Experiences

Dynamic maths with geogebra

Veronica Del Bene

Italy

Vocational School

Maths

Laboratory

Direct

One of the main causes of the difficulties that students encounter in learning maths lies in the fact that students almost invariably limit themselves to mechanically applying mathematical procedures which have only been learnt by rote and are not associated with any sense or meaning. New technologies, of course, are among the tools that can most effectively foster teaching aimed at producing relevance. I am referring in particular to the possibility of using specific software in computer labs, for example Geogebra, which enables the students to master, actively and consciously, more effective learning through activities involving building, experimentation and discovery. As such, Geogebra is an open source software of dynamic maths on a multiplatform that brings together tools for interactive geometry, algebra, statistics and mathematical analysis. Working simultaneously in Graphics View and in Algebra View, which are parts of the user interface windows, the student is able to visualise and easily manipulate mathematical objects. Geogebra’s dynamic and interactive make enhances the visual/spatial mechanisms that support mathematical learning processes and that facilitate the creation of relevance. Considered what has been said, in recent years I have always tried to include teaching experiences that call for the use of Geogebra in my planning. Over time this has proven to be of very considerable assistance in explaining many topics, as well as effective and above all very much appreciated by the students. Among the most significant experiences, I will draw your attention to the one on studying derivatives. In summary, the activity set out that the student, after having drawn a graph of the assigned function, and a given point having been selected, employing the Tangents Tool and the Slope Tool, and selecting the Trace On command, can monitor, when moving the point on the curve, the variations of the derivative as an angle of the tangent line to the graph in the point. In this way, the student easily sees the concept of derivative functions, but above all manages, with no difficulty, to conceive of the curve, the graph of the function, as connected to its straight line tangents and thus, through a purely visual approach, manages to comprehend the intimate relationship that exists between the progress of the function and the sign of its first derivative. The use in the lab of this teaching module has in fact permitted many of my students to rapidly acquire those abilities that pertain to the study of the monotonic function and the study of the possible terminal points relative to a function.