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This study focuses on the effectiveness of games for building adolescents’ geometrical understanding. Two versions of a digital game (with and without narrative) were created based on the Van Hiele Model of geometric thinking. Participants (13-14-year-olds, n = 112) played either an unstructured puzzle geometry game (control), the no-narrative VHM game, or the narrative VHM game for 4-6 school periods lasting 40 minutes each. Results show an improvement in performance across all conditions. Group contrast comparisons found that gains were non-significant for the control condition, but significant for the no-narrative and narrative conditions, which had the largest effect. This builds evidence for the positive impact of theory-based educational games and intrinsically integrated “narrative” as an instructional feature of game-based learning.