The argumentation between parents and children is an important form of parent-child interaction. Arguments in parent-child discussions play an important role in the parent-child relationship and the healthy growth of the mind. As a verbal, social, and rational activity, argumentation aims at convincing a reasonable critic of the acceptability of a standpoint by putting forward a constellation of one or more propositions to justify this standpoint. In the 1970s, Frans van Eemeren and Rob Grootendorst put forward the ″Pragma-dialectics Theory″ based on the classic argumentation theory, logic, pragmatics, discourse analysis and other disciplines. Although the pragma-dialectics theory distinguishes between argument and standpoint as well as three major demonstration schemes: the sign, the analogy and the cause, it is still too general in concrete analysis. We argue that in the analysis of realistic argumentative discourses, Walton's argumentation scheme analysis has made up for the lack of pragmatic argument theory in his work on the proof of scheme details. Therefore, it is worthwhile to adopt the theoretical framework of pragmatic argumentation and take into consideration the resolution process of Walton's analysis of parent-child argumentation disagreements by using argumentation schemes to discuss the inherent characteristics of different argumentation schemes in the hope of providing constructive inspirations for creating a healthy parent-child argumentation atmosphere and improving children's reasoning capabilities  In this paper, “take the baby seat”, a case of argumentation, is taken as an example and is reconstructed from the perspective of pragma-dialectics. We found that the mother used result argument scheme, choice argument scheme and authoritative argument scheme in resolving opinion disagreements. In the meantime, the mother also used multiple argumentation, coordinative argumentation and subordinate argumentation to provide solid proof for their children to ″take the baby seat or not.″ Nevertheless, the mother violated the rules for critical discussion which prevented the resolution of the difference of opinion and led to logical fallacies.  The analysis makes up the insufficiency of argumentation analysis of pragma-dialectics, and is helpful in finding common argumentation schemes between parent-child argumentation and in making use of argumentation schemes to find fallacy, which lay the basis of analyzing parent-child argumentation through corpus analysis. Furthermore, under this research framework, we discovered an argument scheme which was not mentioned by Bova and other scholars through corpus analysis. This discovery has a certain significance in the field of parent-child argumentation. The study of parent-child argumentation enlightens us to pay more attention to parents' argumentation ability, children's rational reasoning ability as well as the importance of argumentation education. Many studies indicated that children's argumentation ability grows with age, so we should cultivate the argumentation ability from a young age. What's more, children acquire argumentation strategy mainly from their parents. As for parents, they should try to improve their own argumentation skills. For researchers, it is crucial to take children’s cognitive ability into consideration to develop a curriculum which suits children of all ages. The studies on parent-child argumentation should focus more on cultivating children's reasoning ability and promoting parents' argumentation skills.