高中数学新教材“圆锥曲线”内容编写比较———以人教 A 版、北师大版和湘教版教材为例

Comparison of the content compilation of “conic curve” in the new high school mathematics textbook: Taking the textbooks of People’s Education Edition A, Beijing Normal University edition, and Hunan Education edition as examples

摘要

基于教材比较研究现状,以“圆锥曲线”内容为例,对国内不同版本高中数学教材从教材编排体系、概念引入、栏目和习题数量、呈现方式、文化渗透等5个方面进行“以点带面”式的对比研究.结果显示:在编排体系上,知识点大致相同,但北师大版划分最为精细;在“量”的比较上,人教 A 版栏目设置更精细,湘教版栏目更具特色,北师大版习题数量最多;在内容呈现方式上,北师大版在编排上更有梯度;在数学文化渗透上,湘教版数学文化融入更为丰富.针对研究结论,从建构基本概念、采取分层教学、整合单元设计3个方面给出“圆锥曲线”部分的教学建议,旨在帮助高中数学教师充分了解不同版本教材“圆锥曲线”内容编写异同,更好地开展教学活动.

Abstract

Based on the current situation of comparative research on textbooks, taking the content of “conic curve” as an example, this paper conducts a “from point to area” comparative study on different versions of high school mathematics textbooks in China from five aspects of textbook arrangement system, concept introduction, column and exercise quantity, presentation method, and cultural infiltration. The results show that in the arrangement system, the knowledge points are roughly the same, but the Beijing Normal University edition is the most finely divided; in the comparison of “quantity”, the People’s Education Edition A has more refined column settings, and the Hunan Education edition has more distinctive columns, the Beijing Normal University version has the largest number of exercises; in the way of content presentation, Beijing Normal University edition has more gradient in the arrangement; in terms of the infiltration of mathematical culture, the Hunan Education edition has enriched the integration of mathematical culture. Based on the research conclusions, this paper gives some teaching suggestions on “conic curve” from three aspects: constructing basic concepts, adopting stratified teaching, and integrating unit design, which aims at helping senior high school mathematics teachers fully understand the similarities and differences in the content compilation of “conic curve” in different versions of textbooks, so as to better carry out teaching activities.

关键词

高中数学教材 / 圆锥曲线 / 比较

Key words

high school mathematics textbook / conic curve / comparison

参考文献

[1] 叶立军, 王晓楠. 中美高中数学教材比较研究:以“几何概型”为例[J]. 数学教育学报, 2012, 21(2): 49-52.

[2] 宋蕾, 杨明. 高中数学新教材“三角函数”部分比较研究:以人教 A 版、湘教版和北师大版教材为例[J]. 中学数学教学参考, 2023(7): 20-23.

[3] 叶立军, 陈思思. 中俄高中数学教材比较研究:以“圆锥曲线与方程”与“椭圆、双曲线和抛物线”对比为例[J]. 中学数学杂志, 2015(1): 16-19.

[4] 向颖怡, 叶明露. 核心素养视角下的高中数学教材比较分析:以立体几何初步为例[J]. 内江师范学院学报, 2021, 36(8): 25-31.

[5] 吴立宝, 王富英. 数学教材习题“七功能”[J]. 教学与管理, 2014(31): 66-68.

[6] 吴立宝. 中澳数学教科书习题比较研究:以人教版和 HMZ8年级教科书为例[J]. 数学教育学报, 2013, 22(2): 58-61.

[7] 中华人民共和国教育部. 普通高中数学课程标准:2017年版2020年修订[S]. 北京: 人民教育出版社, 2020.

[8] 杨姣, 林佳裕. 新课标视角下三个版本高中数学教材习题比较研究:以“圆锥曲线”为例[J]. 中学数学杂志, 2022(3): 5-8.

[9] 刘权华. 高中数学单元教学设计存在的问题及对策[J]. 教学与管理, 2019(4): 55-57.