Reconstructing art with mathematical functions: A qualitative case study integrating mathematics and art through GeoGebra

Source abstract

The increasing use of digital technologies in arts education has created new opportunities to explore connections between mathematical representation, visual form, and creative practice. In this context, dynamic mathematics software such as GeoGebra provides a flexible environment for examining and reconstructing artistic compositions through mathematical and geometric representations. This qualitative case study examined how first-year students in an audiovisual arts program used GeoGebra to reconstruct selected compositions by Yiannis Moralis through mathematical functions and geometric objects. All 72 students enrolled in the course received compulsory introductory instruction in GeoGebra. The assessed semester assignment, which contributed 30% of the final course grade, offered 18 alternative topics; 14 students voluntarily selected Topic 18, the GeoGebra reconstruction task. The analyzed corpus comprised 12 reflective narratives and 12 accessible GeoGebra files, with both data sources available for 11 participants. Reflexive thematic analysis of the narratives was combined with structural and interpretive analysis of the digital constructions. Descriptive theme-presence counts and a case-by-case triangulation matrix were used to examine patterns across this topic-selected corpus. The artifact analysis identified substantial variation in modeling approaches, including dense use of domain-restricted linear and quadratic functions, hybrid combinations of functions and geometric objects, polygonal decomposition, and polynomial curve fitting. Students reported recurring difficulties with complex curves, parameter sensitivity, domain selection, vertical contours, and software use. Their affective accounts were mixed, encompassing curiosity, frustration, persistence, fatigue, incompletion, and satisfaction. The findings indicate that the activity created opportunities for iterative representational experimentation and prompted some students to describe mathematics as an artistic medium. However, the data do not establish generalized learning gains or measured attitude change, and the findings are limited by the small, self-selected topic group and the graded instructional context.