Performance and Difficulties of Students in Formulating and Solving Quadratic Equations with One Unknown

Abstract

This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight symbolic equations and four word problems; furthermore, semi-structured interviews were conducted with sixteen of the students. In the data analysis, the percentage of the students’ correct, incorrect, blank, and incomplete responses was determined to obtain an overview of student performance in solving symbolic equations and word problems. In addition, the students’ written responses and interview data were qualitatively analyzed to determine the nature of the students’ difficulties in formulating and solving quadratic equations. The findings revealed that although students have difficulties in solving both symbolic quadratic equations and quadratic word problems, they performed better in the context of symbolic equations compared with word problems. Student difficulties in solving symbolic problems were mainly associated with arithmetic and algebraic manipulation errors. In the word problems, however, students had difficulties comprehending the context and were therefore unable to formulate the equation to be solved. Thus, it is concluded that the differences in the structural properties of the symbolic equations and word problem representations affected student performance in formulating and solving quadratic equations with one unknown.