This article examines three commonly used pedagogical methods, namely the Socratic method of inquiry, collaborative problem solving, and debate-based deliberation, establishing the relationship of each one of these methods with the strategic promotion of argumentative reasoning, as a commonplace objective and means of inquiry-based educational praxis. Building on the idea that critical thinking has an aporetic element that is missing from contemporary educational positions, I argue that a more normative, structured approach to critical inquiry pedagogical strategies is necessary for teachers to better understand their practice and educational researchers to analyse pedagogical dialogue. For this, I model classroom discourse using four types of argumentation dialogues based on the research of the Canadian philosopher Douglas Walton. Examples of classroom discourse transcripts in different disciplinary areas are analysed according to these types, which correspond to information-seeking, discovery, inquiry and persuasion dialogues. In all these types of dialogue, the aporia is defined as a starting point reflected in both the dialogue's main goal and participants' aims. The side benefits of each one of the four types of dialogue when implemented as pedagogical strategies are also discussed. Finally, suggestions for empowering teachers in identifying and implementing different potentially argumentative dialogues as part of their pedagogical strategies kit are presented.