Abstract:

It is well known that a way to interest children and to teach new topics is playing with them. We can involve children, but not only, using educational games available on the market or construct with them all the pieces and the rules they need to use to develop new games.
In this paper we propose an educational project involving maths and representation

The principal aim is to explain the methodology we use in the construction of original evolutions of the traditional windmill origami base in order to obtain connectable pieces for tessellation (3-4-5-6- edges tesserae equipped with winglets and pockets).

Then we propose how to use the produced tesserae, during both the folding or connecting process, in order to:
• learn geometric language through the modeling of basic paper module;
• educate to the shape reading by decomposing and recomposing it;
•educate to understand the relationship between objects, symbolic representation and descriptive representation

The chosen media is origami, because it is able to surprise participants -children for magic and older students for effectiveness-: it is the ideal tool to show geometry in a seemingly informal but also extremely rigorous way. Moreover, the use of the colored paper allows students to fold, in a cheap way, a lot of funny pieces which can be dynamically and creatively aggregate.

The math lesson starts from the folding passages and continue during the explorations of some geometric topics in the puzzle combinations: geometric properties of polygons, as symmetries, equiestension and isoperimetric problems, can be investigate getting out relationship among tessellation, drawing and maths. For oldest students, teacher can discuss also the construction methodology.

The activity offers the possibility of making concrete reasoning on the relationships between geometric figures: the modular elements, made during practice, become cognitive artifacts to prepare the mind to welcome intuitions and discoveries.

The use, by the teaching staff, of a specific language calibrate according to the participants, to support direct observation, leads to the development of geometrical abilities that become the basis for subsequent implementations throughout the entire educational path, thus becoming part of a vertical distribution of knowledge.

The description of complex shapes during a tangram-based game brings students to read shapes from an outline and viceversa, allows them to create new puzzles, with different levels of complexity and works on drawing as a graphic trace.

The possibility of expressing the experience by a double point of view, math & Art, with the same language let bring us in an exploratory journey in concrete Geometry.

Until now, we proposed these activities in primary and middle school and in training classes for teachers who tested the activity in their schools finding a good interest from participants. We will test this game also in occasion of “Il Salone del Libro di Torino”, for students and generic public as the game can be adapted to adults too, offering games with incremental difficulty.

Keywords:

Geometry, tessellation origami, symmetry, cognitive artefact.