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This study is part of a research project that analyzes the processes of conceptualization of the notion of infinitesimals in college students majoring in Mathematics. The research project originates from an interest in understanding the processes of teaching and learning key concepts of Mathematical Analysis such as limit, real numbers, and continuity among others. From mathematical and cognition points of view, these notions are recognized as complex. In order to conceptualize them, students rely on an intuitive understanding of infinitesimals. In this paper, we describe, analyze, and characterize the epistemological conceptual frameworks associated with the historical evolution of the notion of infinitesimals. We identify seven epistemological concept frameworks: The infinitesimal as a ratio, as an indeterminate, as a difference, as an increment, as an arithmetic ratio, as a symbol, and as a function. Furthermore, ideas, methods, representations, and problems that mathematicians use in specific contexts are presented. [ABSTRACT FROM AUTHOR]

This paper is designed to serve as an introduction and historical background to ethnomathematics as a program of study. The authors wants to show that ethnomathematics includes the mathematical ideas, perspectives and practices of individuals in different cultures as manifested and transmitted in diverse modes. Any study of the history of ethnomathematics and its proponents helps us to clarify the importance of this perspective in terms of mathematics education. The development of ethnomathematics is documented here, principally as a part of the study of the development of scientific and mathematical ideas and practices made by distinct cultural groups. [ABSTRACT FROM AUTHOR]