The purpose of this paper is to explore how university students can develop knowledge in small task-based groups while acquiring hands-on computer skills. Inspired by the sociocultural perspective, this study presents a theoretical framework on co-construction of knowledge and on computer-supported collaborative learning. The participants were selected from student teachers in Rwanda after a training program on searching, retrieving and exploiting web-based literature. The findings show that university students working together in small groups to acquire hands-on computer skills can adopt one of three major learning patterns: individual-led, group-led or individual-group hybrid-led. Moreover, the results indicate that the group-led framework seems to create a supportive environment for knowledge building. Nevertheless, university students showed a need for teacher support to enable them to focus on criterion-referenced reflection to regulate their learning.