本文探討學生學習分數的先備知識，並進行分數啟蒙的教學實驗，以檢驗學生在良好的學習環境中，可能的學習區。 分數概念的先備知識研究是利用一對一半結構式面談法，提供實物，給25位在學校未學過分數的國小二年級學生操作。根據其表現，得知90%以上學生都已具備的能力包括：數數，將偶數個離散物二等分，並且已有使用一半、公平、平分等語詞的生活經驗。 分數啟蒙教學的教案設計依據，包括對學生先備知識的了解，診斷教學原理及現實的數學教育之教育原則。教案設計重點包括選擇生活實例，人數不等的分組討論學習，是否等分的論斷，分量不變性的辨識，與操作一記錄一描述的解題活動等。 實驗教學由兩位國小教師分兩組進行，每組6堂課。教學過程全部錄影。教學後一個月，再面談所有的40位學生，面談過程全部錄音，部分錄影。 面談資料顯示，參加實驗的學生約90%能操作連續量實物的二等分、三等分、四等分，與離散量實物的二等分、三等分、四等分及五等分，能以二分之一、四分之一等分數語言描述連續量分配的結果，但奇數個離散物二等分的結果要用二分之一表達仍有困難。學生處理實物分配問題的策略相當多元化。 從實驗教學過程教師與學生的反應，顯示出許多良好的學習現象。根據診斷教學與現實的數學教育教學原則設計之教學活動，值得進一步落實。

　　　　　This study investigated students' informal knowledge of fractions and explored the teaching and learning of beginning fractions. Questions of what constitutes a good learning environment and an appropriate zone of learning beginning fractions fro second graders were also examined. The informal knowledge of fractions were investigated with one-to-one semi-structured interviews. Second graders (N=25) who had not received formal instruction in fractions were given real objects to manipulate in the context of everyday life situations with words such as a half, fair and equal sharing. As a result of this experience, over 90% of them were able to count and to make equal sharing with even number of objects. Teaching modules for beginning fractions were developed based on the knowledge about students informal knowledge, the principles of diagnostic teaching, and principles of the real-life mathematics education. Some key features of the module included attention to choosing real-life situations, using small group discussion, grouping into different size of groups, diagnosting the awareness of equal parts, recognizing the invariant of different partitioning, and the three steps of learning cycle: distributing-recording-describing. The explorative teaching was conducted by two school teachers in the research group at schools other than their own. Each exploration consisted of six forty-minutes lessons. After one month, all forty students were interviewed to betermine their understanding of fractions. Given a continuous quantity, they are able to solve equal sharing for two, three and four. Given discrete objects, they are able to solve equal sharing for two, three, four and five. The fractions language 1/2 and 1/4 are used appropriately on continuous quantity situations, but not always on discrete objects. Many different strategies of sharing were developed by the students.