A concepção de Jacob Klein sobre a transição da aritmética na época do Renascimento e suas implicações para educação matemática

Abstract

The Mathematical Education is the area of knowledge in which the human beings establish a correlation with the Mathematics learnt at school. However, Mathematics, with all its formal apparatus, seems opposed to Philosophy, since Philosophy deals with rational meanings of various concepts and Mathematics, in its turn, deals with the extensions of concepts. Thus, the Mathematical Education must be under philosophical orientation; seen that this proper orientation allows the educator to think critically in a course that will, factually, grant the construction of knowledge. This theoretical-bibliographical, historical and epistemological research aims to identify, setting out on the work of Jacob Klein, called ‘Greek Mathematical Thought and The Origin of Algebra’, how the concepts of numbers present in the interaction of Arithmetic and Algebra establish themselves and progress in the relationship between object and symbol, as well as to identify the context of the conceptual transformation in Mathematical Physics in reference to the tensions that occurred in the moment of transition between the ancient Greek mathematics (descriptive) and the modern algebraic symbolism (operative). Starting on the comprehension of Klein’s thought (1922), regarding Mathematical concepts present in Plato, Diophantus, Stevin, Vieta and Descartes and grounded on the concept of Complementarity of Otteano’s thinking (1993;2003) and Kant’s (1997), one can understand that, in the beginning of the Modern Algebraic Symbolism is present the transition between the descriptive and operative notions of mathematical concepts. Thus, it offers one the opportunity of indicating the relevance of the concept of Complementarity according to mathematical objects, enabling one of expanding its teaching methods.