从不定积分概念的教学看数学课堂的思想性

On the Ideological Character of Mathematics Classroom through the Teaching of the Concept of Indefinite Integral

通过不定积分概念课的案例设计与教学阐述了课堂教学中数学思想的重要性,指出作为微积分的精髓,局部地以直代曲应该贯穿于微积分的始终,无论是教材的编写还是课堂教学都应该凸显这一重要思想.通过不定积分概念课教学示例,分析了教师数学素养在数学课堂教学中的重要性以及教学与科研之间的关系.

Through the case design and the teaching of the concept of indefinite integral,this paper explains the importance of the mathematical thoughts in classroom teaching.As the quintessence of Calculus,the mathematical thought of replacing the curve by a straight-line locally should be emphasized throughout the whole Calculus,whether in compiling textbooks or in the classroom teaching.Through the teaching of the concept of indefinite integral,the importance of teachers'mathematical literacy in mathematics classroom teaching and the relationship between teaching and scientific research are analyzed.