On the origin and psycho-logic background of Zoltán P. Dienes’s Principles
András G. Benedek, Research Centre for the Humanities of the Hungarian Academy of Sciences
Zoltan P. Dienes extended Piaget’s theory of mathematical abstraction and gave a definition of the operational level of abstract thinking. In the Some Thoughts on the Dynamics of Learning Mathematics, one of the last works that he compiled by Christmas Day, 1995, he summed up his theory of abstraction through examples. Analyzing his widely known principles of learning and teaching mathematics in the light of these examples, I argue that behind his principles we can explore a psycho-semantic problem of communication that is a continuation of her mother’s, Valéria Dienes’s, “evologic” model. Her conception of semiotic meaning creation in the field embodied expression and dance implicitly influenced Zoltán P. Dienes’s principles with due modifications in the context of the psychology of mathematics. His principles and levels of abstraction demonstrated by his concrete heuristic practices exemplify a psycho-logic conception of understanding that extends the emerging model-theoretic semantics of the 1960ies to human activities and embodied experience. This extension helps us to see heuristics as the research of those ways, means, and tools that support mapping our symbolically expressible verbal thought processes to such operational and manipulative models and practices of problem-solving that we are able to put out from our heads. His extended notion of building abstractions includes not just logic or set-theoretic models but all kinds of extra-verbal structures and operations that promote the understanding of why we consider true what we are seeing. These human activities are based on embodied operational experience obtained by using objectified manipulatives just as on our psychological thought processes reproducing and inventing them.
