浅谈反例法在微分中值定理教学中的应用
|
摘要
在数学概念的教学中,不仅要正确使用正面的例子加以阐述,还要重视反例的应用.在高等数学微分中值定理的学习中,学生很难抓住概念的本质特性,不能深刻理解概念的内涵和外延,在教学过程中构造和应用恰当的反例,往往会起到事半功倍的效果.在学习中学会构造恰当的反例是一项必要的数学技能,应该将反例的构造训练渗透于教学过程之中.从微分中值定理的教学角度出发阐述反例法的运用,说明适当的反例应用可以培养学生的学习能力、思考能力和逆向思维的能力.
In the teaching of mathematical concepts, we should not only use positive examples correctly, but also attach importance to the application of counterexamples. In the study of the differential mean value theorem in higher mathematics, it is difficult for students to grasp the essential characteristics of concepts and to understand the connotation and extension of concepts. In the process of teaching, constructing and applying appropriate counter-examples will often achieve twice the result with half the effort. Learning to construct proper counterexamples is a necessary mathematical skill. The training of counterexamples construction should be infiltrated into the teaching process. This paper expounds the application of counter-example method from the angle of the teaching of differential mean value theorem. It shows that proper application of counter-example can cultivate students' learning, thinking and reverse thinking abilities.
In the teaching of mathematical concepts, we should not only use positive examples correctly, but also attach importance to the application of counterexamples. In the study of the differential mean value theorem in higher mathematics, it is difficult for students to grasp the essential characteristics of concepts and to understand the connotation and extension of concepts. In the process of teaching, constructing and applying appropriate counter-examples will often achieve twice the result with half the effort. Learning to construct proper counterexamples is a necessary mathematical skill. The training of counterexamples construction should be infiltrated into the teaching process. This paper expounds the application of counter-example method from the angle of the teaching of differential mean value theorem. It shows that proper application of counter-example can cultivate students' learning, thinking and reverse thinking abilities.
引文
[1] 李文林.数学史教程[M].北京:高等教育出版社,2000.
[2] 崔克俭,薛自学.高等数学[M].北京:中国农业出版社,2016.
[3] 夏大峰,徐晶,王顺凤,等.高等数学的反问题与举例[M].北京:北京理工大学出版社,2010.
[4] 陈燕,朱建国.基于微分中值定理的反问题研究[J].现代农业科技,2008(24):317-320.
[5] 王丽丽,薛然.反例在数学分析教学中的应用[J].通化师范学院学报,2018,39(10):103-106.
[6] 张丽颖.微分中值定理的推广[J].兰州文理学院学报:自然科学版,2016,30(1):6-8.
[2] 崔克俭,薛自学.高等数学[M].北京:中国农业出版社,2016.
[3] 夏大峰,徐晶,王顺凤,等.高等数学的反问题与举例[M].北京:北京理工大学出版社,2010.
[4] 陈燕,朱建国.基于微分中值定理的反问题研究[J].现代农业科技,2008(24):317-320.
[5] 王丽丽,薛然.反例在数学分析教学中的应用[J].通化师范学院学报,2018,39(10):103-106.
[6] 张丽颖.微分中值定理的推广[J].兰州文理学院学报:自然科学版,2016,30(1):6-8.