In argumentation studies, almost all theoretical proposals are applied, in general, to the analysis and evaluation of argumentative products, but little attention has been paid to the creative process of arguing. Mathematics can be used as a clear example to illustrate some significant theoretical differences between mathematical practice and the products of it, to differentiate the distinct components of the arguments, and to emphasize the need to address the different types of argumentative discourse and argumentative situation in the practice. I (...) consider some issues of recent papers associated with mathematical argumentation in an attempt to contribute to the discussion about the role of arguing in mathematical practice and in the evaluation of the products of this practice. I apply this discussion to learning environments to defend the thesis that argumentative practice should be encouraged when teaching technical subjects to convey a better understanding and to improve thought and creativity. (shrink)

ABSTRACT: It is not uncommon, in argumentation and in various professions, to diagnose a gap between theory and practice; and in the next step argue that they should be brought into line with each other. But what does this mean? I shall argue that some version of a gap is sound, as it leaves theory with a critical, independent role in relation to practice – something that an equilibrium view does not.

It is not uncommon, in argumentation and in various professions, to diagnose a gap between theory and practice; and in the next step argue that they should be brought into line with each other. But what does this mean? I shall argue that some version of a gap is sound, as it leaves theory with a critical, independent role in relation to practice—something that an equilibrium view does not.

Robert Fogelin formulated the thesis “that deep disagreements cannot be resolved through the use of argument, for they undercut the conditions essential to arguing.” The possibility of arguing presupposes “a shared background of beliefs and preferences,” and if such a background is not given, there is no way of “rational” dispute resolution. By contrast to this pessimistic view, I will propose a method that has been developed to overcome difficulties as described by Fogelin.