This research is in accordance with four factors including indicator, skill, bug and experts knowledge structure. These factors are carried into questions for tests of “Calculation of Fractions” in elementary school mathematics. The test results will be analyzed for understanding the student knowledge structures. And the results are combined by Bayesian Networks to be the basis of questions-choosing for the Computerized Adaptive Diagnostic Test. In addition, the Computerized Adaptive Remedial Instruction is edited by bug and skill factor, and constituted it as a set of adaptive learning system. The system is tested further and evaluated its performance. Some findings are briefly outlined as follows: 1. Computerized Adaptive Diagnostic Test is effective under Bayesian Networks deduction. The classification accuracy can be increased by combining Bayesian Networks and knowledge structures. The classification accuracy of dynamic cut-point selection is better than fixed cut-point selection. 2. The number of items tested by students in the Computerized Adaptive Diagnostic Test System is 13.7 averagely. This system can save 6.3 items averagely, and the test-taking time is also saved simultaneously. 3. The progress of students is significant after the Adaptive Remedial Instruction. Therefore, Computerized Adaptive Diagnostic Test System and Computerized Adaptive Remedial Instruction, proposed in this study can factually test and remedy students’ abilities individually.
