Fractal Project: From Students’ Alternative Ideas to Understanding Mathematical and Physical Fractals Through Elements of Fractal Geometry

This research investigates high school students’ understanding of mathematical, physical, and biological systems exhibiting Fractal structures, with the aim of enhancing their comprehension of nature’s intrinsic complexity. The research explores the pedagogical integration of Fractal Geometry, emphasizing key concepts such as scaling, self-similarity, and Fractal dimension, and examines their applications in both mathematical and natural systems.

The research employs an instructional intervention designed to evaluate students’ conceptual understanding, the characterization of Fractal sets and systems, and the impact on their motivation for learning Natural Sciences. Both qualitative and quantitative methods were used, including pre- and post-test questionnaires, worksheets, and statistical analyses. Nonparametric tests (Wilcoxon Signed-Rank and Mann–Whitney U) were used due to nonnormal data distributions, and the reliability and validity of the instruments were verified.

The results reveal that Students’ initial alternative conceptions shifted toward scientifically accepted ideas, and their motivation for the Natural Sciences increased substantially. Field-based activities involving authentic Fractal structures proved particularly effective in engaging learners, fostering active participation, retention, and meaningful knowledge construction.

The research demonstrates that the pedagogical use of Fractal Geometry provides an innovative and effective approach to teaching complex scientific phenomena. It bridges theoretical concepts and practical experience, enhances critical and creative thinking, and contributes to scientific literacy, offering new tools for interdisciplinary education and for teaching the natural world.