Determining the misconceptions of students in addition of fractions using a system developed with a hypothetical learning trajectory

One of the most challenging topics for students to learn in mathematics is fractions. Students form a lot of misconceptions while learning fractions, which have a big impact on their future academic careers. On the other hand, determining the misconceptions of that students is extremely challenging in terms of time and money. By conducting assessment and evaluation in a quicker and less expensive manner, the development of computer technologies and computer-assisted assessment tools can effectively contribute to the determination of such misconceptions. In this study, a test for identifying misconceptions in fractions was prepared through a hypothetical learning trajectory, and this test was uploaded to a website called Sorubox. A specific algorithm was applied to the tasks posted on the website in order to determine the misconceptions that students had regarding the addition of fractions. Following the determination of the misconceptions, the students were redirected to Scratch applications developed by the researchers. These applications featured a range of exercises designed to address the conceptual mistakes that were the main cause of the students' misunderstandings. The data were obtained from the misconception determination test and semi-structured interviews with the students. Both descriptive and content analysis were used to examine the data. The findings of the study showed that the Sorubox website was effective in identifying students' misconceptions, but Scratch applications were partially successful in eliminating student errors. The study's findings led to recommendations for the application and advancement of the misconception determination test formed for this study.