﻿ 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

Vol. 13  No. 02 ( 2023 ), Article ID: 61056 , 6 pages
10.12677/AE.2023.132067

1伊犁师范大学数学与统计学院，新疆 伊宁

2伊犁师范大学应用数学研究所，新疆 伊宁

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

Yannan Ban1, Weimin Hu1,2*

1School of Mathematics and Statistics, Yili Normal University, Yining Xinjiang

2Institute of Applied Mathematics, Yili Normal University, Yining Xinjiang

Received: Jan. 1st, 2023; accepted: Jan. 28th, 2023; published: Feb. 6th, 2023

ABSTRACT

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 non-formalized 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.

Keywords:Parallel Lines, Humanistic Edition, Beijing Normal University Edition

1. 问题提出

2. 研究方法及对象

2.1. 研究方法

2.2. 研究对象

3. 研究结果

3.1. 平行线内容的分布的比较

Table 1. Compare the distribution of the contents of parallel lines

3.2. 教材的基本特征比较

3.3. 概念的引入方式比较

Table 2. Introduction and comparison of concepts related to parallel content (Part)

3.4. 概念的定义方式比较

Table 3. Comparison of definitions of corresponding angles, alternate interior angles and parallel interior angles

3.5. 几何推理形式比较

《标准(2011)》提出：推理一般包括演绎推理和合情推理，演绎推理是指从确定的事实出发，例如公理、定理和定义等等，或者从确定的规则出发，例如运算时的顺序、法则和定义等等，按照已经确定的逻辑推理法则来证明或者解决数学中的问题；合情推理指的是推断某些结果时凭借本身已有的直觉和经验。这两种都是几何推理形式，功能不同但是却相辅相成的，演绎推理用于证明结论，合情推理用于引导学生思路最终发现结论。对于推理内容两种版本的教材都是分阶段进行逐步加深的。

Table 4. The process of proving the nature of parallel lines

A Comparative Study on the Related Content of “Parallel Lines” between the Humanistic Edition and Beijing Normal University Edition[J]. 教育进展, 2023, 13(02): 411-416. https://doi.org/10.12677/AE.2023.132067

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8. NOTES

*通讯作者。