Mathematics candidate teachers? understanding of derivative concept and their mistakes

The aim of this study was determined as stating Mathematics candidate teachers' understanding of derivative concept and difficulties they encounter within the process of understanding the concept. Derivative concept is closely related to limit, rate of changeand tangent/slope concepts and it is defined with the help of these concepts. Accordingly this study concerned relations between derivative and limit, derivative and rate of change and finally derivative and tangent/slope while describing Mathematics candidate teachers' understanding of derivative concept.The research is a case-study. The working group was composed of 45 candidate teachers registered to Mathematics Education program in Secondary Schools Science& Mathematics Field Education Department in a state-owned university. The data of the study were gathered with: 3 written exams applied with a week in between (1st focused on relation between derivative and limit; 2nd focused on relation between derivative and rate of change; and 3rd one focused on relation between derivative and tangent/slope) and clinical interviews conducted with 6 candidate teachers. First, the data coming from examinations were grouped in four basic categories as; "fully right answer", "partially right answer", "wrong answer" and "no answer". The rate of each type of answer which fell in the groups was expressed with frequency and percentile. In addition, the wrong answers given by the candidate teachers were also grouped with respect to their similarities and differences, which stated the mistake types committed by the candidate teachers. In order to state opinions directing candidate teachers to right answers and wrong answers, the data coming from clinical interviews were categorized based on their similarities.The study conducted showed that candidate teachers have superficial knowledge about derivative concept. Since candidate teachers, whose understanding were mainly restricted to definitions, they could not fully consolidate the content of definitions. Therefore they had difficulties in interpreting relations between derivative-limit, derivativerate of change and derivative-tangent/slope. It was also determined that they hardly had opinions about the attribution of these relations. As another piece of finding, the research came up with that candidate teachers were more successful the interpretation of derivate concept in algebraic form rather than graphical and table representations.Key Words: Derivative concept, Candidate teacher, Understanding, Mistakes