Stone walls and water flows: Interrogating Cultural Practice and Mathematics

Abstract

Ethnomathematical practice has been criticised for approaches that unwittingly privilege the mathematical gaze. The literature shows that uncritical investigations of mathematical knowledge in cultural practice may lead to ideological colonialism and knowledge decontextualisation. These concerns are legitimate and challenge the basic principles of ethnomathematics. To address these concerns, a general methodological framework is developed in this study. The framework sets out generic questions to guide an ethnomathematical research study investigating a cultural practice. Mutual interrogation as an approach, and as a process of critical dialogue, was developed to allow the researcher to perform the ethnomathematical task of relating the structures of cultural practice to conventional mathematics whilst avoiding the dual dangers mentioned above. Using ethnography, this study describes the knowledge embedded in stone walling and water management, which are two aspects of the rice terracing practice in the indigenous communities of Agawa and Gueday in Besao, Mt. Province, in the Cordillera region, northern Philippines. Exemplars of mutual interrogation between mathematical knowledge and the knowledge embedded in the two practices were then developed. Both mathematics and culture were used as frames of reference in the interrogation process. This study suggests that the general methodological framework can be useful in guiding ethnomathematical research. It also demonstrates how the knowledge embedded in stone walling and water management may be used to interrogate conventional mathematical ideas. The study shows the potential of mutual interrogation in broadening theconception of mathematics, which is one of the goals of ethnomathematics.