Investigation of fraction schemes of middle school students

Fraction schemes are schematic models that represent possible roadmaps of process from the experiencing of the fraction operations to the interiorizing in the face of a particular situation while the concept of fraction is being structured in the mind. This study was designed with the developmental research method in order to examine what kind of fractional schemes students have in grades 5 through 8 and how there is a change and development between grade levels in the application of fraction operations within the schemes. Data were collected cross-sectionally from 5th, 6th, 7th and 8th grade students through an adapted written evaluation tool and semi-structured clinical interviews and analyzed by content analysis. The results of the study showed that although there is no hierarchical structure in the development of fractional schemes, it is seen that the most primitive scheme is the simultaneous partitioning scheme and gradually decreases from grade 5 to grade 8. While in the development process of two different schemes examined, there is a rapid increase in the transition from grade 6 to grade 7; results showed that in the development process of most of the schemes examined, a rapid increase occurred in the transition from 5th grade to 6th grade. Further, some distinctions have been identified regarding the use of fraction operations in the context of fractional schemes. Besides, it was seen that students had difficulty in applying fraction operations on diverse fraction representations.