ABSTRACT
History as a record of human achievement can tell us many things. It can relate what we’ve accomplished, isolate prerequisites, and in a sense, indicate how we have arrived at our present state of being. e history of a speci c intellectual activity, such as mathematics, can do the same. It can answer many questions, such as, When did this mathematics come into being? How was it used? Who was responsible for it? But history is more than a quiz game, more than merely an accumulation of facts, names, and chronologies. Any substantial investigation of the history of mathematics should also seek to reveal and understand the forces and conditions that shape, nurture, and sustain mathematical thinking: How do humans perceive mathematical reality? Why do certain mathematical concepts come into being? What factors a ect the transcendence of mathematics from a purely utilitarian activity to an abstract object of speculation and conjecture? As individuals move from the realm of self to the collective embrace of larger social groups, constraints are imposed on their perceptions of reality. ey are indoctrinated into the rituals, beliefs, and traditions of the group. In the case of mathematics, a child is born with certain basic inherent mathematical capacities. Research has revealed that a newborn infant has a number sense and can discriminate and identify the number of objects in a visual array up to about four and perceives space in a topological manner; that is, identifying and understanding such spatial properties as connectedness and continuity (Butterworth, 1999; Dehaene, 1997; Van Loosbrock & Smitsman, 1990). As these basic mathematical abilities evolve, they and their expressions are modi ed by a series of internally and externally applied lters. Personal sensory experience is shaped by particular physical environments. Certainly, a child living in a dense jungle will develop
di erent spatial perceptions from a peer living in a desert or on a Paci c atoll (Bishop, 1979). Quite simply, they will experience and see the “world” di erently as their worlds are di erent. An individual’s sensory perceptions are readily modi- ed by cultural constraints imposed by the immediate family, clan, or tribe and “traditions.” Further, consuming societal constraints allow for larger, approved social interactions, which bring economic and political considerations into play. Finally, even as a pure intellectual activity abstractly manipulated, mathematics, to be o cially recognized, must adhere to formal systems of analysis and expression established by the mathematics community. In this hierarchy of in uences, very early on and persistently therea er, cultural constraints form a foundation upon which higher levels of conceptual interactions must build. It has been said that “culture makes a person what they are,” so too, with mathematics, culture has played a long role in its development (Saxe, 1991). Let us now attempt to examine this relationship between culture and mathematics.
