核心素养视域下高中数学教材“对数函数”内容的比较研究——基于人教A版、北师大版与苏教版的量化分析

A Comparative Study of the “Logarithmic Function” Content in High School Mathematics Textbooks from the Perspective of Core Competencies—A Quantitative Analysis Based on the PEP A Edition, the BNU Edition, and the Jiangsu Education Edition

摘要: 为比较不同版本高中数学教材“对数函数”内容的编写特点，本文选取人教A版、北师大版和苏教版教材为研究对象，运用内容分析法和鲍建生综合难度模型，从章节编排、概念引入、习题系统综合难度和信息技术应用四个维度进行比较。研究发现：三版教材均依据课程标准组织内容，但在编写取向上存在差异。人教A版和北师大版更突出“函数主线”，注重指数函数、对数运算与对数函数之间的结构联系；苏教版更突出“运算主线”，强调对数运算基础和综合题目训练。习题难度方面，苏教版在运算、推理和知识综合维度上整体较高，人教A版和北师大版难度梯度相对平缓。信息技术应用方面，三版教材均关注函数图像和变化规律，但涉及内容和编排位置有所不同。基于此，教师应结合教材特点和学生学情，对情境引入、运算训练、综合习题和技术应用进行适当调适。

Abstract: To compare the compilation characteristics of the content on “logarithmic functions” in different high school mathematics textbooks, this study selects the PEP A Edition, the BNU Edition and the Jiangsu Education Edition as research objects. Using content analysis and Bao Jiansheng’s comprehensive difficulty model, the study compares the three editions from four dimensions: chapter organization, concept introduction, comprehensive difficulty of exercises, and information technology application. The results show that although the three editions are organized according to the curriculum standards, they differ in compilation orientation. The PEP A Edition and the BNU Edition highlight a function-oriented main line and emphasize the structural relationship among exponential functions, logarithmic operations and logarithmic functions, while the Jiangsu Education Edition highlights an operation-oriented main line and stresses logarithmic operations and comprehensive exercise training. In terms of exercise difficulty, the Jiangsu Education Edition shows higher levels in operation, reasoning and knowledge integration, whereas the PEP A Edition and the BNU Edition present a relatively smoother difficulty gradient. In terms of information technology application, all three editions involve function graphs and variation patterns, but differ in content coverage and arrangement. Based on these findings, teachers should adjust contextual introduction, operation training, comprehensive exercises and technology use according to textbook features and students’ learning conditions.