FRATTART: Measurement and dimension in fractal geometry education at the interface of mathematics, physics, and art.

The FRATTART project investigates how fractal geometry can transform students’ under- standings of measurement, dimension, and the relationships linking mathematics, nature, and art. The study adopts a three-phase Design-Based Research methodology conducted in an upper-secondary school with a strong artistic orientation, where researchers and teachers collaboratively co-designed and enacted interdisciplinary learning activities. These activities foregrounded a comparison between Euclidean and fractal approaches to measurement, with particular emphasis on scale dependence and the concept of fractal dimension. Empirical data were gathered through questionnaires, classroom observations, audio and video record- ings, and analyses of students’ artistic artefacts. The findings indicate substantial shifts in students’ conceptions of dimension and complexity, alongside an increased awareness of the limitations of traditional Euclidean models. Furthermore, the project supported teach- ers in developing inquiry-based, cross-disciplinary pedagogical practices that meaningfully integrate mathematical modelling, physical phenomena, and artistic creation.