Training students the discernment ability is an important task in distance education. To improve the training results, this paper makes following contributions: (1) suggests the web courseware on controversial social issues with different viewpoints for discernment training. (2) To construct training courseware, a method called DRPA (Discriminating via Representative Phrase Assaying) is presented with five algorithms, i.e. algorithms for extracting representative phrases, calculating characteristic array, determining the threshold array, objective judgment, and subjective judgment. (3) A new concept called Gymnastics Threshold is proposed and proved to be more accuracy than traditional threshold. (4) Extensive experiments are given to show that: DRPA is much more efficient and accuracy than traditional method.