A Cross-Age Study of Students' Understanding of Fractals/Um Estudo sobre o Modo como Alunos Compreendem Fractais

The purpose of this study is to examine how students understand fractals depending on age. Students' understandings were examined in four dimensions: defining fractals, determining fractals, finding fractal patterns rules and mathematical operations with fractals. The study was conducted with 187 students (grades 8, 9, 10) by using a two-tier test consisting of nine questions prepared, based on the literature and Turkish mathematics and geometry curriculums. The findings showed that in all grades, students may have misunderstandings and lack of knowledge about fractals. Moreover, students can identify and determine the fractals, but when the grade level increased, this success decreases. Although, students were able to intuitively determine a shape as fractal or not, they had some problems in finding pattern rules and formulizing them.