國小六年級學生以面積及數線模型表徵

The Concept and Practice of Elementary Principals' Instructional Leadership in Taiwan

本研究以臺中市一所國小的80位六年級學生為研究對象，進行分數除法表徵測驗，以探討六年級學生在使用四種不同圖形表徵模型（未等分面積模型、已等分面積模型、未等分數線模型、已等分數線模型），解決分數除法計算問題時的表現。本研究的主要發現為：（一）使用數線模型者的答題正確率顯著高於使用面積模型者；（二）使用數線未等分模型者的解題表現最佳，其次為使用數線已等分模型者及面積已等分模型者，而使用面積未等分模型者的解題表現則最差；（三）學生在使用圖形表徵模型解題時，傾向直接將計算出的答案以圖形表徵模型呈現出來，或只是將被除數及除數分別以圖形表徵模型呈現，僅有17.6%的學生能以圖形表徵模型正確表現出分數除法的計算結果。

This study investigated the performance of the sixth graders in operating four representation models (unevenly divided area model, evenly divided area model, unevenly divided number line model, and evenly divided number line model) to solve fraction division problems. The participants were 80 sixth graders from an elementary school in Taichung City. This study explored the difference in students’problemsolving performance based on the use of different representation models as well as in their performance in solving different items. The findings are as follows: (a) the accuracy of problem-solving through number line models was significantly higher than that of problem-solving through area models. (b) The students’problem-solving performance of using the unevenly divided number line model was the optimal, followed by evenly divided number line model, evenly divided area model, and unevenly divided area model. (c) When the students used representation models to solve problems, they tended to present the calculated answer through the representation model directly or use representation models to separately present the dividend and the divisor. Only 17.6% of the students could use the representation models to mark the relationship between the dividend and the divisor.