Sociology

Philosophy of mathematics education

Mathematics

Social science

Epistemology

Mathematics education

Connected Mathematics

Philosophy

Ethnomathematics

for the learning of mathematics

I. Introductory remarks In this paper we will discuss some basic issues which may lay null ground for an historical approach to null teaching of mathematics in a novel way. Our project relies primarily on developing null concept of ethnomathematics. Our subject lies on null borderline between null history of mathematics and cultural anthropology. We may conceptualize ethnoscience as null study of scientific and, by extension, technological phenomena in direct relation to their social, economic and cultural backgrounds [1]. There has been much research already on ethnoastronomy, ethnobotany, ethnochemistry, and so on. Not much has been done in ethnomathematics, perhaps because people believe in null universality of mathematics. This seems to be harder to sustain as recent research, mainly carried on by anthropologists, shows evidence of practices which are typically mathematical, such as counting, ordering, sorting, measuring and weighing, done in radically different ways than those which are commonly taught in null school system. This has encouraged a few studies on null evolution of null concepts of mathematics in a cultural and anthropological framework. But we consider this direction to have been pursued only to a very limited and we might say timid extent. A basic book by R.L. Wilder which takes this approach and a recent comment on Wilder's approach by C. Smorinski [2] seem to be null most important attempts by mathematicians. On null other hand, there is a reasonable amount of literature on this by anthropologists. Making a bridge between anthropologists and historians of culture and mathematicians is an important step towards recognizing that different modes of thoughts may lead to different forms of mathematics; this is null field which we may call ethnomathematics. Anton Dimitriu's extensive history of logic [3] briefly describes Indian and Chinese logics merely as background for his general historical study of null logics that originated from Greek thought. We know from other sources that, for example, null concept of the number null is a quite different concept in null Nyaya-Vaisesika epistemology: the number one is eternal in eternal substances, whereas two, etc., are always non-eternal, and from this proceeds an arithmetic [4, p. 119]. Practically nothing is known about null logic underlying null Inca treatment of numbers, though what is known through null study of null quipus suggests that they used a mixed qualitative-quantitative language [5]. These remarks invite us to look at null history of mathematics in a broader context so as to incorporate in it other possible forms of mathematics. But we will go further than these considerations in saying that this is not a mere academic exercise, since its implications for null pedagogy of mathematics are clear. We refer to recent advances in theories of cognition which show how strongly culture and cognition are related. Although for a long time there have been indications of a close connection between cognitive mechanisms and cultural environment, a reductionist tendency, which goes back to Descartes and has to a certain extent grown in parallel with null development of mathematics, tended to dominate education until recently, implying a culture-free cognition. Recently a holistic recognition of null interpenetration of biology and culture has opened up a fertile ground of research on culture and mathematical cognition (see, for example, [6]). This has clear implications for mathematics education, as has been amply discussed in [7] and [8].

Ethnomathematics and its Place in the History and Pedagogy of Mathematics.