摘要
函数图象变换是中学数学中的重点和难点,尝试运用动态几何软件呈现二次函数图象平移过程中点的共同运动特点以促进学生的理解.采用准实验设计,实验包括6节课,其中4节用于教学实验,2节用于前测和后测.实验组(n=23)的教学是基于APOS理论以及RMI原则设计的,并在DGS的支持下进行;而对照组(n=22)则运用传统的教学,也无DGS的支持.结果表明:实验组的学生在点的平移、二次函数图象的平移以及复合函数和圆的平移等拓展领域均好于对照组.该实验设计可以扩展到三角函数图象变换教学.
Graph translation of functions is an important but difficult topic in high school mathematics.This study attempts to facilitate students’understanding of graph translation of quadratic functions in a dynamic-geometry-software(DGS)supported environment.A quasi-experimental study design was used.This teaching experiment was carried out in two weeks including six lessons,four of which were used for teaching and two for pre-and post-tests.The experimental group(n=23)received an instruction based on Action-Process-Object-Schema(APOS)theory and Relationship-Mapping-Inversion(RMI)principle in a DGS supported environment.The control group(n=22)followed the traditional instruction without using any DGS.The comparison between students’performance in the pre-and post-tests indicates that the experimental group outperformed the control group not only in items of point translations and graph translation of quadratic functions,but also in items in an extended area including complex functions and circles.This quasi-experimental design can be extended to the teaching of graph transformation of trigonometrical functions as well as geometrical shapes in 2-D and 3-D coordinate systems.
作者
江春莲
胡玲
JIANG Chun-lian;HU Ling(Faculty of Education,University of Macao,Macao 999078,China;Shanghai Branch,Beijing Bytedance Limited Cooperation,Shanghai 201100,China)
出处
《数学教育学报》
CSSCI
北大核心
2020年第6期32-39,共8页
Journal of Mathematics Education
基金
澳门大学研究基金项目——高中生函数学习路径分析(MYRG2020-00277-FED)。
