Mathematical Perspective on Piaget’s Theory and Its Implications for Teaching and Learning

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Objectives. This paper applies mathematical modelling to Piaget’s theory of cognitive development through a system of differential equations. By modelling the progression through Piaget’s cognitive stages, the research aims to assess the stability of mental development. Materials and methods. Stability analysis, including linear and nonlinear methods such as Lyapunov functions, reveals that the system exhibits stable behaviour, suggesting predictable and continuous transitions between cognitive stages. Results. The results imply that Piaget’s stages are stable under typical conditions, with potential implications for designing educational interventions based on cognitive development. Conclusions. This approach provides a quantitative framework to understand cognitive development and its stability within educational contexts.

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