Collaborative argumentation in education, where students work together to construct and critique arguments, is an important social practice in many disciplines and can also develop conceptual understanding. This article addresses the evolution of my research agenda on collaborative argumentation from just scaffolding the generation of counterarguments and rebuttals in students' discourse toward what I call critical, integrative argumentation (CIA). The CIA framework involves teaching students to ask critical questions to assess the strength and cogency of arguments. It also involves generating, in addition to conventional refutations, integrative refutations that (a) weigh costs and benefits (or for scientific arguments, the evidence for and plausibility of alternative models), or (b) involve design arguments (or for scientific arguments, the integration of multiple factors and constraints). Issues related to terminology, instruction, student learning progressions, teachers' professional learning, public discourse, and the need to teach complex, critical thinking to students are discussed.