Elementary Logic as a Tool in Proving Mathematical Statements

Abstract

An analysis of South African school mathematics results indicates that one of the problem areas in the mathematical performance of learners is proof and proving. In an endeavour to improve the mathematical proving ability of first year students at UWC, the MAM 112 class (a first year elective mathematics course) was taught a course in elementary logic. In the initial part of the study, logic puzzles were utilized as a tool to teach students to make logical connections between and from mathematical statements using the rules of inference. Subsequently research was done to determine if knowledge and understanding of logic would translate into improved proving abilities of students. To put proof and proving into perspective the origins and functions of proof was explicated and proving in South African schools was investigated. Consequently reasons are advanced for the dismal high school mathematics results in terms of proof and possible solutions are discussed. Recent discoveries of neuroscience are utilized to delineate the brain structures and cognitive processes involved in learning so as to gain a better understanding of the learning of mathematics. The findings of neuroscience, cognitive psychology and educational psychology are employed to elucidate the influence of emotion, confidence, experience and practice on the learning of mathematics in order to determine which factors can be applied to improve the proving abilities of students. The findings of the study indicate that knowledge of logic does help to improve the ability of students to make logical connections (deductions) between and from statements. The results of the study, however, do not indicate that knowledge and understanding of logic translates into improved proving ability of mathematical statements by students.