HueyMin Wu, ChungLin Lee, and PeiChen Wu

Mathematical augmentation is the foundation and essence of mathematics education. Mathematical argumentation can not only promote deep mathematical understanding, but also learn to connect some abstract ideas in a logical way (Kuhn, 2005; Partnership for 21st Century Skills, 2008). Although argumentation is an important skill, it is not an innately possessed or can be easily acquired skill. Research showed that the performance of the argument is not good for most people (Hahn, Harris & Oaksford, 2012). Mathematical argumentation is often conducted in the classroom through group discussions (Osborne, 2010). Teachers with the professional skills in augmentation could guide students to carry out effective mathematical augmentation. However most teachers don’t know how to implement argumentation teaching in mathematics class (Lin, 2018). Most students in classes are in the middle ability, a small number of students have high or low ability, and it is difficult to group students heterogeneously. Mathematical conjecturing has a power of construing a series of connected mathematics properties or mathematics concepts as an approach to enhancing mathematical argumentation. In this research, the mathematical conjecturing instruction is guided by a tutor agent in the intelligent dialogue-based tutoring system. According to students' abilities, different types of peer agents are used to solve the problem of grouping students heterogeneously in traditional classroom. The effectiveness of incorporating mathematical augmentation in intelligent dialogue-based tutoring system is explored in this study. The questions addressed in this study are: 1) Is the learning gains of incorporating mathematical augmentation in intelligent dialogue-based tutoring system more effective than that of traditional group based instruction? 2) Is the learning gains in mathematical conjecturing of the experiment group more effective than that of the control group?