The importance of teaching the Luria-Delbrück experiment to biology students is increasingly recognized by educators, and improved pedagogical methods for teaching the classic experiment have been proposed and tested in the classroom. However, there are still obstacles that impede the proper teaching of the classic experiment. This note proposes two strategies to further improve the teaching of the classic experiment. The first strategy is to be frank with an inherent limitation of the classic experiment, and instructors should explain from a logical point of view why the classic experiment cannot be used to refute the possibility of directed mutation. The second strategy is to emphasize the pioneering work of Delbrück on developing the mutant distribution that enables researchers to estimate microbial mutation rates using data generated by fluctuation experiments, and instructors should shift their attention to the overlooked essential role of the mutant distribution.