Background and Objective: The present study aimed to identify and compare the mathematical beliefs of fourth and eighth-grade students through metaphor analysis.
Methods: This research employed a descriptive-survey design. The statistical population consisted of fourth and eighth-grade students in Shahrekord. A sample of 361 fourth-grade students and 360 eighth-grade students was selected using cluster-random sampling. Students were asked to propose a metaphor about mathematics and provide a reason for their choice.
Results: Initially, by examining the students' metaphors and their reasons, nine categories were identified, including categories such as "enjoyable," "useful and practical," and "annoying." Subsequently, upon closer examination, some of the beliefs embedded within the metaphors were extracted. Some students held positive beliefs about mathematics, describing it as enjoyable and pleasant, while others had negative views, considering it confusing and difficult. A number of students believed that learning mathematics is beneficial and necessary. Some also believed that learning mathematics requires innate talent; however, only fourth-grade students believed that discovering and creating mathematics is exclusive to geniuses. Some eighth-grade students believed that even if they did not enjoy mathematics, they had to learn it, and a number of them considered success in mathematics to be dependent on memorizing formulas. Positive beliefs (such as being enjoyable and easy) were more prevalent among fourth-grade students, while negative beliefs (such as being difficult and annoying) were more common among eighth-grade students. Furthermore, the categories "easy" and "consisting of parts" appeared only in the fourth grade, and the category "rule-governed" appeared only in the eighth grade. Gender patterns indicated that boys expressed more positive beliefs, while girls emphasized the difficult and anxiety-provoking aspects of mathematics.
Conclusion: Overall, fourth-grade students described mathematics as more enjoyable, while eighth-grade students emphasized its usefulness and difficulty. Although differences were observed between the metaphors of male and female students in the fourth and eighth grades, the results of the chi-square test indicated that this difference was not statistically significant. These findings provide insights for designing targeted educational interventions to improve mathematical beliefs, which can enhance students' academic performance.