Debater: As a pedagogical practice, lecturing embodies hierarchy, since the lecturer is superior to the student in mastery of the subject. But people learn best from peer interaction. Thus, the hierarchy in lecturing is a great weakness. Respondent: By definition, all teaching and learning are hierarchical, for all teaching and learning must proceed from simple to complex. In teaching mathematics, for example, arithmetic must precede calculus. Thus, the hierarchy in lecturing is a strength. The respondent's reply to the debater's argument is most vulnerable to criticism on the grounds that the respondent ['takes for granted that the conceptual structure of mathematics is sufficiently representative of the conceptual structure of at least some other academic disciplines', 'fails to consider the possibility that some characteristics of lecturing other than hierarchy are weaknesses', "concedes one of the major assumptions on which the debater's argument depends", 'applies a key concept to a different aspect of education than the aspect to which the debater applied it']