We apply peer instruction (PI) in the university's quantum mechanics (QM) class to prepare prospective teachers to connect their mathematical knowledge with qualitative concepts and wave forms. Thus, we modified PI to fit the level and the abstractive characteristics of university QM classes and then implemented it in a real class to find out whether it helped pre-service physics teachers to learn not only mathematical formulae but also qualitative concepts and how to draw graphs based on their knowledge. Twenty-two pre-service physics teachers in a class were candidates for the research. After the PI class, they solved three concept questions about the quantum tunneling effect, which is being qualitatively taught to high-school students. After the class, the candidates filled out a survey about the new class, and they indicated that the newly-adopted class had been very useful in helping them to understand consistently the concepts, mathematical formulas, and how to draw wave forms.