ABSTRACT
This chapter presents a certain view of mathematical reasoning together with a discussion of the interrelationship between the structure of mathematical discourse and the structure of normal English discourse. It then outlines the nature of a theory of proof and includes a discussion of the utility of such a theory in mathematical education. The chapter discusses several basic ideas involved in the construction of a usable theory of proof. Mathematical reasoning, or deductive reasoning, is a process through which a person comes to understand, to know, that if certain statements were true then a certain other statement would necessarily also be true. When a man thinks through the axioms and a certain theorem in geometry and comes to know that if the axioms are true then the theorem must also be true, then that man is engaging in mathematical reasoning.
