Weaving Culture and Mathematics: An Evaluation of Mutual Interrogation as a Methodological Process in Ethnomathematical Research

Abstract

This thesis discusses an attempt to implement the methodology of mutual interrogation in an ethnomathematical research study. Mutual interrogation was proposed by Alangui (2010) as a way of resolving issues of ideological colonialism and knowledge decontextualisation in investigations of mathematical knowledge in cultural practice. The process involves implementing a critical dialogue between holders of a specific cultural knowledge domain and mathematicians in order to investigate the interactions that occur between their knowledge systems, and to look at how the diverse ways of thinking about quantities, relationships and space can help broaden or transform our conception of mathematics. The thesis describes an adaptation of the above methodology to a study of food cover (tudung saji) weaving among the weavers of Malaysia. These conical-shaped covers are woven using a specific technique called triaxial or hexagonal weave, where the strands are interlaced in three directions. A three-phase dialogue between several weavers and mathematicians was implemented, with the researcher playing the role of the mediator. Ethnographic techniques of participant observation, audio and video recording, field notes and interviews (both unstructured and semi-structured) were employed to document the dialogue and explore weaving limitations and possibilities. A computer-generated weaving template was also created to mediate investigations. The interactions between the conventions of the weavers and the concepts of the mathematicians uncovered differing perspectives on the construction of the tudung saji and the use of the template. The research findings highlight the role of mutual interrogation in establishing communication between the knowledge systems and the practitioners. Furthermore, mutual interrogation both affected the contemporary practices of the weavers and drew the mathematicians' attention to the way the process of interpreting a cultural activity can lead to the invention of new mathematical structures.