High School Students' Metaphorical Perceptions of Arithmetic and Algebra

The study aimed to identify and examine high school students' mental images related to the fields of arithmetic and algebra. In this context, the phenomenological research design one of the qualitative research methods has been adopted. The sample for the study consists of 184 students attending a public high school. Students were given two forms containing the statements “Arithmetic is like … because …” and “Algebra is like … because …”. Content analysis was used to examine all the collected data. 140 students generated valid metaphors related to arithmetic, and 157 students generated valid metaphors related to algebra. The study concluded that students possess a broad metaphorical understanding of both algebra and arithmetic. As a result of the analysis, the metaphors generated for both arithmetic and algebra were divided into 14 categories each. According to the findings of the study, students emphasized that arithmetic should be clear and straightforward, containing known elements, requiring basic operational skills, having a structured and systematic framework, involving unchanging processes, and being necessary. Regarding algebra, they focused on the fact that it involves unknowns, is full of uncertainties, requires effort, and is difficult. In addition, it was observed that common categories emerged regard to the fields of algebra and arithmetic, such as being fun, requiring expertise and experience, difficulty, and necessity aspect.