Recent research in mathematics education shows that by exploring the properties of figures and making conjectures, especially through dynamic geometry software, students can better develop their understanding of concepts. Furthermore, comparing different geometric worlds and, within them, different representations enhances Euclidean knowledge. In our ongoing experience, high school students are involved in exploratory cooperative learning activities within Taxicab geometry using digital and non-digital tools, starting from Euclidean geometry, and going back to it. In the paper, we focus on the concepts of distance, circle, and conic. We face the issue of promoting students' conceptual understanding and theoretical thinking by transferring their knowledge of concepts or the validity of statements back and forth between Euclidean and Taxicab geometry, with the goal of providing evidence that an instrumental genesis of meaningful learning is activated when students engage in these activities.