Teaching Algorithm Selection: A Spine-Cluster Curriculum Architecture for Vietnamese Olympiad Informatics Training

Students on the specialized informatics track (Vietnamese: chuyên Tin) in Vietnam can memorize and reproduce classical algorithms but frequently fail to recognize which algorithm should be applied to a novel problem. The gap between declarative algorithmic knowledge and the ability for contextual deployment has been widely documented in cognitive science (Chi, Feltovich, & Glaser, 1981; Davies, 1990) but has not been addressed by any existing competitive-programming training curriculum. This paper proposes the Spine-Cluster architecture: a linear spine describing the development of cognitive skills combined with clusters of problem variants for each algorithmic concept. The architecture shifts the axis of organization from algorithmic content to algorithm-selection skill (in Davies's terminology), integrating interleaving, scaffolding fading, and mastery tracking. We describe the system design, an AI-mediated tutor built on Gemini, a simulation experiment executed to validate the correctness of the dispatch policy, and a validation plan targeting specialised-informatics students.