This presentation introduces a novel approach to studying children's cognitive development through the lens of problem solving, a fundamental process in the construction of knowledge. The talk presents the Inhelderian-Dynamic Method, an original methodological proposal that integrates the microgenetic perspective of Bärbel Inhelder with principles from dynamic systems theory. This integration allows us to move beyond linear models of development and to understand cognition as a self-organizing and evolving system, where children's mental schemes are constantly coordinated, transformed, and reorganized in real time.
The presentation draws on empirical data obtained from the Tower of Hanoi task, administered to 32 children (17 girls and 15 boys) across four sessions, spaced two weeks apart. A total of 7,886 moves were recorded, of which 79.4% were error-free. The microgenetic analysis provided a detailed account of the children's moment-by-moment strategies, revealing both quantitative and qualitative changes in their understanding and performance.
A key contribution that will be discussed is the use of phase spaces, a technique adapted from dynamic systems, to visualize the cognitive trajectories of each participant. These representations make it possible to identify zones of stability and instability, corresponding to the activation and coordination of familiar schemes —those stable yet flexible cognitive organizations that, as Bärbel Inhelder proposed, guide the child's adaptation to new problem situations. The use of Markov chains further allows the estimation of transition probabilities between these schemes, offering insight into how integration and reorganization occur across time.
The presentation concludes that the microgenesis of development can be better understood as the dynamic interplay between familiar and emerging schemes—an evolving process of equilibrium and transformation. This perspective renews Inhelder's legacy, showing that the study of schemes through dynamic modeling reveals the living architecture of thought as it unfolds in the child's action and reflection.
