• 作者： 劉祥通、康淑娟
• 作者服務機構： 國立嘉義大學數理教育研究所
• 中文摘要： 本研究是個案研究，個案小美是一位小六學生，在校的數學成績還不錯，且程序性知識頗為完備，但是對於解較難或課外的數學問題卻是沒有信心，因此，研究者以非例行性分數問題作為研究主要施測工具，例如以工作單為基準量不是1，而尋找分數落點的問題，來瞭解小美的解題表現，並藉助結構式工作單的晤談法進行資料蒐集。研究者特別從個案作圖時的下筆順序，以觀察她的解題行為，而綜合討論則從資源、捷思、監控與信念系統四個向度來分析小美的解題表現。主要發現有：(1)資源：擁有完備的工具性理解，但關係性理解不夠，(2)捷思：未能利用等值關係與新單位量以發展解題策略，(3)監控：解基準量是分數的問題時，未對計畫與決策的大方向有監控的表現，(4)信念系統：忽視了已存在的隱藏約定，屢次有自行設定單位長的想法。
• 英文摘要： The research subject, Amy, is a sixth grader. She is used to getting high scores in mathematics. However, she does not have enough confidence to deal with non-routine problems. In order to observe how she overcame obstacles during problem solving, she was given some number line problems involving unfamiliar situations. These fractional problems involving both reference quantity and target quantity had not been taught yet at her school. This case study adopted structurally task based interviews to collect data. To capture her critical thinking in solving problems, the researchers observed how she located each fractional number, especially the sequence of pinpointing all related numbers on number lines. The conclusions of this study were drawn from the aspects of resource, heuristic, control and belief systems. The major findings are as follows: 1. Though Amy had a resourceful instrumental understanding, her relational understanding was insufficient for problem solving. 2. Amy did not utilize the equivalent fractions and new units to develop problem solving strategies. 3. When the reference quantities were fractions, Amy did not control well the planning and decision-making needed for problem solving. 4. Amy didn’t realize the implicit constraints of number line problems. As a result, she often ignored the given unit system and created another unit system which was confused with that conventionally used.
• 中文關鍵字： 分數問題、數線問題、數學解題
• 英文關鍵字： Fractional Problems, Number Line Problems, Mathematical Problem Solving