To understand students' argumentation abilities, there have been practices that focus on counting and analyzing argumentation schemes such as claim, evidence, warrant, backing, and rebuttal. This analytic approach does not address the dynamics of epistemic criteria of children's reasoning and decision-making in dialogical situations. The common approach also does not address the practice of argumentation in lower elementary grades (K-3) because these children do not master the structure of argumentation and, therefore, are considered not ready for processing argumentative discourse. There is thus little research focusing on lower elementary school students' argumentation in school science. This study, drawing on the societal-historical approach by L. S. Vygotsky, explored children's argumentation as social relations by investigating the genesis of evidence-related practices (especially burden of proof) in second- and third-grade children. The findings show (a) students' capacity for connecting claim and evidence/responding to the burden of proof and critical move varies and (b) that teachers play a significant role to emphasize the importance of evidence but experience difficulties removing children's favored ideas during the turn taking of argumentative dialogue. The findings on the nature of dialogical reasoning and teacher's role provide further insights about discussions on pedagogical approaches to children's reasoning and argumentation.