- 學位論文
一位國小三年級教師發展數學課室推理規範 之行動研究
An Action Research of a Third-Grade Teacher Developing Mathematical Reasoning Norms in Elementary Mathematical Classroom
摘要
本研究以國小三年級教師發展數學課室推理規範的行動研究，探討在課室討論文化下建立數學推理規範之行動歷程、遭遇的問題、採用的策略及數學任務的情境脈絡對於數學推理規範的發展。研究對象為苗栗縣某國小三年級天使班17位學生，研究期程為每週五節數學課，為期二個學期。以課室錄影、學生解題紀錄、數學日記、教師教學省思、課室討論成長團體觀議課後教師的回饋、蔡文煥教授的建議等作為資料的蒐集與分析。 本研究形成的社會規範有︰「專心聽」、「面向同學大聲說」、「看（聽）不懂就要問」、「張貼的規範」；社會數學規範有︰「想清楚、說明白」、「發現不同的解題路徑」、「比較不同解題路徑的有效性」、「學生自行布題」；數學推理規範有：「利用已知數學知識作為解題說明」、「有系統地列舉所有可能的答案」、「發現數學關係」、「擴大驗證」、「提出具體事例加以反駁」。 從以上研究結果可知，數學推理規範是社會規範與社會數學規範的延伸、數學任務的情境脈絡會影響數學推理規範的發展，教師若能在行動研究前參與專業成長團體的共同備課及觀議課，可即時解決問題，讓教學更順利。
並列摘要
This research of a third-grade teacher developing mathematical reasoning norms in elementary mathematical classroom, to discuss the course of action, problems encountered, strategies adopted, and the context of mathematic reasoning tasks established in the classroom discussion culture. The research object is 17 third-grade students in Miaoli County. The study period is five math lessons per week for two semesters. The data with videoes, students' problem-solving records, mathematical diary, teacher's teaching reflection journals, the observation feedback and discussion records from mathematical teacher support group , and the suggestion from advisor ,etc. The social norms developing in this research include: listening with concentration , speaking with loud, asking a question when you are confused and posting norm. The developing social mathematical norms in this research include: clearly thinking and explaining , solving a problem with different methods , comparison of the effectiveness of different problem solving paths, and students' problem-posing abilities . The developing mathematical reasoning norms in this research include: using the learned mathematical knowledge as a based to explain problems , listing of all possible answers systematically, finding for mathematical relationships,expanding proof and refuting false proposition . From the above research results,we can see that the mathematical reasoning norms is an extension of the social norms and the social mathematical norms . The situational context of a mathematical task can affect the development of mathematical reasoning norms.Joining mathematical teacher support group can solve problems immediately and make the teaching more successful.