The Students’ Misconceptions in Using Three-tier Multiple Choice Diagnostic Test on the Angle Relationships
Authors: Muryani Desfi Ida , Jana Padrul , Umasugi Sitti Mutia 
Published: March 2023

<span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">Understanding the concept is one</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> ability</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> that students must master in learning mathematics</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> b</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">ecause concepts in mathematics are related to </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">each</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> other. Based on the result of observation, it show</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">ed</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> that not all students ha</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">d</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> a good</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> conceptual</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> understanding</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">. </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">Another finding </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">reported</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> that students ha</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">d met the</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> criteria for understanding concepts, </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">not </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">understanding concepts, and </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">having </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">misconceptions. </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">The conditions where s</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">tudents experience misconception</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">s</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> need</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">to be considered because the misconception is a condition in which students use a concept that is not following the agreement of the expert with full confidence in the correctness of the concept. If misconception is allowed, it will affect the fo</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">llowing </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">concepts. This study aimed to determine the process and results of the analysis of student misconceptions and determined the causes of student misconceptions. Th</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">e design</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> of </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">this </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">research </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">wa</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">s descriptive qualitative with the number of subjects as many as 20 students. Data collection used a diagnostic test in the form of three-level multiple-choice questions and interview results. The method</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">used a test,</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">an</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> interview, and documentation. The </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">steps </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">in</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> the</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> data analysis </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">of this research included</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> data collection, data reduction, data presentation, and concluding. The</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> validity test of the data</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> used triangulation, namely, comparing the test results with the interview</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> result</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">. The research results</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">showed that there were students' misconceptions in the low and medium-level understanding group</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">. </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">Meanwhile, students in the high conceptual understanding group found False Positive criteria where false positive</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">s</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> were part</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">s</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> of the misconception. However, in this study, </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">the </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">false positive</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">s </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">were caused by students' inaccuracy in </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">answering </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN">the questions. The causes of student misconceptions include</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">d</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> using the concept of angle</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">s</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> that </span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">were</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> not following the agreement of the experts; applying angles with the wrong concept; wrong in interpreting images or just seeing based on images; wrong in algebraic addition arithmetic operations; wrongly applying the concept of angles in triangles</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">,</span><span style="font-size: 9.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi; mso-ansi-language: IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="IN"> and not being careful in solving algebraic equations.</span><!--[if gte mso 9]><xml>
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