LOGICAL CONSEQUENCES OF PROCEDURAL REASONING

This presentation makes a link between the common student view of mathematics as a collection of procedures and a certain type of error in constructing or validating proofs. It is well recognized that students commonly view mathematics as a set of procedures (Schoenfeld, 1992). These procedures typically take some mathematical object(s) as an input (e.g. a function) and return some other object(s) (e.g. the derivative of that function). In this presentation we suggest that this view contributes to student difficulty in understanding a point of logic when they are required to construct or validate proofs. This claim is illustrated using the following task, which was given to students during a study that tracked their developing understanding of real analysis (Alcock & Simpson, 2002).