The aim of this study is to examine the mistakes made by students in the use of logical connectives while simplifying and solving algebraic equations and inequalities. The study was conducted among 146 first-grade high-school students. The data was collected from a questionnaire for students comprising items containing inequalities or equations. The data was analyzed according to interpretative theory. The findings identify mistakes in the way students use the mathematical logical connectives when manipulating algebraic expressions. Firstly, the mistakes of using AND include ignoring the AND and replacing it with a comma (，), replacing the AND with OR, and incorrect interpretation of the AND. Secondly, the mistakes of using OR include ignoring the OR, ignoring the OR and replacing it with a comma (，), ignoring the OR and replacing it with a slight-pause mark (、), replacing the OR with AND, and incorrect interpretation of the OR. Thirdly, in the category of ignoring the logical connective and replacing it with a comma (，), the frequency of the mistake of using OR is higher than the frequency of the mistake of using AND. Fourthly, this category of ignoring the OR and replacing it with a slight-pause mark (、) reveals the effect of students’ language background on the use of logical connectives.
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Taiwanese High-School Students’ Mistakes in the Use of Logical Connectives when Solving Quadratic Equations and Inequalities
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