數學魔術對國小不同學習成就之學生數學學習影響之研究

Effect of Mathematic Magic Activities on the Mathematics Learning of Different Academic Achievement Students.

胡哲瑋(Tse-Wei Hu)

指導教授 ： 許慧玉

國立清華大學/竹師教育學院/數理教育研究所/碩士(2020年)

摘要

近年來，台灣學生在數學學習表現上有落差逐漸加大的問題，而數學奠基活動則是透過數學遊戲或數學魔術，在課前為學生奠立數學學習之基礎，希望能解決學習落差的情形。本研究目的是觀察國小中年級不同數學學習成就的學生，在面對數學魔術時，如何從魔術中觀察數學關係、提出解決策略。本研究採用教學晤談法，以新竹市某國小四年級數學學習成就分屬低、中、高的六名學生為研究對象，使用分別包含餘數概念以及因數與倍數概念的兩個數學魔術，進行一對一的魔術活動，隨後進行教學晤談，同時並以錄音、錄影、以及學習單等方式收集資料。

本研究結果顯示出以下四種結論：一、在面對不同數學魔術時，個別學生具有其固定的思維模式。二、不同學習成就的學生在面對數學魔術時，都能提出自己的解決策略，只是深入程度有所差異，其中又以高成就和低成就學生較願意提出自己的策略。三、數學魔術教學可分為四個層次。四、餘數概念不容易透過魔術觀察，六名學生不論成就高低，沒有任何一位能觀察到魔術中使用的餘數概念。本研究結果可作為將數學魔術融入課堂教學時的參考依據、數學奠基活動設計時之參考，最後並對未來研究提供更進一步的建議。

關鍵字

數學魔術 ； 遊戲 ； 教學晤談法

並列摘要

In recent years, Taiwanese students have had a problem of gradually increasing gaps in mathematics learning performance, and the Mathematics Grounding Activity are through math games or math magic to establish a foundation for students to learn mathematics before class, hoping to solve the situation of learning gap. The purpose of this study is to observe when facing math magic, the students of different academic achievement how to observe mathematics relations from magic and propose solutions. This study adopts the teaching interview method, taking six of low, medium, high academic achievement students in the fourth grade of a primary school in Hsinchu City the research object, using two math magics that include the concept of remainder and the concept of factor and multiple. After one-on-one magic activities, followed by teaching interviews, at the same time collecting data by means of audio recording, video recording, and learning slips.

The results of this research show the following four conclusions: 1. when facing different mathematical magic, individual students have their fixed modes of thinking.
2. Students with different learning achievements can come up with their own solution strategies when facing mathematical magic, but the degree of in-depth is different. Among them, students with high achievements and low achievements are more willing to propose their own strategies. 3. Mathematics magic teaching can be divided into four levels. 4. The concept of remainder is not easy to observe through magic. Regardless of the achievements of the six students, no one can observe the concept of remainder used in magic. The results of this study can be used as a reference basis for integrating math magic into classroom teaching, a reference for the design of the Mathematics Grounding Activity, and finally provide further suggestions for future research.

並列關鍵字

mathematical magic ； game ； teaching interview

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