Mathematical Modeling: Cognitive, Pedagogical, Historical And Political Dimensions

Ubiratan D'Ambrosio

Abstract


The book by Steven Mithen became a basic reference on human evolution. The introductory words of Mithen encouraged me to write a paper on Mathematical Modeling. Although having practiced Mathematical Modeling only with situations which are not complex, I believe my paper contributes to the foundations of the field. In the late sixties I became interested in the emerging field of Mathematical Modeling. I practiced some easy modeling and I supervised a number of dissertations, dealing with more complex situations. This was an exciting experience and I immersed myself in the relevant literature of the field. Although I never got interested in practicing more advanced modeling, the emergence of new fields of research after the sixties convinced me of the central importance of Mathematical Modeling in explaining knowledge. The objective of this paper is to show some of this centrality as I see it. Particularly, I will try to explain why I do recognize Mathematical Modeling as a strategy per excellence of human beings for generating knowledge and for learning. My exposition is based on assuming some concepts. First of all, what is knowledge? Knowledge is one of these concepts for which we do not have a definition and philosophers take for granted that the reader will understand what they mean when they refer to knowledge. I do the same. But I distinguish individual knowledge and general, or simply, knowledge. Individual knowledge is generated by each individual. Socialization leads individuals to acquiring and learning knowledge generated by other individuals, and this process is in a symbiotic relation with the continuous generation of new knowledge by the individual. Socialization depends on communication in the broad sense. Language, as the main form of communication of the human species, allows for sharing, transmitting and diffusing the complex of experiences and explanations accumulated by mankind in the course of its history, since early hominids through the modern homo sapiens sapiens. This leads to general knowledge, or simply knowledge.

Keywords


Mathematical Modeling, Knowledge, Mathematics Education, Problem Solving

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