INVESTIGATION OF THE SKILLS IN SOLVING AND POSING RATIONAL NUMBER PROBLEMS IN CONTEXT OF MULTIPLE REPRESENTATIONS

Abstract

In this study, it is aimed to examine the problem solving and problem posing skills of seventh grade
students with rational numbers in the context of multiple representations. When the literature is
examined, although there is a study examining the relationship between multiple representation and
rational numbers, there is no research examining the relationship between students' problem posing
skills in addition to this relationship. It has been considered important to examine problem posing in
the context of multiple representation, which helps students to look at the subject from a new
perspective and allows them to understand it more deeply. The research was carried out with 25
students attending a public secondary school in Istanbul in the 2022-2023 academic year. The case
study method, which is one of the interactive designs included in the qualitative research approach,
was used in the research. The "Rational Numbers Multiple Representation Test" developed by the
researchers was used as a data collection tool. In line with the data obtained, the representation
preferences of the students and the interpretations of the success in these preferences were given
using descriptive statistics. In addition, the problems posed by the students were evaluated using the
problem posing assessment rubric introduced by Katrancı (2014). The reason for choosing this
rubric is that it allows grading students' problem posing performance. According to the research
findings, the most preferred representation types in problem posing questions were verbal (textual),
table, number line, algebraic (numerical) and model representation types, respectively. The
problems posed by the students were found to be 64 points out of 100 according to the problem
posing evaluation rubric. When the transition between representations were evaluated, it was found
that the transition from the verbal representation type to the table representation type was the most
successful, and the transition from the number line to the model type was the least successful. The
type of representation that the students liked to solve the most was the model type (40%), while the
number line (36%) took the second place. The types of representations that the students liked least
were expressed as algebraic and verbal. Considering the reasons for liking the model representation
type more, the reasons such as being visual, comprehensible and easy to construct were stated. On
the other hand, reasons such as being easy and practical are shown in the reasons for liking the
number line representation type.