The design of interactions among peers plays a key role in collaborative learning. Various strategies have been applied to assist learners in collaborating and creating a continuous effort to construct and maintain shared knowledge, such as utilizing a concept map as a representational tool during discourse. Some previous studies have revealed its positive effect on both the learning achievements and the attitudes of the students. A strategy for improving the quality of explanation of the students during collaborative concept mapping is to enable them to externalize their thinking in their private spaces beforehand. However, students may face difficulties when they need to integrate their individual propositions with the group concept map. This study employs the reciprocal kit-build (RKB) approach to help students externalize their ideas, understand and clarify their partners' perspectives, integrating with their comprehension, hoping they can construct a high-quality collaborative product. The study is conducted in a linear algebra class in an Indonesian university. The effect of the RKB as learning activities on the group outcomes is evaluated. How students change their propositions, from the individual to the collaborative phase, following the visualization of the difference map provided by the RKB system is also presented. Perceptions of the students during these activities are examined to measure the effectiveness of the approach from the viewpoints of the participants. The findings convey that the RKB is promising for learning in a collaborative context despite some limitations in the practical classroom experimental settings.