The process of cognitive biases characterization becomes one of consideration in acquisition. In educational context, it refers to the term of intuitive heuristics processing, which is also important to the development of teaching-learning strategies. This study investigates the roles of intuitive heuristics regarding to the process of how students acquiring English grammar and how it relates to the discovery learning. For this purpose, a descriptive qualitative research study was completed based on data that obtained through observation and semi-structured interviews for two postgraduate students from English department and non English department. The result of this study revealed that intuitive heuristics allowed the participants to generate answers in the lack of requisite knowledge. This study furthermore revealed that intuitive heuristics have a close relation to the process of thinking for problem solving. The results of this study suggest the need to monitor the thinking of those sacred gifts, develop and apply analytical ways of reasoning, because without it, they would lead themselves astray.