Goal: The problem of the authenticity of teacher questions has not received sufficient attention from educational researchers interested in the intersection between dialogue and argumentation. In this paper, we adopt a definition of authentic questions as dialogical units that prompt teacher-student interactions that are both productive (i.e., several students participating) and constructive (i.e., students produce arguments of high complexity). Our goal is to analyze whether and how specific types of dialogue prompts can encourage students' engagement in more sophisticated argumentative interactions, as manifested through the construction of high-complexity arguments. Method: We describe the implementation of our analytical approach to a large corpus of classroom interactions from five European countries. The corpus was segmented into dialogical sequences, which were then coded according to the argumentation dialogue goal expressed in the sequence. We also coded students' arguments according to Toulmin's elements and distinguished between low- and high-complexity arguments from a structural point of view. Findings: Our findings show the predominance of the so-called Discovery questions as prompts that are both productive and constructive and Inquiry questions as prompts of argumentative constructive interactions. We discuss the importance of these findings for teacher professional development purposes.