# The Accurate Measurement of Students' Learning in E-Learning Environments
## 2 Background  
### The Needs for a Common Metric in MOOCs  
In MOOCs, a common metric is necessary for several reasons. First, a common metric allows us to measure students' learning properly. Student learning is typically operationalized as the gain scores between pre- and post-tests [11]. Researchers may use the same set of items for both the pre- and post-tests. However, in such a case, students are exposed to the same set of items, and therefore, practice effects may be confounded with students' actual learning. When different sets of items are used in the pre- and post-tests, a common metric needs to be established between the pre- and post-test scores. Without a common metric, scores from the pre- and post-tests are not comparable, and therefore, learning gain cannot be properly measured.  
Second, a common metric allows us to evaluate students fairly. In MOOCs, students can freely navigate a MOOCs course and can design their own learning process. As a result, students in a MOOC are likely to solve different sets of items across a course because of the self-paced nature of MOOCs [12]. For fair evaluations, therefore, it needs to be considered that students might solve different sets of items or different forms. For example, in many MOOCs, students can obtain certificates if they meet certain criteria on their performance in the course (say a 70% proportion correct on homework, quizzes, and exams). Given the fact that students may solve different sets of items, it might not be fair to use percentage scores for decisions about certificates because percentage scores do not reflect different levels of item difficulties that students encounter on homework, quizzes, and tests.  
Third, a common metric allows us to reuse MOOCs items more efficiently. Since MOOCs started, a considerable number of items (or learning resources in general) have been created. Therefore, researchers and practitioners began to consider how to reuse existing learning resources. For example, the edX MOOCs platform provides a custom course on the edX (CCX) with which high school teachers can create their own MOOCs by editing the learning resources in the existing edX MOOCs [13], and the Digital Assets for Reuse in Teaching (DART) project from Harvard university allows any instructor at Harvard to add edX resources to his/her residential courses in the Canvas Learning Management System (LMS). Item parameters, such as difficulty and discrimination parameters, calibrated on a common metric can maximize the benefit of reusing items by allowing us to customize a set of items that are specifically designed to achieve a certain level of difficulty and discrimination.  
Fourth, a common metric allows us to prevent cheating in MOOCs by using multiple test forms. Cheating is a long-lasting problem in testing. In an online environment, cheating occurs in many different ways: online communication [14], copying and pasting from online sources [15], illegitimately obtained answer keys [16], and so on. The use of multiple test forms can reduce cheating and therefore can enhance fairness. A prerequisite for using multiple test forms is to establish a common metric across multiple test forms to make scores from different forms comparable.