Examining students' reflected game functions on mathematical games in an a-didactic milieu

A-didactic milieu design in the Theory of Didactic Situations was utilized and the aim of this study was determined as examining students' approaches and purposes of playing mathematical games based on concrete material presented in an a-didactic milieu. Students' plays were analysed through the concepts of reflected game functions. The study was designed as a case study. The study was carried out in the spring semester of the 2016-2017 academic year with the participation of 8 students who attended the 7th grade of a central secondary school in Eskişehir. Two games, based on concrete material and designed according to a-didactic milieu principles, were proposed to students. The students played the games during six hours. The data were collected through video and audio of each group, the students' notes and semi-structured interviews, which were held with each group at the end of the implementation. In the analysis of the data, content analysis method was used in determining the reflected game functions and descriptive analysis method was used for observing the evolution of a-didactic situations. As a result of the study, it was determined that the students performed plays more heuristic function with later explanatory function and fewer checking function. It was determined that there was a hierarchical relationship between a-didactic situations and the reflected game functions.