One of the important problems in mathematics education is how to make develop a deep understanding of definitions، theorems and mathematical structures. In order to achieve this، the teacher should explain all the knowledge and tools to be used and the student should try to understand. This paper first discusses the concept of mathematics is the subject of academic debate mathematical methods will be discussed، in both areas، the practical examples of how the project is presented. First، the proposed an algorithmic approach، the implementation of the algorithm، to create a deep understanding of concepts derivative ، and second in the debate about discussion education method for a deep understanding of concepts derivative and the concept of function is expressed. In this paper، using the results of a study in the Shahrood University and other documents، effectiveness of the discussion method، is shown.