Seminar: 3/17 - Geoff Saxe
11:00 to 12:30 PM at:
Tolman Hall, 5101
How do collective systems of representation in mathematics emerge in the social history of human communities? How do individuals come to use and alter collective representations in everyday practices, seeding new collective developments? In my talk, I present framework for exploring interplay between collective and individual activity in the creation of mathematical representations, with a focus on social history of communities. As an illustrative case, I present fieldwork on mathematics in Oksapmin, communities that are located in a remote highland area in central New Guinea. The Oksapmin, like their neighboring Mountain-Ok groups to the West, traditionally use a 27-body-part counting system for number (see Figure), and there is no evidence that Oksapmin used arithmetic in pre-history. Based upon field studies completed in 1978, 1980, and 2001, I analyze a change from a subsistence-oriented to a cash-oriented economy in which arithmetical activities are increasingly important, and the accompanying (and remarkable) shift in functions of a word form related to these activities. The word form has shifted from its use as an intensive quantifier that means “a complete group of plenty” to one that means double the value of a body part. I show how the analytic framework affords a multi-level inquiry into genetic processes of change in the Oksapmin case and argue that the approach is useful for understanding the interplay between cultural and developmental processes in cognition more generally. As a second case, I illustrate the use of this framework in the analysis of schooling in Oksapmin communities, showing how the 27-body part non-base system is shifting over the social history of schooling such that the body system more closely aligned with the structure of Western base-structured systems. Like the case of ‘doubling’, the historical processes that have given rise to the shift in the body system are largely invisible to participants.
Department of Education, UC Berkeley
"Studying Cognition in Flux: Towards a Coordinated Treatment of Culture and the Individual in the Analysis of Mathematical Thought"