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Emphasis is placed on whether they internalize the meanings and relational dimensions of matrix concepts and operations. Data were collected from 26 teacher candidates at a university in Eastern Anatolia through a written exam, with responses analyzed by two field experts. Results indicate incomplete understanding of matrix concepts and operations, frequent misconceptions, and weaker performance on proof-based items, while rule-based or logic-only problems were handled more successfully.",{"@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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/teacher-candidates-understanding-and-appraoches-to-errors-about-matrices/603116/",{"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/teacher-candidates-understanding-and-appraoches-to-errors-about-matrices/603116.png","ImageObject",300,407,{"name":92,"@type":93},"MrHarris58","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main aim of the study about matrices?","Question",{"text":112,"@type":113},"The study aims to examine pre-service mathematics teachers’ ability to detect errors made while solving questions about matrices, focusing on how well they internalize the meanings and relationships of relevant concepts and operations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the research conducted and analyzed?",{"text":117,"@type":113},"The study involved 26 teacher candidates. They completed a written exam, and their responses were analyzed by two field experts.",{"name":119,"@type":110,"acceptedAnswer":120},"What were the key findings on teachers’ understanding and error detection?",{"text":121,"@type":113},"The results showed that pre-service teachers did not fully understand matrix concepts and operations. They produced various errors, including misconceptions and incomplete understanding, and they were less successful with proof-based questions compared to logic or rule-based problems.","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},603116,1792904617,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"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},687212988360,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Teacher Candidates’ Understanding and Appraoches to Errors About Matrices  \nŞükrü İLGÜN1  \nKafkas University  \nSolmaz Damla GEDİK ALTUN2  \nNevşehir Hacı Bektaş Veli University  \nAlper Cihan KONYALIOĞLU3  \nAtatürk University  \nAbstract  \nThe aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26 teacher candidates at a university in the Eastern Anatolia Region. They were given a written exam, and their responses were analyzed by two field experts. The results showed that the pre-service teachers did not fully understand the conceptsand operations of matrices. They made a variety of errors, including misconceptions and incomplete understanding. They were also not very good at solving proof-based questions. However, they were more successful at solving problems that were based on plain logic or could be solved using rules.  \nKeywords: Error, Error approximation, Linear Algebra, Matrices  \nDOI: 10.29329/epasr.2023 .600.9  \nSubmitted: 05 May 2023 Accepted: 25 June 2023 Published: 30 September 2023  \n1Assoc. Prof., Faculty of Education, Kafkas University, Kars , Türkiye, ORCID: 0000‐ 0002‐2842‐2032  \n[Correspondence](Correspondence: mat.ilgun@hotmail.com)[: mat.ilgun@hotmail.com](Correspondence: mat.ilgun@hotmail.com)  \n2 Assist. Prof., Faculty of Education, Nevşehir Hacı Bektaş Veli University, Nevşehir, Türkiye, ORCID: 0000-0002-6205- 6603 Email: [sdgedik@nevsehir.edu.tr](sdgedik@nevsehir.edu.tr)  \n3 Prof., Faculty of Education, Atatürk University, Erzurum, Türkiye, ORCID: 0000-0002-6009-4251 Email: [ackonyali@atauni.edu.tr](ackonyali@atauni.edu.tr)  \nIntroduction  \nIt is important to know the errors that students make and the misconceptions they experience in learning environments so that meaningful learning can take place and a qualified education can be provided (Altıntaş et al., 2021). According to Baştürk (2014), it would be possible to say that error hasan indisputable place in mathematics. In this context, with some changes made in mathematics education, mathematical errors have gained an important dimension.  \nAn important way to use error in mathematics in a positive way is error detection studies. With these studies, it can be revealed whether the correct information is truly internalized or not. Is the indicator of knowing just giving the right answer, making the right solution? It is of course important to give the right answer and to make the right solution, but the individuals who are assumed to know about any subject should have the ability to see the errors made about what they knows. It should be known that this is an indication that knowing what is true is necessary but not sufficient for learning (Durkaya et al. 2011) .  \nBeing able to detect errors correctly is a very important phenomenon. While Tirosh (2000) explains the fact that the subject knowledge reach a certain level explaining with awareness of errors, this situation is also seen as a factor of having in-depth subject knowledge emphasized in NCTM (2000) . Again, error detection, Ball et al. (2008), is included in the special content knowledge that a person who can correctly question the error has internalized the related concept to a large extent (Konyalıoğlu et al., 2010; Konyalıoğlu et al., 2012) . The correct approach to the error and the correct solution proposal is one of the components that can be used in determining the adequacy of the subject knowledge (Durkaya et al. 2011) . Borasi (1986; 1989) stated that the nature of mathematics can be better understood with error approaches (Demirci et al., 2017) .  \nLinear algebra is one of the branches of mathematics related to abstract structures that represent various concepts and systems that contain different properties ","cbCaibpxeF18PUrK","https://ap.wps.com/l/cbCaibpxeF18PUrK","pdf",755679,21,"English","# Abstract\n# Introduction","[{\"question\":\"What is the main aim of the study about matrices?\",\"answer\":\"The study aims to examine pre-service mathematics teachers’ ability to detect errors made while solving questions about matrices, focusing on how well they internalize the meanings and relationships of relevant concepts and operations.\"},{\"question\":\"How was the research conducted and analyzed?\",\"answer\":\"The study involved 26 teacher candidates. They completed a written exam, and their responses were analyzed by two field experts.\"},{\"question\":\"What were the key findings on teachers’ understanding and error detection?\",\"answer\":\"The results showed that pre-service teachers did not fully understand matrix concepts and operations. They produced various errors, including misconceptions and incomplete understanding, and they were less successful with proof-based questions compared to logic or rule-based problems.\"}]","Teacher Candidates’ Understanding and Appraoches to Errors About Matrices | PDF",1792095740,53]