The open space characteristic and the lack of a strict script in the Virtual Learning Environment (VLE) often pose the learners in a state of confusion or being lost. This phenomenon adversely affects the learning outcomes. Curious learning companions, who detect interesting learning objects tailored to the learner's current level of knowledge, can unobtrusively prevent them from experiencing such confusion. Hence, we present a comprehensive computational model of curiosity based on the psychological theory by Berlyne. For modeling the complex relationships between curiosity stimulating factors, we employ Fuzzy Cognitive Map (FCM). To test our model's effectiveness, we implement it into a learning companion and conduct two case studies. These case studies demonstrate our model's consistency with the underlying theories, and a small scale field study proves our hypothesis that curious learning companions can help the learners to explore more knowledge in the VLE.