Pre-service elementary mathematics teachers’ conception of derivative from commognition perspective

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2013
Yiğitcan Nayir, Özge
The purposes of this study were to investigate pre-service elementary mathematics teachers’ discourse on derivative in group, classroom and individual discussions and determine their conception of derivative. In order to examine pre-service teachers’ discourse on derivative communicational approach to cognition (commognition) was applied. Pre-service teachers’ words and their uses, visual mediators, narratives and routines were analyzed. This study was designed as a qualitative study. Data were collected from pre-service mathematics teachers in the fall semester of the 2009-2010 academic year. Pre-service mathematics teachers were freshmen students enrolled in a public university. Derivative test results, group discussion records, classroom discussion records and interview records were analyzed to determine pre-service teachers’ discourse on derivative concept and their conception of derivative. According to the results of the study, group discourse reveals that pre-service mathematics teachers in the observed group have the conception of derivative as slope. However, individual discourse shows that interviewed pre-service teachers had the conception of derivative as limit of the slopes. Some pre-service teachers have common usages related to the tangent value in the group and classroom discourses. Group discussions develop pre-service teachers’ discourse on the rate of change of a function in the observed group. Analysis of the words, visual mediators, endorsed narratives and the routines of the group, classroom and individual discussions reveal that pre-service teachers have some difficulties related to the concept of derivative. Some of them have problems to understand the instantaneous rate of change. They can not differentiate it from the average rate of change. Some of them have difficulty to understand the relation between the function properties and the first and second derivatives of the function. They also have problems to give meaning to the relations between the first and second derivatives. Most of the pre-service teachers have tendency to depend more on rules related to the concept of derivative. Some pre-service teachers have problems for the transition of one form of the representation into another form. Moreover, visual mediators are useful to understand what pre-service teachers mean in their words and endorsed narratives. The fact that what some pre-service teachers actually say and what they mean are totally different from each other is observed. Findings obtained from this study showed that pre-service teachers have some deficiencies related to the concept of derivative. Therefore, in calculus and mathematics teaching method courses, these deficiencies should be emphasized more. Besides, it is found that there can be differences what pre-service teachers say and what they actually want to say. Therefore, what pre-service teachers would like to say in their words, endorsed narratives, visual mediators and routines should be paid more attention. Group discussions enable pre-service teachers to improve their ideas in terms of the rate of change. Therefore, pre-service teachers have the chance of sharing and developing their ideas with the help of group, classroom and individual discussions. And also analyzing these discussions could enable us to notice the problems that pre-service teachers have while learning the subject of derivative.

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Citation Formats
Ö. Yiğitcan Nayir, “Pre-service elementary mathematics teachers’ conception of derivative from commognition perspective,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.