Imagine Calculus with Mathematica

Teaching and Learning Facilities

Roberto Cavaliere
Dario Sacchetti

Scisoft s.r.l. 
University of Rome “La Sapienza”

Abstract

The idea is to represent theoretical concepts of calculus by means of dynamic visual tools fully implemented with Mathematica and related technologies such as GUIKit.

We conceived a general framework where the lesson will take place, similar to a traditional blackboard.

Into this framework we put different lessons related with different concept. For each lesson we had to conceive special features, enabling graphic simulations aimed at representing basic concepts.

For that, the key research activity was the breakdown of each self-contained concept in a series of cognitive elementary units, related to each other by logical-functional rules. These rules considered the learning complexity of each singular concept. From an operative point of view, such elementary units are presented using a set of graphic objects, visualized in an unique dynamic frame. If needed, the images are supported by text sentences to formalize what appears in the figure. In that way, a lesson is structured in a sequence of visualizations, managed and commented by the teacher that, step by step, allow the construction of a mental image representing an approximation of the concept.