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| 基于数学实验室的高中生数学抽象能力的培养研究
摘要
本文通过文献法、测验法、分析法等研究方法，得到在传统数学课堂教学中，培养数学抽象能力存在的问题：倾向单一讲练，难以经历抽象概念法则的观察概括；囿于教师板演，难以实现抽象原理方法的总结归纳；不易创设情境，难以体验抽象数学模型的探索发现.利用TI图形计算器针对上述三个问题提出具有操作性的方法：图像定位追踪，刻画符号表征；多维视角演示，动态“逼近”本质；直观操作工具，检验抽象模型.选取芜湖市第十二中学两个班级共计105名学生进行实验研究，标记为实验班级和对照班级.实验前进行数学抽象能力测试卷的前测，利用SPSS26.0分析两个班级成绩无显著差异，试验结束后进行后测，统计整理数据发现两个班级成绩存在差异.具体表现为：实验前对照班、实验班级均分74.7、75.4，独立样本检验值0.735，实验后对照班、实验班级均分76.5、81.2，值0.005.得出如下结论：基于数学实验室的数学抽象能力的培养方法是有显著效果的.
关键词：数学抽象能力，数学实验室，高中生，培养方法
Research on the Cultivation of High School Students' Mathematical Abstract Ability Based on Mathematical Laboratory
Abstract
In this paper, through the literature method, test method, analysis method and other research methods,it is found that in the traditional mathematics classroom teaching,the development of mathematical abstract ability exists difficulties: tendency to single practice,difficult to experience the observation and generalization of abstract concept rules; confined to teachers' board performances, it is difficult to achieve the summary of abstract principles and methods; it is difficult to create situations and mine problems, it is not easy to experience the exploration and discovery of abstract mathematical models. Using TI graphic calculator,this paper puts forward three operational methods for three problems: image positioning and tracking, depicting symbolic representation; multi-dimensional perspective demonstration, dynamic "approaching" the essence; intuitively manipulate tools, validating abstract models. A total of 105 students from two classes of Wuhu No.12 Middle School were selected for experimental research,which were labeled as experimental class and control class. Before the experiment,the pre-test of mathematical abstract ability test paper was conducted, and SPSS26.0 was used to analyze that there was no significant difference in the scores of the two classes.After the experiment, the post-test was conducted,and the statistical data showed that there were differences between in the scores of the two classes. Specifically: before the experiment,the average score of the control class and the experimental class was 74.7 and 75.4, and the P value of the independent sample t-test was 0.735.After the experiment, the average scores of the control class and the experimental class were 76.5 and 81.2, and the P value was 0.005.The conclusion is as follows: the cultivation method of mathematical abstract ability based on mathematical laboratory has remarkable effect.
Key words: mathematical abstract ability,mathematical laboratory, high school students, training methods
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