A phenomenographic study on the responses of students and instructors about some decisive questions and related answers regarding the teaching and learning of derivatives in mathematics education

This study attempts to identify the misconceptions, lack of fullconceptualization, and diverse approaches by surveying the views of some studentsand teachers from all around the world on the questions and answers found in ?AskDr. Math?, an international website, relating to derivation in calculus that constitutesthe core of Advanced Mathematics. For this purpose, 12 questions from ?Ask Dr.Math? have been selected and put in an order.Collection of the data was done in a phenomenographic fashion. The datacollected were analyzed using ?content analysis?.Three cadets who were students at the Turkish Military Academy during2005-2006 academic year and two math teachers who were teaching these cadetsparticipated in this study.It is hoped that the findings of the research will bring a different insight intoteaching and learning of derivation for they are expected to provide guidance inteaching math class. Teachers may enable the students to comprehend conceptscorrectly and effectively provided that they take notice of the subjects studied and thesuggestions presented here.