基于逻辑推理素养的高中数学教材分析——以人教A版“立体几何初步”为例

Analysis of High School Mathematics Textbooks Based on Logical Reasoning Literacy—A Case Study of “Preliminary Solid Geometry” in PEP Version A (2019)

摘要: 为了深入探究教材对学生逻辑推理素养的培养效果，研究以人教A版(2019)高中数学教材中的“立体几何初步”章节为研究对象，以范希尔几何思维水平理论为分析框架，通过分析教材的内容结构、编排逻辑、定理证明及习题设计等方面，探讨教材怎样系统性地培养学生的逻辑推理素养，并辅以与北师大版教材的横向对比。研究发现，人教A版(2019)高中数学教材通过从整体到局部的编排逻辑、直观感知与抽象推理有机结合的定理证明等系统化的教材设计，有效地为教师在立体几何教学中培养学生的逻辑推理素养提供了清晰的路径和可靠的载体。

Abstract: To thoroughly explore the effect of textbooks in cultivating students’ logical reasoning literacy, this study takes the chapter Preliminary Solid Geometry in the PEP Version A (2019) high school mathematics textbook as the research object and adopts the Van Hiele Levels of Geometric Thinking as the analytical framework. By analyzing the content structure, organizational logic, theorem proofs and exercise design of the textbook, this study investigates how the textbook systematically cultivates students’ logical reasoning literacy, supplemented by a horizontal comparison with the Beijing Normal University (BNU) Edition textbooks. The study reveals that the PEP Version A (2019) high school mathematics textbook, through its systematic designs including the organizational logic from the whole to the parts and theorem proofs that organically integrate intuitive perception and abstract reasoning, effectively provides teachers with clear paths and reliable carriers to develop students’ logical reasoning literacy in solid geometry teaching.