## 2 Research Objectives  
The purpose of this study was to introduce a framework for an adaptive formative assessment system using computerized adaptive testing (CAT) and dynamic Bayesian networks (DBNs) that can adaptively assess a learner's ability over multiple measurement time points. Since previously established online formative assessment systems administer fixed, identical tests to learners, the adaptive function has not yet been implemented. The adaptation is achieved with several statistical algorithms from CAT. The fundamental concepts of the adaptation in CAT are (1) A learner's ability and the standard error of measurement about the learner's ability are estimated based on IRT, and (2) CAT selects the item from the item bank that maximizes the discriminatory and informative values for the given examinee's ability from the item bank. This procedure is repeated until a certain level of measurement precision regarding a learner's ability is satisfied. Since CAT chooses the next item based on the learner's answer to the previous item, all learners with different abilities take different items adaptively. The length and path of the test vary in terms of a learner.  
CAFT is an assessment system created by combining CAT and DBNs. The adaptive system of CAT is applied at the item and test levels over multiple time points by adaptively selecting the next item of a test and the next test in sequential testing, respectively. In addition, DBNs offer real-time updates on the estimation of a learner's ability across multiple tests. The feedback system between CAT as an adaptive selection method and DBNs as a real-time estimation method is the core goal of CAFT as an integration of artificial intelligence methods into an e-learning system. Therefore, this study developed CAFT with several layers. The first layer is a test generation system, which contains (1) an instructor that generates items and publishes tests from an item bank and (2) calibration of item characteristics including item difficulty and discrimination. This layer provides basic storage for an adaptive formative assessment. The second layer is a CAT engine, the parameters of which a user can customize through a graphical interface in order to choose different item/test selection statistical algorithms. The third layer consists of DBNs, which estimate a learner's past, current, and future abilities across different measurement time points. This offers probabilistic real-time updates of a learner's ability through interaction with the CAT engine.  
Therefore, in this study, first, we developed an adaptive formative assessment system using CAT and DBNs, called CAFT. After this, the validity, reliability, and efficiency of CAFT were evaluated by simulation study and application studies. In the simulation study, the learners' estimated abilities and the simulated learner's true abilities were compared for evaluation of the validity and reliability. The number of items used in CAFT was also measured in order to compare how many items are required to reach the same level of measurement precision under CAFT as when the full item set was used. Additionally, an application study was conducted for examining the reliability and efficiency of the system using data collected from the introduction to statistics course of an online university.