Students’ game-based actions in abstract strategy board games: opening the black box

Abstract

Abstract Abstract strategy board games, which do not involve elements of luck and specific context, have potential to develop players’ mathematical skills, especially reasoning. In this study, the actions performed by the students in the reflected games, which aim at strategy development and implementation, were examined within the concept of milieu of the theory of didactical situations. An abstract strategy board game with a winning strategy (the square game) was chosen, and the game-playing process was designed as intra-group and inter-group games according to the main characteristic of an a-didactical milieu. Eight 7th grade students participated in the study and their games related actions were analyzed according to the reflected game functions. 13 indicators of reflected game functions were identified: 8 in the heuristic function, 3 in the explanatory function, and 2 in the checking function. The interactions between these indicators were analyzed in terms of transition between perceptual and theoretical levels to observe the evolution of the game milieu. The findings of the study showed that a number of the indicators of reflected game functions (predicting a winning move or the winner, analyzing possible moves, and perceiving a winning puzzle for the heuristic function, expressing a strategy orally or by playing for the explanatory function; generalizing strategies for the checking function) played a key role in the development of a strategy. These indicators were found to be critical in the evolution of the milieu as they allowed transitions between theoretical and perceptual levels.