本研究旨在了解國小三年級學童代數推理解題表現情形及教學實驗效果,樣本為公立國小三年級學童30名。研究分三階段進行,首先,參考文獻資料和《九年一貫課程綱要》能力指標,先行設計代數推理解題評量工具,檢測學童解題表現,並透過觀察訪談,瞭解學童在代數推理歷程產生之困難、錯誤觀念或欠缺的能力技巧,做為第二階段課程活動設計及教學的依據,俟教學完後,再進行解題後測,並伴隨觀察訪談蒐集資料,藉以比較教學前、後學童代數推理解題表現情形。根據結果發現,大多數小學三年級學童在代數推理解題前測的表現不盡理想,對代數推理各項活動產生困難,透過課程設計與教學實施後,學童能表現出更為優異的推理解題能力。 從學童作業結果分析,發現本研究設計之課程,可以誘發學生根據其學習經驗與認知發展,進行代數推理解題,符應所謂的從描述進步到符號化的學習歷程。最後,根據研究結果,作者提出相關建議,以作為未來代數融入國小數學教學的參考。
The purpose of this study is to investigate the third graders' performances on algebraic reasoning and the effects on the curriculum design and teaching effects of algebraic reasoning. The subjects were 30 students from a southern Taiwan elementary school. For the purpose, there are three stages on trails for the students, including a pilot test, and then four periods of teaching, and after three months, the students took the post test. However, to understand whether the process of algebraic reasoning of students is necessary, the researcher observed how students used strategies to their thinking patterns. After that, the researcher interviewed students. Researcher summarized some main findings and offered some suggestions of learning algebra for young children and teachers.