This case study examined team-based computer-game design efforts by children with diverse abilities to explore the nature of their collective design actions and cognitive processes. Ten teams of middle-school children, with a high percentage of minority students, participated in a 6-weeks, computer-assisted math-game-design program. Essential processes of collective design cognition and operation emerged from the data: (a) collective exploration of design constraints during "problem framing", (b) aggregation of identity, experience, and memory for "collective solution generation", and (c) development of coalition and task interdependence during "design execution". Salient contexts supporting collective design included "team-role fulfillment" with "presence of leadership" and "scaffolding for mutuality in design talk". The study findings also indicated perceived learning of school children during collaborative math-game design.