基于HPM教育的人教版、苏教版高中数学教材对比研究——以“函数”为例

A Comparative Study of HPM-Based High School Mathematics Textbooks: People’s Education Press vs. Jiangsu Phoenix Education Press—Taking “Functions” as an Example

摘要: HPM (数学史与数学教育)是现在数学教育里的一个重要话题。本研究以HPM理论为视角，对人民教育出版社A版(人教A版)和江苏凤凰教育出版社出版(苏教版)的高中数学教材中“函数”这一核心章节进行了对比分析。研究采用王子悦建立的统计分析模型，从插图与旁注、引入环节、专题板块等维度，对两版教材在数学史内容呈现、来源选取和文化功能实现上进行了量化和质性比较。研究发现，两版教材在HPM教育理念的实践上呈现出不同的路径：苏教版采用“弥散式浸润”策略，通过高频率、广覆盖的微观栏目渗透数学史元素，注重国际化与现代化视野；人教A版则采用“聚焦式深挖”策略，虽然微观栏目中数学史内容较少，但在专题部分设计了更多深度探究和实践任务，注重本土化史料的挖掘和数学建模素养的培养。论文最后基于对比分析，为教材修订和一线教学实践提出了突破静态阅读、整合中外资源、激活微观栏目功能等建设性启示。

Abstract: History and Pedagogy of Mathematics (HPM) has become an important topic in contemporary mathematics education. From the perspective of HPM theory, this study conducts a comparative analysis of the core chapter “Functions” in two high school mathematics textbooks: the A Version published by People’s Education Press (PEP A Version) and the version published by Jiangsu Phoenix Education Publishing House (JPEP Version). Adopting the statistical analysis model established by Wang Ziyue, this research carries out quantitative and qualitative comparisons of the two textbooks in terms of the presentation of mathematical history content, the selection of sources, and the realization of cultural functions, from the dimensions of illustrations and marginal notes, introductory links, and special topic sections. The study finds that the two textbooks present different paths in the practice of HPM educational concepts: the JPEP Version adopts a “diffused infiltration” strategy, infiltrating HPM elements through high-frequency and wide-coverage micro-columns, with an emphasis on an international and modern perspective; the PEP A Version adopts a “focused in-depth exploration” strategy—although it contains less mathematical history content in micro-columns, it designs more in-depth inquiry and practical tasks in special topic sections, focusing on the excavation of local historical materials and the cultivation of mathematical modeling literacy. Based on the comparative analysis, the paper finally puts forward constructive enlightenment for textbook revision and front-line teaching practice, such as breaking through static reading, integrating Chinese and foreign resources, and activating the functions of micro-columns.