結合鷹架教學與非例行性數學問題發展學生數學解題能力之研究

本研究的目的在於探討教師及同儕鷹架，影響學生解非例行性數學問題時的解題表現及解題思維。研究個案是從屏東縣某國小二年級學生中，依據在校數學成績，篩選三位學生，其中兩位為數學高程度，一位是中程度；由三人組成一共同學習小組，安排每週一次約一小時的非例行數學問題解題學習，研究時間為期十週。研究期間，研究者透過教室觀察、訪談記錄、文件蒐集……等多元方式來蒐集資料。研究所得結果如下：一、鷹架的運作提升學生對於題意的理解；二、透過學生的近側發展區，鷹架之運作有助於提升學生數學建模及解題能力到達他們自力難以到達的程度；三、鷹架運作能提升學生問題表徵的能力；四、在多元解題的數學同儕鷹架運作下，學生的解題歷程更加精緻化；五、透過不同層次鷹架的搭建，有助於多元化學生的解題策略及提升學生的解題表現。

關鍵字

非例行性問題；數學解題能力；鷹架

並列摘要

The focus of this research is on the impact of teacher (expert) scaffolding and peer scaffolding on students' problem solving performances and thinking processes on non-routine mathematics problems. Three second graders students at the local elementary school in Pingtung County in southern Taiwan were selected based on their mathematics achievement. Two of them are high-achievement students when the third one is a middle-achievement student. Subjects were grouped together to receive one hour non-routine mathematics problem solving training once a week for ten weeks. The research used qualitative research method in data gathering and analysis. The study obtained following findings: 1. Scaffolding enhances students' understanding of meaning of these non-routine questions. 2. Scaffolding helps students promote their problem solving abilities through their proximal development zone. 3. Scaffolding stimulates students' problem-solving thinking, and helps them to build suitable mathematics model to solve mathematics problems. 4. Peer scaffolding enhances diverse mathematics problem solving strategies and students' problem solving performances.