Abstract:

The study of functions and their graphs is done in high school both with pen and pencil work and with the help of graphical calculators. Nevertheless the time they spend with this study, students reach the university showing enormous difficulties in elementary calculus courses, namely in what involves the knowledge of graphs of functions, for instance, they always show to be insecure in computing the value of areas, volumes and length of lines.

Teaching at university is essentially formal and abstract, and poorly prepared students quickly give up, and ending choosing to study something else that doesn’t require mathematics.

The project described in this work was designed for students finishing high school or starting the university, and its main scope is to interest students in the study of functions in a playful and not conventional way. Students are invited to create a mathematical model for sketching known objects like glasses or bottles. With some practice they can begin drawing animals and even understand how they can give the illusion of movement. This project helps students to better understand the behavior of function graphs under geometric transformations, and also develops their skills in what concerns defining the appropriated limits of a restriction of a given function. These skills are fulcra when they need to evaluate an area or a volume.
We present a collection of cartoon images and their associated "mathematical recipes", produced by ourselves or by our students under our supervision.

Keywords:

Functions, graphs.