Developing Teaching Approaches to Concepts of Calculus

Topic:
Calculus
This GeoGebra Book shows teaching approaches of function, continuity, differentiability and differential equations, which are referenced in theoretical elements developed by Tall and his colleagues. We develop approaches for Calculus’ concepts: function, differentiability, continuity and differential equation. For the concept of function, we show examples of piecewise defined functions and a function, defined by a sentence which the graphs is a curve with interruptions. The concepts of continuity and differentiability are explored by the notion of local straightness which helps to develop a formal conceptualization and it is emphasized an example of a continuous everywhere but differentiable nowhere function. Concept differential equation, y’ = f(x, y), is explored through a qualitative approach to seeking the solutions, which begins from the analysis of their field directions. Teaching Calculus requires the use of materials that supports learning. The material presented in this article fulfills that requirement and it is prepared with reference to theoretical elements designed by a specialist area for this purpose. Besides that, it is possible to identify GeoGebra’s tools, commands and predefined functions that enable the development of the necessary teaching materials that are meaningful for teaching and learning concepts covered in Higher Education, especially the differential and integral calculus.
Developing Teaching Approaches to Concepts of Calculus