Abstract
The article concerns the question of the construction of mathematical knowledge by pupils, namely the mechanism of individual and shared construction of knowledge on the example of re-discovery of Pythagoras' theorem within square grid paper. The theoretical background of work consists of the theory of generic models and constructivist approaches to the teaching of mathematics.
A study was carried out of pupils of an 8-year secondary grammar school, working in groups and solving carefully chosen problems. The data were gathered through participation observation, field notes of the researcher and external observer, pupils' works and mainly videorecordings.
The analysis of data via techniques based on grounded theory is briefly described. The results of the experiment include the characterisation of categories of (relatively) individual and shared constructions of knowledge, including their dimensions.
Concrete examples of these constructions are given. The merits and limits of the presented study are summarised and possible questions of further research outlined.