比與比值初始概念的教學初探

The Exploration of Teaching Initial Concept of Ratio

本研究目的是依據Lamon（1993）的比與比值語意結構的分類，提出比與比值初始概念引入的替代性教學設計及試驗性教學初探。採用文獻評析，提出影響學生學習比值的重要因素及分析教科書的架構；以內容分析法，分析現行六年級教科書在比與比值單元的題目情境類型。本文亦提出比與比值起始概念引入的關鍵概念：比的使用之適當性、比感的建立、及比值相對關係。兩數量在題目中需符合固定倍數關係、情境可類推性、對應關係意義化三種條件，使用比的符號，才具意義性。本研究的替代性教學設計包含教學目標及教學布題，可作為教科書編輯及教師教學設計的參考。

The study was indented to explore an alternative approach of teaching initial concept of rate and ratio by taking the view of the nature of mathematics in which is based on Lamon's four semantic structures of proportion problems. Main factors of influencing students' solving proportion problems and the framework of analyzing current textbooks were addressed by literature reviewing. The semantic structures of the proportion problems were compared and contrast among three textbooks. The key initial concepts of ratio includes: the use of ratio, the sense of ratio, and the meaning of the relationship between two numbers. Particularly, the study claims that students learned the sense of ration by emphasizing the use of ratio in which ratio can only be used when the contexts of problem is inferred and the numbers are patterns. The inference of contexts being embedded into the problems are two essential elements of developing sense of ratio. The alternative instructional design can be as a reference for curriculum writing committees.