Abstract: Numerical analysis is a course on offer to introduce fundamental theories and basic methods of scientific computing. The interpolation method is most fundamental in numerical methods, while the interpolation remainder is the core of the interpolation method. In the teaching process, the emphasis should be laid on the elaboration of its origin and proof of the interpolation remainder. Besides, a detailed explanation must be given to some notes that are in need of due attention so as to lay a sound foundation for the learning of content like the function approximation, numerical calculus and numerical solutions for differential equation in numerical analysis.