本研究之目的在建構一套兼顧加速、充實等面向，以及兼顧國小數學資優生的數學天分，與批判思考能力、溝通分享能力、創新思考能力及瞭解自我能力發展的國小數學資優課程方案。
本研究採發展性研究，透過數學成就測驗甄選出國小四年級數學資優生20人，授課教師為任教國小20年，且具參與此類型國小數學資優生培育的教學經驗，課程方案的建構歷時兩年半，每學期授課約12次，每次授課3小時。
研究結果主要有兩項，其一是發展一套國小數學資優課程方案，包含教材與教法。教材有開放性問題、傳統數學問題、挑戰性問題、改變傳統數學問題條件導出新問題、比較解題策略異同與完整性的問題，以及數學史。教法則有教師示範提問、鼓勵學生互相提問、鼓勵學生說明解題策略、要求學生辯證解題策略、要求學生詳細記錄解題時的思考歷程、鼓勵學生在同一個問題使用不同表徵解題、引導學生省思表徵與算式間的一致性、各組互評解題策略、讓學生練習擬題。該方案能夠有效的促進國小數學資優生四項能力的發展，其二是針對國小數學資優生的四項能力分別提出其發展層次。
最後根據研究結論，提出幾個推廣應用本國小數學資優課程方案與未來研究的建議。
關鍵字：發展性研究、國小數學資優生、國小數學資優課程方案

The purpose of this research is to construct an elementary mathematically-gifted curriculum for both acceleration and enrichment in learning, taking into account the development of the elementary mathematically-gifted students' mathematical talent as well as their four abilities on critical thinking, communication and sharing, creative thinking and self-understanding.
The research is a developmental research. Through the mathematics achievement test, the researcher selected 20 fourth-grade elementary mathematically-gifted students. The teacher has been teaching experience for 20 years, and had involved in the program of the elementary mathematically-gifted students for years. The construction of the elementary mathematically-gifted curriculum lasted for two and a half years. The instruction time is about 12 lessons per semester and each lesson lasts 3 hours.
There are two major results. First, it is to develop a project for elementary mathematically-gifted curriculum, including teaching materials and teaching methods. The materials compose of open-ended questions, traditional mathematics questions, challenging questions, inducing new questions from changing traditional mathematic questions, comparing and contrasting solving strategies and their completeness and the history of mathematics. The methods include teacher-demo questioning, encouraging students to question each other, encouraging students to explaining their solving strategies, asking students to give dialectic their solving strategies, asking students to record the details of their thinking process, encouraging students to use different representations for solving same problem, providing guidance for students to reflect the congruence between their representation and formula, evaluating other groups’ solving strategies and making students to practice question-posing. It is proved that this project could effectively facilitate students’ development on the four abilities abovementioned. Second, we propose the mathematically-gifted students’ developmental hierarchy of these four abilities.
The conclusions put forward some suggestions for the applications of the elementary mathematically-gifted curriculum and future research.
Keywords: developmental research, elementary mathematically-gifted student, elementary mathematically-gifted curriculum