As the Common Core State Standards (CCSS) for English language arts (ELA)/literacy and the Next Generation Science Standards (NGSS) highlight connections across subject areas, convergences and discrepancies come into view. As a prominent example, this article focuses on how the CCSS and the NGSS treat "argument," especially in Grades K-5, and the extent to which each set of standards is grounded in research literature, as claimed. Analysis of both sets of standards and relevant bodies of research literature on argument in ELA/literacy and science education indicates that what counts as argument (i.e., disciplinary norms) and when argument is expected developmentally and whether children are capable of engaging in argument (i.e., developmental progressions) differ substantially and often contradict. Such discrepant information presents a dilemma to practitioners, especially classroom teachers who are faced with the real-time work of resolving these differences in their classrooms. I consider implications for classroom teaching and recommendations for educational policies and research agenda.