Abstract:

In teaching Maths, it is often difficult to combine the discovery dimension with that of training, even though both are needed for the acquisition of mathematical knowledge. For this reason, as teachers of the Maths Teaching Laboratory of Politecnico di Torino, we propose some activities focused on experimentation and discovery, with the aims of creating interest in Maths and of stimulating its study.

The "Mathematical journey on a desert island" is an activity we have experimented with groups of students (from primary school to university) and families, as part of the Biennale Tecnologia event organised by the Politecnico di Torino. In a time of about two hours, we propose a path involving definitions, examples, and conjectures. The point of arrival is a special case of a theorem by the American mathematician Marston Morse: the activity we describe is inspired by one of his lectures, the video of which was very kindly made available to us by the Library of Institute of Advanced Studies in Princeton (New Jersey, USA).

Depending on our interlocutors, the problem has been posed with different levels of formalism: here we will present a version of the activity suitable for children and families.

The starting point is the description of points of maximum, minimum and saddle points of functions of two variables described as mountain peaks, lakes and passes. The formula we get to, links the numbers of the different types of points and involves only sums and subtractions.

Participants in the activity are guided to the discovery of the formula through different steps in the form of observation and manipulation games.

The proposed path is intended to exemplify what the mathematical approach consists of: posing a problem, visualising, studying examples and particular cases, formulating conjectures and translating them into an appropriate language, proving and asking new questions.

Keywords:

Active learning, tangible tools, mathematical objects, student-centered learning.