In this review essay I respond to issues raised in Mijung Kim and Wolff-Michael Roth's paper titled "Dialogical argumentation in elementary science classrooms", which presents a study dealing with dialogical argumentation in early elementary school classrooms. Since there is very limited research on lower primary school students' argumentation in school science, their paper makes a contribution to research on children's argumentation skills. In this response, I focus on two main issues to extend the discussion in Kim and Roth's paper: (a) methodological issues including conducting a quantitative study on children's argumentation levels and focusing on children's written argumentation in addition to their dialogical argumentation, and (b) investigating children's conceptual understanding along with their argumentation levels. Kim and Roth emphasize the difficulty in determining the level of children's argumentation through the Toulmin's Argument Pattern and lack of high level arguments by children due to their difficulties in writing texts. Regarding these methodological issues, I suggest designing quantitative research on coding children's argument levels because such research could potentially provide important findings on children's argumentation. Furthermore, I discuss alternative written products including posters, figures, or pictures generated by children in order to trace children's arguments, and finally articulating argumentation and conceptual understanding of children.