在對話式智慧家教系統中，教師代理人會以自然語言與學生對話，依據學生所輸入的文字，教師代理人會給予適當的回應，引導學生進行有效學習。對話式智慧家教系統已發展出雙代理人教學方式，除了介面設計不一樣之外，其對話設計機制也有差異。然而，不同的對話模式設計是否會影響學生的數學學習成效和學習興趣，仍然是一個值得探究的議題，故本研究設計雙代理人和單代理人之對話式智慧家教系統，以探討學生透過雙代理人和單代理人對話模式之引導，其數學學習成效與學習興趣之差異。本研究以畢氏定理為內容，開發單代理人與雙代理人之對話式智慧家教系統，研究對象為中部八年級8個班的學生共202位，其中隨機分派3個班接受單代理人對話式智慧家教系統之教學（實驗組一），3個班接受雙代理人對話式智慧家教系統之教學（實驗組二）、2個班接受團班教學（控制組）。研究結果顯示：接受單代理人與雙代理人對話式智慧家教系統之學生，其數學學習成效顯著優於接受團班教學之學生。雙代理人對話式智慧家教系統比單代理人對話式智慧家教系統更能有助於提升低成就學生的畢氏定理學習成效；運用雙代理人對話式智慧家教系統學習的學生，其學習畢氏定理的興趣高於運用單代理人對話式智慧家教系統的學生。

Pedagogical agents are embodied animated avatars that help students learn by holding conversations with the students in the dialogue based intelligent tutoring systems. There are different trialogue designs (two agents interacting with a human student) that address different pedagogical goals for different classes of students. The impact of different trialogue designs on learning outcome is still unknown. The core question is whether the learning outcomes show improvement over typical human-computer dialogues (one human student and one tutor agent) and conventional pedagogical interventions. The purpose of this study is to develop two agents and one agent dialogue-based intelligent tutoring systems for learning the Pythagoras Theorem for junior high school students. The effectiveness of two agents and one agent dialogue-based intelligent tutoring systems for learning the Pythagoras Theorem is evaluated in this study. In this study, the “Pythagoras Theorem” unit of mathematics utilized in Taiwanese junior high schools is adopted to construct tasks in the dialogue based intelligent tutoring system. The 202 students from the eighth grade of Taiwanese junior high school were selected to participate in the field experiment in this study. The results indicated that the students with two agents dialogue-based intelligent tutoring system can get a higher score than that with traditional instruction. Students who received two agents dialogue-based intelligent tutoring system outperformed those who received the traditional group-based remedial program. The low mathematics achievers with two agents dialogue-based intelligent tutoring system get a higher score than that with one agent dialogue-based intelligent tutoring system. Students with two agents dialogue-based intelligent tutoring system get a higher score in learning interesting than that with one agent dialogue-based intelligent tutoring system.