Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method.

The purpose of this study was to explore how university students construct the relationship between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. The participants in this study were 33 pre-service mathematics teachers. An open-ended questionnaire, knowledge test, tasks, and participants’ dynamic constructions were used as data collection tools. The analysis of participants’ products was based on descriptive analysis and Toulmin’s model. As a result of the analysis, it was found that the participants constructed the relationship between the concepts of differential and derivative as well as the concepts of tangent and slope by using them within the geometric framework. Due to the integration of GeoGebra and the ACODESA method, the participants explored the relationships among true change, estimated change, and error by using the geometric interpretation of the concept of differential. It was found that with this method, they deduced that Δx and dx were two different symbols for the same variable. [ABSTRACT FROM AUTHOR]