Building cognitive support for the learning of long division skills using progressive schematization: Design and empirical validation

The design and empirical validation of a computer-based learning environment for acquiring long division skills, called the long division machine (LDM), are described. The construction of the LDM is primarily based on the didactic method of progressive schematisation. It offers the student a game-like environment for solving division problems by simulating the cooperation with an expert teacher or co-student who is responsible for the lower-level, routine, arithmetic subtasks of the overall division task. In a pilot study and two experiments the effects of several aspects of the LDM user interface on solution behaviour and performance were investigated, including the effect of gradually forcing the student to adopt a more efficient solution strategy, whenever this was possible. The ability of students to transfer their acquired knowledge and skills to an unaided problem solving context was also investigated. The results show that the LDM has the potential to improve and supplement current didactic methods for teaching long division skills.