摘要
类比思想是从事数学研究过程中一项重要的思维工具。本文针对高等数学教学中不定积分的学习和计算这一难点和重点,探究类比思想在其中的应用及效果,提出了类比思想的思维模型,然后通过多个计算案例对这几种类比方法的运用做了详尽的演示与归纳,并以试验的形式分析了类比思想运用于不定积分计算时的效果。实验结果表明:在不定积分的计算过程中运用类比思想能够明显提高解题的正确率与效率。
Analogical thinking is an important thinking tool in the process of mathematical research. And solutions to many problems canbe found by using this important tool effectively. Therefore, this article focuses on the difficulty in learning and calculating indefiniteintegrals in advance mathematics teaching, and explores the application and effect of analogy thought. The studies show that by comparingsome features of integrand, the application of analogy can be attributed to three categories:structural analogy, conceptual analogy,and principle analogy. In this paper, an analogical thinking model is proposed, and several examples of calculations are used to demonstrateand summarize the use of these analogies.Finally, the effect of analogical thinking on the calculation of indefinite integrals is analyzedin the form of experiments.The experimental results show that using analogy in the calculation of indefinite integrals can significantlyimprove the accuracy and efficiency of problemsolving.
作者
张峰
ZHANG Feng(Department of Navigation,North District,Anhui Vocational and Technical College of Communications,Hefei 230051,China)
出处
《遵义师范学院学报》
2020年第5期78-82,共5页
Journal of Zunyi Normal University
基金
安徽省级规划教材项目(编号:2017ghjc329)。
关键词
类比法
思维模型
不定积分
解题方法
analogy
thinking model
iIndefinite integral
problemsolving mode
