高中生三角公式理解的实证研究——以上海为例  

Empirical Study on Senior High School Students’ Understanding of Trigonometric Formulas in Shanghai

作　　者：何忆捷[1,2] 彭刚[1] 熊斌[1,2] 

机构地区：[1]华东师范大学数学系,上海200241 [2]上海市核心数学与实践重点实验室,上海200241

出　　处：《数学教育学报》2016年第1期51-56,共6页Journal of Mathematics Education

基　　金：上海市核心数学与实践重点实验室课题(13dz2260400)

摘　　要：近几十年来，国内外学者就理解的分类及层次提出了各种理论与观点．以工具性理解、关系性理解和创新性理解这3种理解层次为视角，研究上海高中学生对三角公式的理解情况．基于调查与测试，发现学生的工具性理解质量总体较好，但在关系性理解的多个方面均显出不足．研究者同时设计了一个有助于考察创新性理解的任务系列，并借此初步揭示了学生的一些表现特征．研究亦发现，相对于高一学生，高三学生在关系性理解与创新性理解的某些方面更具优势，同时他们对公式的理解表现出更多工具性的特点．In recent decades, scholars from home and abroad have put forward various theories and opinions about mathematical understanding. This paper examines Shanghai＇s high school students＇ understanding of trigonometric formulae from the perspective of instrumental understanding, relational understanding and innovative understanding. In terms of research and testing, the researchers discover that students generally perform well on the instrumental understanding level, but are lacking in many ways in their relational understanding. A series of tasks which is designed by the researchers reveals certain characteristics of these students＇ innovative understanding. This research also shows that while Senior Three students perform better than Senior One students in some aspects of relational and innovative understanding, they also demonstrate a higher level of tendency towards the characteristics of instrumental understanding.

关 键 词：三角公式 工具性理解 关系性理解 创新性理解 迁移性理解 

分 类 号：G420[文化科学—课程与教学论]