Abstract:

In the last 20 years we have been involved in training math teachers for basic and secondary school. As we have to accompany them in some of their training classes, we realized that one of the main problems they had to deal with was how to motivate students and keep them interested in classes. As a matter of fact, this is also our problem in our classes in university first year courses. To overcome the problem, it is necessary to give students the right answer to the old question “what is this for?”

Our experience showed us that, actually, students don’t want to know the use of math topics in real life. They just want to be able to use them by themselves, even if they are solving fake problems.

After attending some conferences, where links between art and mathematics were the main topic, we decided to introduce, whenever possible, in our classes for future math teachers some not conventional ideas to approach themes in an appealing way. Though not conventional, these ideas are very simple and can be easily used in a high school classroom. For instance, twisting balloons can be a very good tool to introduce some basic concepts of Graph Theory or to motivate the study of polyhedrons. In Portuguese high school there is a course called Mathematics for Social Sciences, which is attended mostly by students that don’t like math at all. One of the chapters of this course is about graph models. Together with our students –future teachers – we prepared a practical activity with balloons on topics such as Euler’s Theorem for Euler circuits and Euler paths. Some ideas around Euler’s Theorem for Euler circuits and Euler paths are better understood when we twist one or more balloons with the form of the graph. Also Euler Theorem for polyhedrons is very well demonstrated when we twist balloons with the form of different polyhedrons.

Also related with the geometry of polygons and polyhedrons is the use of modular origami. The construction of a “sonobe” piece is a good departing point to apply Pythagoras’ theorem or some trigonometry concepts to study the angles and measures of each peace and of the polyhedrons that can be assembled with several of these pieces.

Another activity that became very popular between young students is what we have called “self-raising polyhedra”. This, actually, is a funny way of building the so-called platonic polyhedron departing from a planar net.
In this work we give account of the use of these ideas for teacher training and also of their actual application in the classroom.

Keywords:

Teacher training, Motivation, Applications.