investigation of students' misconceptions and graphical understanding of the concept of first derivative of a function
This research attempts to investigate the misconceptions, and their causes, of the students in the concept of the first derivative of a function defined graphically, and to explore students’ understanding of this concept based on the Action-Process-Object-Schema (APOS) theoretical framework. A comprehensive literature review shows that students have some common misconceptions in the concept and that students vary in understanding this concept. A group of 90 participants was chosen from two official secondary schools in the southern suburb of Beirut, together with their 4 teachers. A two-context-test (context I, where the graph of functions was given and derivatives were to be found, and context II, where the derivative(s) of a function at a point and to other calculus concepts that were closely related to the subject were given and convenient graphs were to be drawn) was prepared, and all the participants were examined in this test. The results of the test were categorized depending on the misconceptions of the participants, and then 36 participants were chosen to have one-to-one interviews, together with their teachers. The misconceptions of the participants vary among seven forms and the reasons of these misconceptions vary among eight eventual causes. The results of the participants’ understanding of the concept, based on the APOS theory, differ from one context to another within each level, but most of the students approached the object level in context I and the process level in context II. (Author's abstract)