Using multimedia and peer assessment to promote collaborative e-learning

Collaborative e-learning is increasingly appealing as a pedagogical approach that can positively affect student learning. We propose a didactical model that integrates multimedia with collaborative tools and peer assessment to foster collaborative e-learning. In this paper, we explain it and present the results of its application to the “International Seminars on Materials Science” online course. The proposed didactical model consists of five educational activities. In the first three, students review the multimedia resources proposed by the teacher in collaboration with their classmates. Then, in the last two activities, they create their own multimedia resources and assess those created by their classmates. These activities foster communication and collaboration among students and their ability to use and create multimedia resources. Our purpose is to encourage the creativity, motivation, and dynamism of the learning process for both teachers and students

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio