ABSTRACT
The classic geometry class is essentially a year-long exercise in inductive and deductive reasoning using classical proofs to justify mathematical theorems and concepts. 'Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations'. We know there is a need to have proofs in the study of mathematics. The ELF problem requires reasoning to solve it. As students work through the solution, they are beginning to develop the skills required for proofs. The reasoning development is an essential part of the development of the ability to construct proofs. NCTM has identified Reasoning and Proof as one of the Standards teachers should be inserting throughout the curriculum. Although elementary students are not going to be overly formal in their beginning proofs, the reasoning and verification of things is an essential developmental skill.
