This qualitative study explores the mathematical modeling processes of eighty-seven pre-service mathematics teachers in Turkey, focusing on their approaches to real-world problem-solving and the integration of technology. Utilizing a case study design, participants engaged in the Demijohn Problem, a modeling activity centered on quadratic functions. Data were collected through audio and video recordings, worksheets, and reflective essays. Findings indicate that while participants effectively understood and simplified problems, they faced challenges in model development and verification, often over-relying on technology without critical evaluation of their outputs. The study emphasizes the dual role of technology as both a facilitator and a potential barrier to deeper understanding. Recommendations for future research include comparative studies, focused investigations on interpretation and verification processes, and interventions promoting self-reflection on technological outputs. This research highlights the need for a balanced approach to mathematical modeling that fosters critical thinking and robust problem-solving skills.