數學在現今的社會當中是很重要的能力，它在許多領域的應用都十分廣泛。然而現今台灣的數學教育，老師往往都是要求學生用死記公式的方式來解題，缺乏讓學生真正了解概念後來進行解題，使得學生無法把數學視為與生活相關的重要性知識，最後形成了對數學學習的排斥感、缺乏學習動機，導致學習成效較差的問題。有鑑於此，因此本研究在協作式多點觸控桌上開發了一套等值分數互動學習系統，讓學生能夠在此平台上進行討論、協商，並透過數學表徵的轉換，讓學習者能夠在不同的表徵之間做轉換，促進對數學概念的理解。
本研究以國民小學四年級的學生作為研究對象，共包含50位實驗參與者，透過實證研究比較方式，採用控制組與實驗組做為學習成效上之對照。並深入探討實驗組學生在協作式多點觸控桌上之同儕互動行為、系統操作行為與其學習成效之關係。接著再探討學習者之合作學習態度，在進行互動式學習時，是否會影響其學習成效。最後再調查學習者對於協作式多點觸控桌互動學習系統的接受程度，以及在數學上的學習動機。
在最後的研究結果中發現，控制組與實驗組在學習成效上有顯著差異。此外，本研究所設計的「圖卡轉換功能」之操作行為、「同儕互動行為」，也顯著地影響學習成效。而在合作學習態度方面，則發現無論學習者的態度高或低，皆不會影響到學習成效，因此重點在於學習者的同儕互動行為與系統操作行為。最後，大多數的實驗參與者一致認為本研究所開發之多點觸控桌互動學習系統，可以有效增強其數學的學習動機，並有高度的持續使用意圖。

The ability of Mathematic is important, and it extensively applies to many fields. However, Mathematic education in Taiwan, teachers always ask students memorize the formula to resolve problems, it results students lacking concept of mathematic to answer the mathematic questions and they cannot regard mathematic as the important knowledge of the life and forms an attitude of exclusion in mathematic learning, lack the learning motivation and fail in their mathematic achievement. In the view of this phenomenon, this study developed a set of equivalence fractions interactive learning system in collaborative multi-touch table that allow students discussing, negotiating, and through the conversion of mathematic representation so that promote learner’s mathematic concepts when they convert between different representation.
This study conducted 50 elementary school students to participate. And further explore the relationship among behavior of using system, behavior of peer interaction, and learning effect in experimental group. Moreover, we explored learner’s collaborative learning attitude whether affect their learning effect when they proceeding interactive learning. Finally, we investigated the acceptance of collaborative Multi-touch table interactive learning system and the motivation of mathematics.
In the result of the study, the results show that there are significant in learning effect between control group and experimental group. Moreover, the operational behavior of conversion of graphical card which is designed by this study and the behavior of peer interaction would affect the learner’s learning effects. In the collaborative learning attitude, we found that either the attitude high or low, all without affecting the learning effect, so that the key point is based on the peer interaction and behavior of system operation. Finally, the most of the participants who are in the experiment group agree unanimity that this interactive learning system can effectively enhance their motivation of mathematic and have a strong intent for using this system in the future.

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