表徵與國小學生代數思考之初探性研究 An Exploratory Study of Mathematical

本研究旨在透過不同表徵問題，檢驗理解學生一般化表現情形，依據表現顯示之難易度，解析學生一般化適用之表徵類型，並探索表徵可提供何種相關啟示來協助學生一般化。研究樣本為國小五、六年級學生，共423人，利用測驗調查及訪談方式蒐集資料，資料分析採量化與質性併陳方式進行。研究發現包括：一、六年級學生一般化的表現較五年級學生佳，且有顯著差異存在；二、學生在 各問題的反應呈現以表格表徵的問題表現最佳，其次是文字與圖形表徵，再者為圖像表徵問題的表現，而數字表徵則最感困難；三、表格、圖形與文字表徵的問題可適用於學生一般化歷程發想、問題的理解、變數的辨識、結構關係的連結和發展；四、圖像與數字表徵問題可激發學生對變數關係的發展加以推理與臆測，形成規則進行解題。 This study provided various representation problems with which to evaluate students’ performance in generalization. The types of representation appropriate for generalization were determined according to the difficulty and characteristics of the representation problems. A total of 423 fifth and sixth grade students underwent generalization tests and interviews, the results of which were subjected to both quantitative and qualitative analysis. The results showed that sixth grade students significantly outperformed fifth grade students in generalization problems. In addition, students performed most favorably in table representation problems, followed by text, graphs, and pictorial representations. The students felt that numeric representation was the most difficult. We found that representation problems adopting tables, graphs, and text are suitable for thinking in the process of generalization problems, variable recognition, and the connection and development of structural relationships. Pictorial and numeric representations were shown to stimulate students to speculate about variable relationships and form rules with which to solve problems. We believe that the results of this study provide a valuable reference for researchers in terms of algebraic thinking and instructional development