中年級學童「部分－全體」運思的發展：文字題選圖與解題作業表現的差異

THE DEVELOPMENT OF PART-WHOLE OPERATION: THE PERFORMANCE DISCREPANCY BETWEEN DRAWING-CHOICE AND PROBLEM-SOLVING TASKS

在數學教材中，常見使用圖形來說明抽象概念或問題解法的教學建議。本研究在加減運算範圍，探討圖形表徵理解能力的發展，透過選擇題作業，實驗一觀察916名二至四年級學童對文字題與圖形表徵（長條圖或方格圖）轉譯的辨識表現。實驗二觀察466名三、四年級學童對文字題與線段圖（單線段或雙線段）轉譯的辨識表現，來探討學童概念的發展，以及圖形型式對學童轉譯辨識表現的影響。實驗三透過236名三、四年級學童解題作業上的表現，探討附加線段圖在解題過程中所扮演的角色。綜合三個實驗的結果，各項作業上皆呈現年級效果，顯示「部份－全體」關係的掌握，在中年級仍持續的發展。圖形型式並未影響選圖表現，學童選擇圖形表徵時的困難，與各數量間的關係有關，而與各個數量的本身無關，問題語意與線段圖型式的契合假設亦尚未獲得支持。比較實驗二、三的結果，顯示學童解題表現優於圖形選擇表現。在文字題上附加線段圖，有時能增加學童正確解題的機會，但是，效果相當有限或不穩定可靠。在「部份－全體」運思發展的架構下，進一步討論實驗結果的意涵，以及可能的數學教學建議。

With addition and subtraction word problems, this study was to explore students' abilities of text-picture translation in their middle grades, and to explore the effects of drawings in the problem solving processes. In Experiment 1, there were 916 second, third, or fourth graders who were observed on multiple choice task. Two forms of drawings were used: square and bar graph. Students were asked to choose a correct drawing that agreed with the word problem specified. In Experiment 2. there were 466 third or fourth graders who were examined on multiple choice task. Two different sets of drawings were chosen: single-line-segment and double-line-segment drawings. In Experiment 3, there were 236 third or fourth graders who were tested on problem solving task. The same word problems as in the Experiment 2 were used. and half of them were presented with additional line-segment drawings. Grade effects were found in all three experiments. There was no effect of drawing forms. The results suggested that the difficulties on choosing correct drawings were related to the translation of the relations of quantities but not the quantities themselves. The finding also did not support the matching hypotheses between situations and drawings. By comparing the results in the last two experiments. it is clear that the performance on problem solving task was better than that on drawing choice task. Finally, the additional line-segment drawing on problem presentation had little effect on students' performance. All results were discussed in the framework of the development of part-whole operation.