The First Derivative of an Exponential Function with the “White Box/Black Box” Didactical Principle and Observations with GeoGebra

This paper shows how GeoGebra—a dynamic mathematics software—can be used to experiment, visualize and connect various concepts such as function, first derivative, slope, and tangent line. Students were given an assignment to determine the first derivative of the exponential function that they solved while experimenting with GeoGebra. GeoGebra enables students to experiment, model, and research their ideas in order to get desired results for mathematical problems. The software package, GeoGebra, enriches the educational process and opens up new questions and possibilities. Learning and teaching mathematics in contemporary, technology-rich surroundings requires new didactical approaches. The findings in this paper are based on the “White Box/Black Box” didactical principle. Recommendations for mathematics teachers are shared.