Graphical Understanding in Mathematics Education: Derivative Functions and Students’ Difficulties

Effective teaching is one of the most important factors to improve students’ achievement. Therefore, many researchers in mathematics education are looking for several ways to improve the quality of learning. The purpose of this paper is to investigate an overview of specific difficulties based on the graph of derived function, another words, how students find the connections between the graph of derived function and the some properties of the original function.The subjects were 102 high school students in grade 11. The study was conducted during the fall semester in two calculus classes. The data of the research has been collected from 5 diagnostic the graph of derived function involved the chance in slope, decreasing, increasing, a local maximum, a local minimum, the point of inflection.The questionnaires were designed to assess how well the students had learned procedures the connections between the graph of derived function and the some properties of original function. Each student was asked explain how you arrived at your answers. While working on the answers of the students, not only the accuracy of the students’ answers was examined but also the methods were being analysed even if they were incorrect.The results indicated that the students find it difficult to make connections between the graph of derived function and the original function. Usually, they were to interpret the graph of derived function as the graph of function. The students did not use the mathematical language to describe the graph of derived functionEffective teaching in calculus course should be informal, intuitive and conceptually based on graphs and functions in order to improve the quality of learning and develop the understanding of calculus concepts.