Abstract:

Ludodidactic is an exceptional tool for observing and training basic skills, or life skills, which in recent years have been at the center of the training objectives of schools. In fact, they train problem solving skills, spirit of initiative, critical sense and creativity. Bruner (1972) defines play as "a particular type of violation of fixity" thanks to which standardized learning patterns are broken and socialization processes are developed, increasing the ability of adolescents to relate to others and to communicate. According to Piaget (1962) the stages of the game promote the cognitive stages of the child and accustom him to what we now call citizenship competence: respect for others and rules.

This paper describes the experimentation of a ludodidactic activity carried out among the laboratories designed in the Mathematical High School Project, perfectly integrated into the curricular activity and consistent with the national indications of the Italian Ministry of Education.

The purpose of the workshop is to deepen the theme of geometric transformations. It is a flexible activity since it can be used from primary school students in its simplest version, to university students in its most complex version.

The experimentation took place in four extracurricular meetings organizing a class tournament in which teams of two or three students participated, thus exploiting the advantages of cooperative learning: peer teaching in teamworking, exercise of dialogue and argumentation, active participation that increases inclusion. The activities have been developed both in the analog version in presence and in the online version remotely thanks to the integration on the GeoGebra software. The GeoGebra software was also used in presence and the various matches were projected on a screen to allow all students to attend the competitions. The matches are played on an original "polar chessboard" with theoretical help cards and special ones to advance in the game and hinder the progress of opposing teams.

The experience is centered on students both because it allows them to self-evaluate their performance and to be an active and responsible protagonist of their learning. The methodology is constructivist, inclusive and cooperative among peers. Traditional teaching-learning schemes are broken to motivate a-didactic situations that make the student the real protagonist of the construction of his mathematical culture through learning, respect for rules, interaction with peers, problem posing and problem solving. Players in making their own play must imagine all the possible scenarios that arise from it by hypothesizing the moves of the next opponent with a certain probability. Each game is therefore a problem-solving activity for each team. The moves are performed by applying knowledge about geometric transformations: symmetries, rotations and translations, and also using game strategies.

With reference to representations of Game Theory, the rules of the game determine the moves allowed in each situation. All possible player moves can be represented through a tree diagram. Non-terminal nodes (leaves) represent the moves of the game. In particular, a match is represented by the path that ends in a leaf (terminal node) of the tree.

The paper will describe the salient didactic aspects of the ludodidactic activity and the educational impact both in terms of students’ acquired contents and of involvement and participation.

Keywords:

Mathematical High School, education, ludodidactic, game-based learning, geometry.