The Wheeler's delayed-choice gedanken experiment is introduced, the necessity and challenge in the quantum mechanics teaching are discussed. In order to faciliate the acceptance and understanding for undergraduate students, by solving the time-independent Schrodinger equation, the reflectivity and transmissivity of the single and double δ potential scattering for free particles are obtained, the correspondence between the scattering and Mach-Zender interferometer is further discussed. Finally a way to introduce the delayed-choice experiment into the quantum mechanics class teaching is designed via the one-dimensional δ potential barrier scattering, in expectation to provide new materials and shed new light on the teaching and understanding of wave-particle duality.