Pre-service elementary mathematics teachers’ understanding of derivative through a model development unit

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2014
Kertil, Mahmut
The purpose of this study was to investigate pre-service mathematics teachers’ understanding of ‘big ideas’ involved in derivative such as covariational reasoning, rate of change, and the graphical connections between a function and its derivative. In this design-based study, a model development unit was designed, experimented, and evaluated in a real classroom setting as a part of a course offered to pre-service mathematics teachers in two iterations. The data were collected from the 20 pre-service mathematics teachers attending to the course and enrolled in a middle school mathematics teacher education program at a public university in Ankara during the fall semester of 2011-2012. The implementation of the model development unit was continued for 8 weeks. Multiple data collection methods were used in this study, and the data was analyzed by using qualitative and quantitative methods. The data revealed that, at initial phases, pre-service mathematics teachers had difficulties in covariational reasoning, rate of change, and the graphical connection between a function and its derivative. In the progress of the model development unit, considerable improvements were observed in pre-service teachers’ covariational reasoning abilities. Similarly, while they were unaware of the concept of rate of change, they realized it as being a different interpretation of derivative, slope, and difference quotient. However, their confusions between rate (of change) and amount (of change) continued. Furthermore, pre-service teachers’ understanding of the graphical connection between a function and its derivative shifted from thinking only by procedures to thinking by making sense of those procedures. These findings of the study revealed that even university students who already completed calculus courses could not learn the essential ideas involved in derivative. The data of this study also showed the potentials of mathematical modeling activities in promoting students’ contextual understanding of the ideas involved in derivative.
Citation Formats
M. Kertil, “Pre-service elementary mathematics teachers’ understanding of derivative through a model development unit,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.