Abstract:

Infinity is an intriguing concept that has fascinating philosophers and mathematicians for centuries. Aristotle, one of the greatest philosophers of ancient times, identified two types of infinity: potential and actual infinity. Potential infinity refers to infinity as an endless process, while actual infinity considers infinity as a completed process. However, according to Fischbein (1979), as humans, we are more accustomed to dealing with finite realities that exist in space and time, which makes it difficult to understand the concept of actual infinity. Students, in particular, tend to perceive infinity mostly as potential infinity, that is, as an ongoing process, rather than an actual infinity (Monaghan, 2001).

Although the concept of infinity is not explicitly studied in school mathematics curricula, the word infinity is used in classrooms and textbooks, leading students to develop an intuitive understanding of the concept. In this study, we aim to identify the perceptions formed by primary and secondary school students about the concept of infinity, and investigate whether differences arise at various stages of school education.

The research study used quantitative methods to investigate the perceptions of infinity in Greek school education, which is divided into three stages: primary school (grades 1-6), middle school (grades 7-9), and high school (grades 10-12). A total of 377 students participated in the study, including 124 6th graders and 154 9th graders, and 99 12th graders. We administered a questionnaire to the students and extracted the basic perceptions of infinity in each educational level. We then analyzed the data using the statistical program SPSS to explore any developmental progression in the perception of the concept at different educational levels.

According to the data analysis, students in these grades have three basic perceptions of infinity: finite perception, procedural perception, and actual perception. Students with finite perception consider infinity to be finite. Students with procedural perception view infinity as a never-ending process. Students with actual perception see infinity as a completed process. Procedural perception is the most common across all three grades, but the differences between students' perceptions of these levels are not statistically significant.

References:
[1] Fischbein, E., Tirosh, D. and Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics,10, 3-40
[2] Monaghan, J. (2001). Young peoples’ ideas of infinity. Educational Studies in Mathematics, 48, 239-257

Keywords:

Infinity, intuition, perception.