Aldo Ramirez-Arellano, Instituto Polit cnico Nacional, Ciudad de Mexico
Jose Maria Sigarreta Almira, Universidad Autonoma de Guerrero, Mexico
Juan Bory Reyes, Instituto Politecnico Nacional, Ciudad de Mexico

Abstract: The quantification of learning acquisition in a blended and online course is still slightly explored from the complex systems lens. The fractional online learning rate (fOLR) using fractional integrals is introduced. The notion of fOLR is based on the nonlinearity of the individual students learning pathway network, built from Learning Management System log files. Several learning pathway networks from students that pass or fail the course were constructed. The Akaike information criterion shows that the minimum number of boxes to cover these networks follow a power-law model. Further analysis shows that the fOLR model and its parameters were significantly compared with the online learning rate model. Thus, the fOLR was computing power and delayed power models, inspired by the "law of practice." The results show that the fractional definition is a better model and has a nonlinear relationship with the overall grade. Also, engagement and disengagement mould the fOLR curve. It means that the student's performance is affected by the engagement, and it is necessary that they are encouraged to pay more effort and attention to the learning activities, and those activities need to be designed to be fun and pleasant to improve the learning achievements.

Keywords: higher education, eLearning, engagement, fractal network