Examining the visual proof processes of 7th grade students on equations

Proof-making expresses the essence of mathematics. This is because the concept of proof encompasses various skills such as reasoning, making inferences, making predictions, persuading others, and presenting evidence. Accordingly, individuals who can construct proofs possess advanced skills in these areas. As can be understood, the importance of proof-making in mathematics education cannot be underestimated. This study aims to examine and support students' visual proof processes related to the topic of equations. Eight 7th-grade middle school students participated in the study. The study was designed as a case study, which is defined as an examination of specific cases within a particular context. For this purpose, worksheets containing nine questions related to the topic of equations were prepared. During the application, focus group interviews, researcher observations, and field notes were used to examine the development of students' visual proof processes. The process was recorded using voice recorders to prevent data loss. The data obtained during the application process were analyzed, reported, and visualized using MAXQDA software. Descriptive analysis was employed in the analysis of the study. A coding-scoring key was used in the data analysis of the study. The findings from the study revealed that students had difficulty in constructing visual proofs. Moreover, it was observed that students who attempted to develop visual proofs showed improvement in mathematical skills such as establishing relationships and making generalizations throughout the process. Additionally, it was found that students found visual proofs interesting, explanatory, and different. Based on these findings, it was concluded that the use of visual proofs in mathematics education would be beneficial.