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A total of 107 students from three schools participated, and data were analyzed using Kruskal Wallis and Mann Whitney-U tests, supplemented by interviews with six students. Results show lower performance in the pictorial representation test than in the other two, and mathematics averages of 4–5 do not guarantee equivalent success across all representations.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/comparison-of-high-achieving-sixth-grade-students-performances-a-study/588882/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/comparison-of-high-achieving-sixth-grade-students-performances-a-study/588882.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the study compare among sixth grade students?","Question",{"text":112,"@type":113},"The study compares performances on written computation, symbolic representation, and pictorial representation tests.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How were the data analyzed in the study?",{"text":117,"@type":113},"The data were analyzed using Kruskal Wallis and Mann Whitney-U tests, and interviews were conducted with six students.",{"name":119,"@type":110,"acceptedAnswer":120},"Which test showed lower performance for high-achieving students?",{"text":121,"@type":113},"High-achieving students performed particularly lower on the pictorial representation test compared with written computation and symbolic representation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},588882,1792231703,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","COMPARISON OF HIGH-ACHIEVING SIXTH GRADE STUDENTS’ PERFORMANCES ON WRITTEN COMPUTATION, SYMBOLIC REPRESENTATION, AND PICTORIAL REPRESENTATION TESTS  \nSuphi Önder BÜTÜNER  \nAbstract: The present study was conducted to compare the performances of high-achieving sixth grade students on written computation, symbolic representation, and pictorial representation tests.  \nThe study enrolled 107 sixth-grade students in three schools. Data were analyzed by using the Kruskal Wallis and Mann Whitney-U Tests and interviews were conducted with six students. The Mann Whitney U test was utilized to explore the groups that were favored by the difference. Student performances were lower particularly in the pictorial representation test than the other two. It is interesting that the students with mathematics grade average points of 4 and 5 atthe end of the first academic term failed to show the same success that they showed in the written computation test in the two other tests as well. Therefore, it can be said that the teachers evaluate the students who are good at doing operations as successful in mathematics.  \nKey words: High-achieving sixth grade students, written computation, symbolic representation, pictorial representation, test  \n1. Introduction  \nEffective computational skills in a student, in other words, his/her skills in performing operations quickly and accurately by using mathematical rules and algorithms, do not necessarily mean that the student has learned the relevant mathematical concept in a meaningful way (Fan & Bokhove, 2014; NCTM, 2000; Zeeuw, Craig & Hye, 2013) . Yang and Wu (2010) stated that excessive dependence on rules and algorithms in mathematics teaching reduces students’mathematical thinking skills and prevents their conceptual learning. Many researchers have reported the need for the use of different assessment tools to demonstrate the mathematical performance of students (Cai, 2001; NCTM, 2000) . Representation is among the mathematical process standards laid out in the principles and standards of school mathematics (NCTM, 2000) . Students with the skills in translating among multiple representations have a deeper understanding of mathematical ideas. On the contrary, it is difficult to say that students with poor skills in translating among multiple representations have a deep and conceptual understanding (Meij van der & Jong de, 2006). Using multiple representations flexibly is a sign that students have meaningfully learned the mathematical concepts and the relationships among them (Brenner, Herman., & Zimmer, 1999; Debrenti, 2013; NCTM, 2000) . Students’ skills in translating among multiple representations is crucial for mathematics learning and problem-solving (Acevedo Nistal, van Dooren, Clareboot, Elen & Verschaffel, 2009; Fennell & Rowan, 2001; Gagatsis & Shiakalli, 2004; Pape & Tchoshanov, 2001). When they solve problems, students ought to be able to choose and apply the right forms of representation and possess the skills to translate among multiple representations.  \nStudies have demonstrated that high-level mathematical thinking and problem-solving strategies maybe developed through the flexible use of multiple representations as well as a deep comprehension of mathematical concepts (Akkuş, 2004; Cramer, Post & delMas, 2002; Hines, 2002; Sert, 2007) . Indeed, many previous studies have revealed a significant relationship between skills in mathematical problem-solving and translating among multiple representations in mathematics teaching (Hitt, 1998;  \nOwens & Clements, 1998) . The skills of translating among multiple representations are considered tobe a crucial process standard for students in understanding mathematical concepts as well as the relationships between them. Presenting mathematical knowledge in different forms leads to meaningful learning (Ainsworth, 1999, p. 148-149; Akkoç, 2005; İncikabı, Biber, Takıcak, & Bayam, 2015) . Indeed, certain earlier studies have mentioned the favorable eff","cbCailewKBBMHE3Y","https://ap.wps.com/l/cbCailewKBBMHE3Y","pdf",944419,23,"English","# 1. Introduction\n## 1.1. Why fractions and fractions-related subjects?","[{\"question\":\"What does the study compare among sixth grade students?\",\"answer\":\"The study compares performances on written computation, symbolic representation, and pictorial representation tests.\"},{\"question\":\"How were the data analyzed in the study?\",\"answer\":\"The data were analyzed using Kruskal Wallis and Mann Whitney-U tests, and interviews were conducted with six students.\"},{\"question\":\"Which test showed lower performance for high-achieving students?\",\"answer\":\"High-achieving students performed particularly lower on the pictorial representation test compared with written computation and symbolic representation.\"}]","COMPARISON OF HIGH-ACHIEVING SIXTH GRADE STUDENTS’ PERFORMANCES - A STUDY | PDF",1792066117,58]