A Fractal Geometric Approach to Teaching Fractions for Mastery in Key Stages Two and Three: Open Problems and a Combined Theoretical Framework with Intelligent Practice

Fractions continually gift substantial conceptual and procedural hurdles for number one and early secondary college students (Key Stages Two and Three) in arithmetic schooling. Traditional coaching techniques regularly war to bridge the space among concrete expertise and summary illustration, main to rote memorisation in place of actual mastery. This article proposes and explores a singular pedagogical technique: leveraging the inherent homes of fractal geometry to train fractions. Fractals, with their self-similarity, scaling, and recursive nature, provide intuitive visible and structural analogues for fractional principles along with components of an entire, equivalence, ordering, and operations. The paper outlines the conceptual demanding situations normally confronted with the aid of using college students and information how a fractal geometric angle can deal with those. It identifies key open issues that warrant similarly empirical investigation, which includes curriculum integration, trainer training, and efficacy throughout numerous mastering populations. Furthermore, it synthesises a blended theoretical framework, drawing on cognitive load theory, constructivism, inactivism, embodied cognition, and Vygotsky's Zone of Proximal Development, to underpin the fractal technique. Finally, the object explores the combination of sensible exercise methodologies to decorate and support mastering inside this framework, offering a pathway toward attaining deep conceptual mastery of fractions.