Researchers have been attempting to implement effective e-learning methods that improve educational outcomes and consider their conformity with human psychology and current state of the technology. Hence, e-learning systems with a particular focus on cognitive-related aspects have emerged as a potential solution. This research study aimed on enhancing students’ conceptualisations and mental perceptions of mathematical geometric concepts using an e-learning system that was developed based on key aspects of the Cognitive Theory of Gärdenfors’ Conceptual Spaces (Gärdenfors, 2000), which utilises a combination of visual and audio. The research achieved this through an effective agent-based model that was designed to help in teaching basic mathematical geometric in primary school. The e-learning systems adapts to the individual student’s needs and pace to conceive the geometric concepts while maintaining the design objective of a flexible and proactive approach for the agents that is semi-autonomous. This research study investigated the instruction of geometric concepts for primary school students based on three national curricula (UK, New Zealand and Saudi Arabia). Sets of questions were developed to study the students’ understanding of selected concepts through a rigorous process of surveying primary school math teachers, determining the appropriate level of question difficulty and requesting the verification and appraisal of the type and format of the questions from the mathematical instructor community. Based on the generated sets of questions, a prototype of an e-learning system was developed and used in a pilot experiment that was conducted on students from the UK and Saudi Arabia to investigate whether students’ misconceptions were consistent with Gärdenfors’s Conceptual Spaces cognitive model. In addition to the variations in students’ answers, the experiment revealed consistent misconceptions based on the mistakes made on specific questions, which confirmed several aspects of the Conceptual Spaces cognitive model. These results led to the implementation of the CABELS e-learning system, which was developed based on this theory, to enhance student conceptualisations of the previously determined common misconceptions in a way that assimilates their mental perceptions of the studied concepts. CABELS includes two parallel modules, which are the language-based and visualbased modules, and involves three stages: a pre-test, lessons explaining the concepts and a post-test. The CABELS system was first used in experiments on primary school students in Saudi Arabia, which highly improved their understanding of lines and shape concepts. Furthermore, a statistical analysis of the experiment data showed that there was no noticeable effect of the teaching methods, groups, classrooms or genders on the students’ scores nor any interdependence between these variables. Therefore, these results reinforce the effectiveness of CABELS for teaching basic geometric shape concepts to primary school pupils. The effectiveness of the CABELS system was also evaluated through post-session interviews with students to assess their satisfaction and experiences with CABELS. The results showed an overall satisfaction of students regarding the use of this system, which the students indicated was mainly due to its usability and usefulness.