Promoting Prospective Mathematics Teachers' Understanding of Derivative across Different Real-life Contexts



This study investigates prospective secondary school mathematics teachers' developing conceptions about the meaning of derivative (as rate of change) while working on a series of tasks involving different non-motion real-life contexts. The study was conducted by employing a case study method. The participants of the study were 25 prospective secondary school mathematics teachers enrolled in the mathematics teaching methods course. A series of contextual tasks involving different real-life situations about derivative was designed and implemented in the form of problem-based learning as a regular part of the course. Pre and post questionnaires, written group solutions to the tasks, individual reflection papers, and video-recorded online classroom discussions were the data sources. A constant comparative analysis method was employed in analysing the data. The results showed that prospective teachers have difficulties in interpreting the meaning of derivative in different real-life contexts. While they were frequently using “amount of change†and “slope†interpretations, they started to use “rate of change†interpretation. However, the classroom discussions showed that most of the prospective teachers were using the “rate of change†expression as a memorized term without engaging in its contextual meaning. We made some inferences about the teaching and learning of derivative and also the professional development needs for teachers.   

Author Biographies

Mahmut Kertil, Marmara University

Mahmut Kertil has received her bachelor (B.S) degree in the Department of Mathematics Education at Boğaziçi University in 2004, M.S. degree in Mathematics Education at Marmara University in 2008, and PhD degree in Mathematics Education at Middle East Technical University in 2014. He worked as research assistant at Marmara and Middle East Technical Universities through his M.S PhD education. During these years, he participated in Scientific Research Projects (BAP) funded by Marmara University and TUBITAK. He continues to participate various research projects as researcher funded by TUBİTAK and Marmara University. He published various research papers at national and international journals. His research interests are mathematical modelling and problem solving, mathematical thinking, and teacher education. Mahmut Kertilhas been working currently at the Department of Mathematics and Science Education, Marmara University since June 2014.   
Research Interests: Mathematical modelling and problem solving, Mathematical thinking, Teacher education


Hande Gülbağcı Dede, Marmara University


Ph.D., Marmara University, Faculty of Education

Department of Mathematics and Science Education,

34722 Kadıköy - Istanbul - Turkey,


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