Abstract:

We proceed from an extensive experiment carried out by ourselves, in which we let children (aged 5–6) with no experience of the conventional language used to describe three-dimensional objects to graphically and verbally describe a cube structure. Children worked in pairs (drawer – builder), without direct sight of each other. The goal of the drawer was to depict a structure made out of six differently colored cubes on paper, so that the builder could use it as a plan to build the same structure on their own. If the builder failed to do so, the drawer either verbally described the mistakes in the builder’s structure, modified the original depiction, etc. so the builder could build it again. The experiment demonstrated that many children are able to take their everyday natural language using a directed communication about a specific mathematical object and use it to build the basics of a conventional language and further develop it in the same manner. We then introduce the results of the same experiment carried out with a group of adults (aged 19–22), who had been at various rates introduced to conventional languages used to describe the three-dimensional space. In this experiment, we did not examine the ability of adults to create a conventional language, but focused on comparing the similarities and differences of their results with the results of the experiment carried out with children, and on possible generalizations of common prototypes of understanding some spatial aspects. We emphasize and demonstrate the considerable potential of creating a conventional language of mathematics in the direction from the pupil to the language (the pupil has a need to create the language) and not the other way round from the language to the pupil (the pupil is provided with a ready-made language) which has been common for the Czech education system until recently. The article contributes to the current trend of constructivist approach to mathematics teaching, which is currently gaining much traction in the Czech Republic.

Keywords:

Communication, language of geometry, 3D space, cube buildings, constructivism.