On-line Data-analysis of e-Learning Response Time using Gamma Distribution

抄録

This paper proposes a new automatic characteristics analysis method of e-learning contents using the response curve of e-Learning time data in the learning historical data-base. Many researches concerned with the mathematical model of the response time data have been studied, but they have a disadvantage that it is very difficult to interpret the parameters and estimate the parameters. The proposed model of e-learning time data in this paper is derived from maximizing the Entropy as same as Nagaoka, Wu (1989), but the unique feature of the paper is to derive the model with the following two parameters by employing the maximizing Entropy method with some restrictions to make the parameters interpretation more easily. The two parameters α and β in the model are respectively interpreted as follows: The parameter α means "Complexity of the content (which means the numbers of simple understanding processes to understand or solve the content)" and the parameter β means "Expected time of the simple understanding process in the content". That is, this means that the average of the learning time for a content is divided into the two parameters α and β. In the other words, the average of the learning time for a content is equivalent to the product of the two parameters α and β. Using these properties of the parameters, this paper proposes a new content evaluation method using α-β plain, which is called" α-β chart". Furthermore, the authors developed a LMS (Learning Management System) which it is inserted into, and show the effectiveness of the system by practical use.