Abstract:

This paper describes an activity to visualize the ½ fraction using traditional LEGO bricks: it is based on creating an urban landscape and on discovering the different perception of area, when they are unitary or widespread.

Why game based learning?
Because playing is a metacognitive process that develops imagination and creativity and helps understanding transformations as a first design act.

Why with LEGO?
Because there are many and shared educational experiences with LEGO (LEGO Education, Salmaso 2013) and the one I present is intended to visualize the basic geometric concept of one-half, and to discuss it simultaneously from a different cognitive point of view, the perceptive one (Piaget, Inhelder 1976).

The activity:
The proposed activity is a playful, tactile, graphic, descriptive, perceptive and design experience through which the child can build, dismantle and reconstruct a shape by observing its dynamics and recording its transformations.
By a shared language (Cera 2009, Farnè 2016), the game is played with a squared dashboard (16x16) and many bricks distributed in horizontal layers of tiles of homogeneous color in every single layer.

The first phase:
Creation of a model under geometric dictation: the children have to cover half the square dashboard with a single color, covering the area identified according to a median.
Then they repeat the same instruction covering half of the surface of the previous layer, operating with respect to medians which are, layer by layer, perpendicular to each other and keeping full/covered the anchored area at the same point. The intrinsic repetitiveness of the operative sequence favors the deduction born from the empirical experience (Kanizsa, 1980). They proceed until they reach a boundary layer, with only one brick, a 1x1 block.
The activity allows to visualize fractions and their relations in a two-way round trip between multiplications and divisions; also, it allows to read their superficial distribution, according to rhythms, axes and modules in full respect of the 'good form' of Gestalt (Marotta, 2012).

The second phase:
Deconstruction of what has been achieved together with the conservation and registration of the pieces coming from individual layers. The possible declinations of this phase open multilevel design scenarios (Ferraris, 2014).

The third phase:
Reconstruction of the model by the previous layers bricks, without dictation, with a random distribution and according to a single rule: the pieces of each layer must always rest on a block belonging to the previous layer.
The experience turns out to be propaedeutic to the reading of relations between empty and full, and to overcoming the difficulty of visual and perceptual re-aggregation of scattered elements and the consequent complexity in giving them meaning.

The fourth phase:
Critical reading of the experience: it is possible to observe how the first constructed tablet is characterized by a series of squares and rectangles that in sequence underline the ½ ratio while the last tablet lends itself to the description of a chaotic landscape characterized by a series of different heights and sections that are very far from the canonical representation of the concept of "one-half". It is also possible to continue the game by the aggregation of individual urban landscapes for the creation of a shared and dynamic urban mosaic.

In conclusion, in our activity the game becomes a synthetic process of informal knowledge.

Keywords:

LEGO landscape, perception, gestalt psychology, unitary area, widespread area.