排灣族傳統文化中「數學」知識之初探

Investigation of the Mathematics Knowledge in Traditional Paiwan’s Culture

本研究採個案研究法，根據Bishop（1988）提出的數學和文化的關係來設計訪談大綱，以10位部落耆老為對象，進行13次的半結構式訪談，以建構排灣族傳統文化中蘊含的數學知識。結果發現，排灣族的數字系統是十進位，最大的數是萬。雖有分的概念，但平分並非最主要的考量，且未發展出分數與小數的概念，常以譬喻的方式來描述大數。在測量概念上，傳統文化常以個別物品（如手扠量長度），或大自然的現象來進行測量（如太陽位置量時間）。在幾何概念上，文化製品中常出現的幾何形體，如三角形，有些來自大自然的現象或動物，具有文化意涵；有些則因製作的方法而自然形成。排灣族傳統文化中的數學知識，在強調實用與凸顯文化意涵的前提下所發展，由於缺乏文字紀錄及採師徒制方式來學習專業技能，所以並未發展出數學一般性的規則，因而未建立抽象化與系統化的數學知識。

"The aim of this study is to investigate the mathematics knowledge in traditional Paiwan’s culture by interviewing tribe elders through case study method. Based on the framework of Bishop (1988) which pointed out the relationship between mathematics knowledge and human culture, the author designed the outline of interview. Ten Paiwan’s elders were interviewed with 13 semi-structured items in total. The results indicated that the mathematics knowledge in Paiwan’s traditional culture could be classified into number, measurement and geometry. In the domain of number, base-ten numeric system was used for daily life, and the biggest number was ten thousand. They have the concept of division, but equally divided was not the crucial consideration. The concepts of fraction and decimal were not developed. People usually used a metaphor to describe extremely large or small number. On measurement, they used specific object such as a span to measure the length, or observed the natural phenomena such as location of sun in the sky to know the time. On the concepts of geometry, some geometric shapes that were often appeared on the artificial cultural and art products, such as triangle, came from images of animals and natural with special culture meanings, or naturally formed by its making skills and methods. The development of mathematics knowledge in Paiwan’s traditional culture were emphasized on the practical utility of life and the meanings of culture. Paiwan people did not develop the generalization of mathematics knowledge because of lacking of words record and adopted apprenticeship to learn professional skills. They also did not build an abstract and systemic mathematics knowledge."