This study is an ethnomathematical study in children playing Minecraft in an after-school club. It investigates the question “What mathematics are children using and developing when they are playing Minecraft in an after-school club, and what are the effect of the clubs cultural, social and physical environment?” The backgrounds of the study are partly motivational problems in primary and lower secondary school mathematics , and partly a wish of gaining insight in informal mathematical learning and doing. Minecraft was chosen as the game for this study based on its popularity and wide-spread use in child-culture, as well as its breadth of possibilities in its open-world game-play.
The epistemological framework for the study is based on constructivism, and the theoretical foundation is that of ethnomathematics, as described by d'Ambrosio, Bishops universal categories of mathematical activities and Mariottis understanding of semiotic mediation. An ethnographic fieldwork of seven boys age 10, which are playing Minecraft in their after-school club, constitutes the empirical framework of the study. The design of the empirical data gathering consists of interviews, hand-held camera recordings in the club where Minecraft is played, as well as observations made during the fieldwork.
The culture of the club in the study is positive in regards to children playing computer games, and the physical environment allows for friends to play them together. This is an important factor in how much games are played, where most children in the study play less at home than in the club. It also has an effect on how Minecraft are played, as the club involves larger constructions in the game and long lasting game worlds than it does for them at home. Therefore the environment in which the game is played have a large impact on what is being played, and thus also what kind of mathematics that are involved.
The video material is analyzed on basis of Bishop, where a broad description of the mathematical phenomenon presents as part of the children’s play is present. The mathematics that was found in the children’s play is based on the construction of things; symmetries, geometric reflections, approximation of round shapes in a cubic virtual environment, decorative patterns, the use of compound numbers as a consequence of the games design, the use of virtual electric wiring under the ground, as well as the new knowledge that are discovered by the children as they play.
The study uses two cases from the above data, to analyze what role the semiotic mediation is having for the actions of the children. One is a boy that builds a bridge around a corner, and connects it to a nearby mountain, and another is a boy that builds a copy of a spiral staircase in an approximate round tower. In the first, the uses of various tools used to construct such a bridge between mountains are demonstrated, and how the design of the game, as well as the three-dimensional perspective creates challenges that he must solve. The second case demonstrates how the boy are challenged by the perspective, in terms of remembering the shape of the steps in the staircase, and how he changes strategy from counting blocks in a step to working with named figures in a strict order.
The conclusion of the study is that the environment of the after-school club, contributes to a game playing setting that contains a large amount of mathematical activity. The cases likewise show that the children also develop mathematical abstractions in their game activities.