Adaptive collaborative learning support (ACLS) involves collaborative learning environments that adapt their characteristics, and sometimes provide intelligent hints and feedback, to improve individual students' collaborative interactions. ACLS often involves a system that can automatically assess student dialogue, model effective and ineffective collaboration, and provide relevant support. While there is evidence that ACLS can improve student learning, little is known about why systems that incorporate ACLS are effective. Does relevant support improve student interactions by providing just-in-time feedback, or do students who believe they are receiving relevant support feel more accountable for the collaboration, and thus more motivated to improve their interactions? In this paper, we describe an adaptive system we have developed to support help-giving during peer tutoring in high school algebra: the Adaptive Peer Tutoring Assistant (APTA). To validate our approach, we conducted a controlled study that demonstrated that our system provided students with more relevant support and was more effective at improving student learning than parallel nonadaptive conditions. Our contributions involve generalizable techniques for implementing ACLS that can function adaptively and effectively, and the finding that adaptive support does indeed improve student learning because of the relevance of the support.