With the practice of the new structures of competence indicators, there are more variations emerging than ever both in the teaching modes for teachers and in the learning conditions for students. Therefore, the largest challenge teachers nowadays are facing is how to effectively evaluate the new structures of competence indicators. This research is primarily aimed at not only offering students in grade 4 the computerized adaptive diagnostic test in Mathematics, but also creating an accurate remedial instruction system based on the qualification rate of the new structures of competence indicators afterwards. In addition, by using such a test and such a system, it can save the time of a test and teachers would spend less time in the process of teaching and evaluating but more efficiently. Furthermore, with this kind of help, students will truly be given a proper remedial instruction specialized for every individual student. To conclude, the main purposes of this research are as follows: 1: To build an available database that can be utilized in a computerized adaptive diagnostic test on a basis of the new structures of competence indicators in Mathematics in order to pave the way for the further development in the future. Finally, it can be achievable to minimize the numbers of mathematic questions comprising a test, to cut short the time students should need while taking a test like this, or to provide the learning conditions to teachers, students, and parents as immediately as possible. 2: To initiate an online remedial instruction system so as to maximize the effect of a remedial instruction, to shorten the time spent in carrying out a remedial instruction, to help students learn more successfully, and to alleviate the burdens teachers and parents are bearing.
