## 3 Materials and Methods
### Methodology  
#### 3.5.1 Statistical Functions of the CAFT Software  
We developed the CAFT engine in such a way that it can administer adaptive formative assessments. Figure 3 shows a screenshot of the graphical user interface in the CAFT engine. CAFT consists of seven sections containing functions including (a) test options, (b) item options, (c) IRT model selection, (d) adaptive options: adaptive selection algorithms, (e) learner estimation method, and (f) output files and simulation. The (A) area comprises the options related to general item information. It consists of (1) the number of items in the item bank, (2) the maximum number of items for the administered test, (3) the minimum number of items for the test, and (4) the stopping criterion for the adaptive test. In addition, this part provides the output files related to the item characteristics including item difficulty, discrimination, and information curve. The (B) area consists of the options related to the general test information, which is more connected to implementing adaptive formative assessments. It contains (1) the number of tests that the sequential formative assessment will have, (2) the maximum number of tests in a set of tests, and (3) the desired outputs related to the formative assessment including a learner's learning progression and test usage trace. The (C) area provides the options related to the IRT models, namely, Rasch, 1 PL model, 2 PL model, and GRM, which would be chosen depending on the item characteristics. Figure 3: An example of CAFT using the CAT system: Engine Window. (**A**): options related to general item information; (**B**): options related to the general test information; (**C**): options related to the IRT models; (**D**): core part of the adaptive system; (**E**): the examinee’s ability estimation area; (**F**): area for selecting data files or conducting a simulation. The (D) area is the core part of the adaptive system. It contains different adaptive algorithms that a user can choose from. Moreover, it contains the methods for the first item selection, which determines what method is used to generate the first item from the item bank. The user can choose one of the options for implementing adaptive item selection. The first method is maximum Fisher information (MEI), which is used for finding items that maximize the Fisher's information for a learner with the interim proficiency estimate and the number of items administered [33]. The next method is likelihood weight information criterion proposed by [PERSON] and [PERSON]. In the likelihood weight information method, the information function is summed through the ability and weighted by the likelihood function after item administration has been performed. The last item selection option is the minimum expected posterior variance (MEPV) [34]. This method uses predictive distribution, and it selects items that yield the minimum predicted posterior variance given previous responses. The system picks the item \(i_{k}\) at stage \(k\) remaining in the item bank that minimizes the expected posterior variance. The (E) area is about the examinee's ability estimation. It contains the method options for ability estimation and standard error calculation. This software provides two methods for estimating a learner's ability, including the maximum likelihood estimate and the expected a posteriori estimate. The maximum likelihood estimate is used to estimate a learner's ability by maximizing a likelihood function.