Consider the propagation of parallel polarized waves of plane electromagnetic waves obliquely incident on a three-layer medium. Based on the cognitive model of physics problem-solving and electromagnetic field theory, the reflection and transmission coefficients under arbitrary conditions are derived, and the formulas for reflection and transmission coefficients under normal incidence in textbooks such as electromagnetic fields and waves are extended. Several special conclusions are discussed in specific situations, which can enrich the content of the textbook and prepare for future updates on electromagnetic fields and waves. This has positive significance for cultivating college students' innovative consciousness and research ability, and also provides innovative teaching research cases for science and engineering teachers to conduct teaching research.