Investigating the limit of peer collaboration: Insight from worked-example in multivariable calculus

Abstract

This study validates the superiority of individual learning over peer collaborative learning when studying worked examples in a multivariable calculus course. It examines cognitive load dimensions and the quality of students' conceptual understanding to provide empirical recommendations for instructional design in higher education. A mixed-method approach with a concurrent triangulation design combined quantitative and qualitative analyses. The quantitative aspect involved experimental comparisons of cognitive load, comprehension tests, and surveys, while the qualitative analysis focused on interaction patterns through discussion transcripts. Participants included 131 undergraduate students (41 male, 90 female, average age 19.25 years) from a state university in Banten, Indonesia. They were randomly assigned to individual (52 students) and peer collaboration (79 students) groups. The results revealed that students in the individual learning condition achieved significantly better comprehension than those in peer collaboration, though cognitive load showed no difference between the groups. Peer collaboration presented notable challenges in supporting the effectiveness of worked-example learning. In most cases, collaboration was either ineffective or partially effective. However, instances of effortful understanding and clarification-seeking suggest collaboration may be supportive if instructional design encourages deeper engagement and problem-solving. These findings provide insights for optimizing collaborative strategies in worked-example learning. © 2025, STKIP Siliwangi Bandung (IKIP Siliwangi). All rights reserved.