Game-oriented participation and mathematical communication: Refining the Chocolate–Broccoli Engagement framework

Abstrak

Mathematical communication is essential in mathematics learning because it enables students to express, explain, and justify mathematical ideas. Although gamified learning may support student engagement under particular conditions, the relationship between game-oriented participation and meaningful mathematical communication remains insufficiently understood. This study aimed to examine and refine a preliminary Chocolate–Broccoli Engagement Framework describing the relationship between game-oriented participation and mathematical communication in gamified mathematics learning. A multiple case study was conducted across six mathematics classrooms from different secondary schools in Indonesia involving various mathematical topics and gamification environments. Data were collected through classroom observations, teacher reflection notes, and students’ mathematical communication artifacts and analyzed using cross-case thematic analysis. The findings revealed that students demonstrated recurring evidence of Chocolate Engagement characterized by enthusiasm toward competition, rewards, points, and leaderboards. Broccoli Engagement was observed in classroom interactions involving mathematical explanation, evaluation, reflection, and correction of solutions. Mathematical communication was documented through representation and procedural explanation across the cases, whereas justification and argumentation were identified in a more limited set of case-level episodes. Cross-case analysis showed that mathematical discussion was associated with the co-occurrence of game-oriented participation, concept-oriented engagement, and mathematical communication. These patterns informed the refinement of the preliminary Chocolate–Broccoli Engagement Framework, which does not posit a causal, mediating, or temporal sequence. The findings suggest that gamified mathematics activities may provide richer opportunities for mathematical communication when they incorporate structured opportunities for explanation, evaluation, reflection, and justification.