The rapid penetration of "open source" virtual worlds (VWs) on the configuration and development of three-dimensional (3D) multi-user virtual platforms, in conjunction with interfaces of two-dimensional (2D) educational environments to learn novice users basic algorithmic structures were currently the central axis that exposed for investigation in our study. Notwithstanding the radical restructuring of instructional formats with VWs, like Open Simulator (Open Sim); however the disambiguation of students' presence indicators which are positively correlated to their meaningful engagement in Computer Science courses in a virtual community of inquiry (VCoI) is still lacking. In fact, for the requirements of these courses we had configured specific collaborative virtual areas in order to be explored and utilized from students a variety of non-uniform geometric solids from Open Sim and to be constructed a 3D (assembled) "mind trap" puzzle. Alongside, each piece of this puzzle was programmed according to a specific serial sequence with Scratch for Open Sim (Scratch4OS). The current case study seeks to present firstly a valuable framework for the implementation of the teaching and learning process in a VW, and subsequently the results from linear correlations between the cognitive, social and teaching presence of a VCoI from eighty-one (81) students of the Greek Secondary Education. The study findings indicated that the social presence (communication and cohesiveness of a group) don't only have a direct correlation with the cognitive presence (learning process for the construction of knowledge), but also has a positive association with the teaching presence (organization, planning and guidance of learning activities in the 3D space), and compulsory reinforced both of them. The added value of this study highlights the fundamental issues of the cooperation, socialization, retention and attendance rates between members of a VCoI which avouch multiple dimensions encircle or empower students' managerial and learning responsibilities based on the affordances that a 3D technology-enhanced environment can replicate.