Abstract:

Several studies suggest the development of cognitive processes is not chaotic. It has certain regularities called knowledge development mechanisms. The same mechanisms could be found in psychogenesis as well as in the history of science. Piaget pointed to the parallel development of science and ontogenetic development of individual knowledge (Rybár, 1997).

In our paper, we would like to focus on this parallel. Especially the transition from the concrete operational stage to the formal operational stage, which is happening around the age of 12 according to Inhelder and Piaget (1958). At this time children advance from logical reasoning with concrete to abstract examples and become able to consider only logical relationships between different elements while ignoring their concrete content. Therefore, the tasks we have chosen allow algebraic and geometric strategy (or interpretation) for solving.

Our target group was two groups of pupils at lower secondary school (11/12 and 13/14 years old). In order to answer our research questions “Can students develop their algebraic thinking without focusing on specific tasks in mathematics lessons” and “What approaches pupils use while solving context tasks”, we have made two kinds of analysis of obtained data. Firstly, we have been looking for specific categories of the answers and explanation of pupils’ solutions. Secondly, we have used software C.H.I.C. to identify similarities between the groups in comparison to the historical phylogenesis.

Results show that the mentioned parallel could be identified in the answers of the pupils of both groups. Their strategies have a lot in common with historical approaches, for example, we can find similar approaches in solving the tasks with the Babylonians' one.

Keywords:

Algebraic thinking, algebraic and geometric strategies, historical development, Piaget’s stages of mental development.