• 作者： 姚如芬
• 作者服務機構： 國立嘉義大學數理教育研究所
• 中文摘要： 本個案研究主要目的在探討17位國小低年級學童對「加法交換律」的認識、並討論這群個案學童對於「等號」的相關想法。經由補救教學期間的觀察、晤談與相關文件的綜合分析，研究發現：多數學童在補救教學前知道「50 + 25」與「25 + 50」結果相同，但係透過計算而非「加法交換律」的應用；經由補救教學引導，學童關於「加法交換律」的認識可以逐步進階，依序為計算階段、認知階段、等式表徵前階段、等式表徵階段，而這些不同的認識階段與這群學童對「等號」的認識息息相關；研究者綜合此些發現，於文中提出了關於學童「加法交換律」的發展階層及其與「等號」認識之關聯圖；同時針對「加法交換律」相關的教學與探究，提出若干省思與建議。
• 英文摘要： The main purpose of this case study was to investigate 17 children’s understanding of the commutative law of addition and the equal sign. Various data was obtained through observation, interview and the collection of relevant documents. From analyses of the data it was noticed that prior to any instruction most students could recognize 50 + 25 = 25 + 50 through counting but not through the application of the additive commutative law. After instruction, students’ understanding of the additive commutative law improved, and this understanding was related to their understanding about the equal sign in equation. According to these findings, the researcher developed a model to show the progress of students’ understanding of the additive commutative law in addition to their understanding of equal sign. Reflections and suggestions are also presented in this article.
• 中文關鍵字： 加法交換律、低年級學童、個案研究、等號
• 英文關鍵字： Additive Commutative Law, Children, Case Study, Equal Sign