Mistakes Made by Students with Logical Connectives When Solving Equations and Inequalities, and How Teachers Assess These Mistakes

Abstract

The aim of this study is to examine the mistakes made by students in the use of logical connectives while simplifying algebraic equations and inequalities, and the extent to which teachers are aware of these mistakes and how they assess them. The study was conducted among 50 ninth grade students and 63 practicing teachers of mathematics. The data was collected from two questionnaires: a questionnaire for students comprising items containing inequalities or equations, and a questionnaire for teachers comprising students’ solutions of different items. The data was analyzed according to interpretative theory. The findings identify common mistakes in the way students use the mathematical logical connectives OR, AND, IF … THEN when manipulating algebraic expressions. The findings further indicate that teachers were not aware of the errors made by students in working with the mathematical logical connectives, where the most common mistake identified among students was ignoring the logical connective entirely. Moreover, the findings indicated that teachers may assess solutions as correct even when they use mathematical logical connectives wrongly.