人教版和北师大版教材“平行线”相关内容比较研究

A Comparative Study on the Related Content of “Parallel Lines” between the Humanistic Edition and Beijing Normal University Edition

本文采用文献研究法、内容分析法对小学和初中有关平行线相关内容的分布、教材基本特征、概念的引入方式、概念的定义形式以及几何推理形式这几个方面进行了比较分析。从而得出以下结论:1) 有关平行线的内容的分布是根据学生的认知发展规律采用分段编排呈螺旋上升式结构;2) 两种版本教材都是采用图文结合的方式,将数学与现实生活相联系;3) 概念的引入方式上,人教版大都是让学生动手操作观察思考,而北师大版一般是直接展示生活实例,增加学生感性认识;4) 概念的定义形式上,两种版本都是采用图文结合的方式,但是人教版是较为细致的概念表述,而北师大版直接就是利用图片进行定义;5) 几何推理形式上,两种版本都在七年级使用合情推理以及非形式化的演绎推理,但是北师大版在八年级用更加严谨的数学语言采用演绎推理的方式对平行线内容进行更进一步的推理论证。

In this paper, literature research method and content analysis method are used to compare and analyze the distribution of the content related to parallel lines in primary and junior high schools, the basic features of textbooks, the way of introducing concepts, the definition of concepts and the geometric reasoning forms. The following conclusions can be drawn: 1) The distribution of the content of parallel lines is based on the law of students’ cognitive development. The use of segment arrangement is a spiral structure. 2) The two versions of the textbook use the way of graphic combination to connect mathematics with real life;3) In terms of the introduction of concepts, most of the Humanistic Edition requires students to operate, observe and think, while the Beijing Normal University Edition usually directly shows examples of life to increase students’ perceptual understanding;4) The definition form of the concept, both versions adopt the way of combining text and text, but the Humanistic Edition is more detailed concept expression, while the Beijing Normal University Edition directly uses pictures for definition;5) In the form of geometric reasoning, both versions use reasonable reasoning and nonformalized deductive reasoning in the seventh grade, but Beijing Normal University Edition uses more rigorous mathematical language and deductive reasoning in the eighth grade for further reasoning and demonstration of the contents of parallel lines.