPM implementation and find effective tools in mathematics teaching" as an entry point to stimulate discussion and reflection among participants. Subsequently, Professor Wang introduced Liu Hui's "Unifying Technique" (Qitong Shu), highlighting its fundamental position in mathematics. Through specific cases combining algebraic operations with geometry, he explained the innovative applications of "seeking common ground while preserving differences" thinking in fraction operations and geometric series summation, and reinterpreted the mathematical significance of Mei Wending's sine theorem.

Zhao Shuang's chord diagram intuitively reveals the algebraic essence of the Pythagorean theorem through geometric assembly, serving as an exemplar of "different forms with equal quantities." For instance, in the Pythagorean square problem, by constructing the area relationship between a right triangle and its inscribed square, geometric segmentation is transformed into algebraic equations. Students gain insight into the unified relationship between geometric variation and numerical conservation through dynamic decomposition. Professor Wang proposed that in teaching the sine addition formula, teachers can guide students to use Zhao Shuang's chord diagram supplementation concept to transform geometric problems into algebraic problems, providing concrete support for abstract formulas.

Following this, Professor Wang Xiaoqin, quoting Xunzi's "Without accumulating small steps, one cannot reach a thousand miles," led students to retrace the thinking paths of ancient mathematicians. Through Liu Hui's implicit derivation of infinite series, he vividly interpreted the philosophical meaning of "quantitative change leading to qualitative change": "Seemingly scattered fractions continuously accumulate, ultimately breaking through the finite to point directly to the essence of infinity." Professor Wang particularly noted that current classrooms often teach knowledge points in isolation, while truly effective teaching should follow ancient scholarly methods: "Building a mountain through accumulated earth is not achieved in a single day; one must develop depth of thinking through problem chains."

"Square objects are grouped by category, things are separated by type. Those of the same numerical type are never distant, those of different numerical types are never close." Liu Hui proposed "categorizing by type and grouping by nature" in "The Nine Chapters on the Mathematical Art," emphasizing that mathematical objects should be classified and integrated according to their essential properties. For example, Hua Hengfang used symbolic derivation systems to systematically demonstrate the hierarchical relationships of proof steps, embodying the logical coherence of "those of the same type are never distant." In teaching conic sections, Professor Wang suggested that teachers can use equations to guide students in observing the morphological transformations of parabolas, ellipses, and hyperbolas through parameter adjustments, understanding the deeper connections of "categorizing and grouping."

At the conclusion of the lecture, Professor Wang Xiaoqin engaged in an interactive session with students present. Students actively asked questions and engaged in in-depth exchanges and discussions with Professor Wang. Professor Wang patiently answered students' inquiries and shared his insights and experiences.

This lecture served not only as an academic feast but also as a starting point for teaching practice among graduate students in Subject Teaching (Mathematics). Through Professor Wang Xiaoqin's in-depth analysis of ancient Chinese mathematical thinking, students not only gained concrete understanding of the HPM theoretical framework but also comprehended practical pathways for integrating mathematics history into classroom instruction through classic cases such as "Liu Hui's Unifying Technique and Zhao Shuang's chord diagram." The lecture inspired participants to reexamine the cultural origins of mathematical knowledge. For instance, behind the multiple proofs of the Pythagorean theorem lies both the dialectical thinking of "different forms with equal quantities" and methodological support for interdisciplinary integration such as geometric modeling and physical motion analysis. This lecture, combining traditional Chinese mathematics history with local practice, not only ignited students' enthusiasm for reconstructing instructional design from a historical perspective but also transformed "applying ancient wisdom to modern contexts" from a slogan into operational lesson plan strategies, providing graduate students with rich materials and clear pathways for their teaching practice and research.

 

Text | Gao Jiangyuan

Photos | Wang Qi

Review | Zhao Xiaoyan