本研究以十二年國民基本教育數學領域課程綱要為藍本，發展悅趣化數學文化教案以培養具備歸納推理能力的數量與代數素養。分別對臺灣國中生與高中生施以「撲克牌數學魔術」與「中國益智遊戲九連環」教案，並探究與反思所開發之悅趣化學習方式的兩個數量與代數素養教案的活動實施歷程。研究結果發現幾乎所有同學都認同所參與教學活動，活動有助於培養學生歸納推理能力與提升數量與代數素養。運用玩中學魔術對很多同學是很新鮮的經驗，藉由結合八年級數列單元的觀念，讓同學體會數學的妙用，確實增進學生對於等差數列單元概念理解與學習興趣，培養學生歸納推理的能力，進而運用數學規律，實際表演魔術。高中生可以藉由操作九連環遊戲培養觀察、探索、發現、分析與溝通能力，連結十年級指數、數列、級數與遞迴關係等單元，惟有些同學在數學表徵的敘述上出錯，研究顯示做更深入的抽象代數思維對十二年級高中生仍有其困難性。

This research was based on a 12-year compulsory education syllabus in the field of mathematics, and it integrated mathematical culture to develop game-based lesson plans to cultivate students' inductive reasoning ability for quantitative and algebraic literacy. The teaching plans for “Mathematical Card Magic” and “Chinese Ring of Chinese Puzzle Games” were given to Taiwanese junior and senior high school students, respectively. This research was a theoretical and reflexive study on the implementation of the two quantitative and algebraic teaching plans. The results of the study demonstrated that most students were receptive of the teaching activities. The activities helped to cultivate students' inductive reasoning ability and improve their quantitative and algebraic literacy. The use of mathematical card magic was a new experience for many junior high school students. Combining the concept of number sequences in Grade 8 can effectively arouse students' interest in learning and study, cultivate students' ability of inductive reasoning, and then apply the patterns of mathematics to perform magic tricks. High school students can develop observation, exploration, discovery, analysis, and communication skills by operating the Chinese ring. Teaching activities can link the concepts of logarithm, number sequences, and series and recursions in Grade 10. However, some students made mistakes in mathematical representation. It remains difficult for Grade 12 high school students to do more in-depth, abstract algebra thinking.

代數教案; 悅趣化學習; 數量與代數素養; 數學文化; 數學魔術

lesson plans for algebra; game-based learning; quantitative and algebraic literacy; mathematical culture; mathematical magic