While there are many studies on students' collaborative learning at the small group level, pedagogies and strategies for supporting students' collaborative learning at the class level are underexplored. This study proposes a pedagogical model named the Spiral Model of Collaborative Knowledge Improvement (SMCKI) to inform the design and implementation of multi-layered collaborative learning activities in a networked class where there are many groups of students working collaboratively. Starting with a phase of individual ideation, the pedagogical model scaffolds students to go through five phases of intra-group and inter-group knowledge improvement and refinement, with the goal of supporting the advancement of their individual and collective knowledge. An exploratory case study is presented to illustrate how this model was used in a pre-service teachers' technology-enhanced learning (TEL) activity design lesson in a Computer-Supported Collaborative Learning (CSCL) environment. The results show that the participants significantly improved the quality of TEL design throughout the five phases of SMCKI. The implications of the findings on designing and implementing CSCL activities in authentic class environments are discussed.