As quantum physics (QP) requires substantial mathematical knowledge, a thorough elementarization by reduction of complexity or with help of visualizations is needed without neglecting the goal of deeper understanding. First, we present how the visualization of the Dirac formalism could contribute to a deeper understanding of the central concepts of QP. Then, we present two teaching/learning proposals (TLP) for high school students based on the Dirac notation. Both approaches show how suitable strategies can improve student understanding of topics rooted in math and indicate significant success of the students in understanding, interpreting and implementation of the basic concepts of QP. The first approach presented here uses the concept of “wavity” or “wave-particle-duality” in the context of Dirac notation. The second approach emphasizes the measurement process and, on this basis, moves on to discuss the quantum state. It is asked whether and how it is possible to use the formal structure of these concepts to support students in interpreting them. In an inquiry-based teaching–learning sequence on high school level, educational strategies for consolidating the grasp of quantum concepts through math were developed and implemented in teaching experiments conducted in the framework of design-based research. Results of data analysis in both cases show that the adopted strategies are largely successful.