This paper is aimed at combining the advances in argumentation theory with the models used in the field of education to address the issue of improving students’ argumentative behavior by interacting with an expert. The concept of deeper or more sophisticated argumentative strategy is theoretically defined and used to advance two new coding schemes, based on the advances in the argumentation studies and aimed at capturing the dialectical, or structural, behavior, and the argumentative content of each dialogue unit. These coding schemes are then applied for a qualitative analysis of a study designed to investigate how students’ argumentative behavior can be influenced by the interaction with an expert, who used specific types of attacks to the interlocutors’ positions. The twofold coding shows at which dialogical level expert–peer interactions can directly and more stably affect students’ argumentative behavior, and what effects such more sophisticated strategies can have on the discussion and the analysis of disagreements. In particular, this paper shows how a specific type of deep-level attack, the underminer, can open dialogues of a different level, focused on unveiling and debating background beliefs underlying a specific position.