Tinkering learning is a pedagogical strategy that emphasizes hands-on exploration, experimentation, and learning from mistakes in STEM education. It involves using personal fabrication tools, such as a 3D printer, to develop and improve ideas through interactive play. Design-based making activities have gained popularity in K-12 classrooms as they provide students with this authentic learning experience. This descriptive case study aims to understand the impact of students' interactions with a 3D printer on their tinkering learning during a formal design-based making activity. Specifically, the study explores what types of learning paths students follow when developing and improving their ideas through tinkering and what factors negatively affect this iterative design experience. In this design-based making activity, students tinker both in the digital world with Tinkercad and in the physical world with a 3D printer. Approaching real-world problems through iterative design can change their production-oriented actions. To understand the impact of this change on their tinkering learning, the study observes students' actions and collects their reflections on their tinkering through multiple surveys. The analysis revealed that students followed one of three different paths that led to varying levels of tinkering learning and that their tinkering experiences were negatively impacted by five major factors.