In this article, a critical overview of the argumentation theories was given and some research topics for the science of Korean education was proposed. Argumentation is a verbal and social activity to resolve the difference of opinions and conflicts reasonably. It will be characterized as being done in concrete contexts, being developmental, reflecting specific cultures, and having generic functions. There have been three main approaches to argumentation theories: logical, pragma-dialectical, and rhetorical. The first one focuses on argumentation as a product, the second one as a procedure, and the third one as a process. These three approaches have merits respectively which have to be served for describing the real argumentation. And the philosophical, theoretical, analytical, empirical, and practical researches are to be added to the argumentation theories. If we agree that the target of language education is the person as a language-user, as far as language is a medium of person's cognition and practice between him/herself and the real world, we have to adhere to the perspective that the contents of language education are not formal ones but functional and critical ones. From this standpoint, I proposed some research topics for the science of Korean education. The basic ones are designing the model of argumentation theory, surveying the argumentative competence, and describing the argumentative culture. And the practical ones include establishing the objects, constructing the contents didactically, and developing teaching-learning methods and evaluation practices. 【Key words】 science of Korean education, argument, argumentation, argumentation theory, logic, pragma-dialectic, rhetoric.