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<article-title>The Reasons Behind Students&#8217; Incorrect Solutions While Solving Quadratic Equations in One Unknown</article-title>
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<author>Makbule Gozde Didis<sup>1</sup> and Ayhan K&#252;rsat Erbas<sup>2</sup>  </author>

<aff><sup>1</sup>Gaziosmanpasa University, Turkey  </aff>
<aff><sup>2</sup>Middle East Technical University, Turkey </aff>

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<title>ABSTRACT</title>
<p>Quadratic equations are the fundamental learning area of school algebra. However, some research indicated that solving quadratic equations is procedurally and conceptually challenging for many students (e.g., Vaiyavutjamai &amp; Clements, 2006), and students have a tendency to make many errors while solving quadratic equations. For example, Kotsopoulos&#8217; (2007) research has demonstrated that factoring simple quadratics (i.e., ax<sup>2</sup>+bx+c where a = 1) sometimes might be quite difficult for students. Many different types of factors may contribute to students&#8217; incorrect solutions. Therefore, in addition to knowing students&#8217; errors and difficulties in solving quadratics, to teach effectively, the fundamental reasons oferroneous solutions should also be known by teachers. For this reason, in this study, we aimed to explore the reasons for students&#8217; incorrect solutions in solving quadratic equations in one unknown. 217 tenth grade students from three public high schools in Turkey were the participants of this study. A test prepared by the authors was used as data collection tool. This test comprised three parts, and total of seventeen items. The first part of the test included symbolic computation items, the second part involved mathematical scenario with both a quadratic equation and a solution belonging to it, and the third part consisted of word questions. The test was administered by the mathematics teachers while the regular class and students in the study were given forty-five minutes to complete the test. For this study, the data analysis of the first part of the test will be presented. The data of the first part of the test were qualitatively analyzed. The data analyzed in two-stage. In the first stage, students&#8217; incorrect solutions were determined by analyzing students&#8217; solution ways item by item. After that, in the second stage, the common reasons of students&#8217; mistakes were identified by analyzing students&#8217; incorrect responses. The data analysis revealed that three issues can be addressed as the common reasons for students&#8217; incorrect solutions in solving quadratic equations in one unknown <i>(i)</i> misapplication of cross-multiplication rule by factoring; <i>(ii)</i> misremembering quadratic formula; calculation errors while applying discriminant or quadratic formula and <i>(iii)</i> neglecting one of the roots of a quadratic equation. Briefly, our data support that students had knowledge about the algebraic procedures, rules and formulas to solve quadratic equations. However, because students memorize the algebraic procedures, rules and formulas without understanding their meanings, they are more likely to forget them quickly and they cannot transfer their knowledge to solve quadratic equations in one unknown.  </p>
<p><italic>Keywords: </italic>Mathematics education, Algebra, Quadratic equations. </p>
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