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Using a teaching experiment with four university students, interviews with GeoGebra-based activities reveal rapid, flexible links between visualization and formal definitions.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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is linear algebra harder to teach than other mathematics courses?","Question",{"text":63,"@type":64},"Because students often face special difficulties in understanding the concepts, which can result in misconceptions and reliance on memorizing definitions and rules.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which linear algebra concepts were linked with visual equivalents in the study?",{"text":68,"@type":64},"The study focused on linear combination, linear dependency/independency, and spanning, relating each to visual representations in R2 and R3.",{"name":70,"@type":61,"acceptedAnswer":71},"How was GeoGebra used in the research?",{"text":72,"@type":64},"Interviews were conducted using GeoGebra-prepared activities, and the participants used the concepts flexibly while quickly relating visualization to definitions.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},588142,1792165382,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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KIYMAZ  \nAbstract: Linear algebra differs from other mathematics courses because of the special difficulties that students have in understanding the concepts. Teaching without concreticing the concepts of Linear Algebra encouraged students to memorize definitions of concepts and rules has been articulated. Many researchs show that technology-supported teaching is effective in concretizing abstract concepts. In this study, it was examined how pre-service mathematics teachers relate the definitions of concepts (linear combination, linear dependency /independency and spanning) and their visual equivalents in R2 and R3. The study was conducted with four students who attended the Linear Algebra-2 course in the Elementary Mathematics Teaching, Faculty of Education of a state university in Turkey. The study was conducted by the teaching experiment method.  \nInterviews were conducted using activities prepared in the GeoGebra program. It was observed that the participants used these concepts in very flexible way and they established a relationship between visualization and definitions in a very short time compared to the time spent during an educational period.  \nKey words: Teaching linear algebra, geogebra environment, visualization  \n1. Introduction  \nThe results of studies on teaching linear algebra show that students have many difficulties and misconceptions in learning concepts (Aydın, 2007; Dubinsky, 1997; Dorier, 1998) . Although in general linear algebra is taught at university level, in some countries, it is also included in high school curricula. For instance, Güzel, Karataş and Çetinkaya (2010) stated that some linear algebra concepts are taught at high school level in countries like Turkey, Germany and Canada. In a study conducted in Turkey, the high school level linear algebra teaching has been found to be inconsistent, incomplete and mostly just computational (Ençerman, 2008) . A study conducted by Akyıldız and Çınar (2016) revealed that pre-service elementary mathematics teachers have a hesitant attitude towards linear algebra and low level competence in the language that they use in expressing the concepts. It was also claimed that they have difficulties in relating the notions of linear algebra to one another since the concepts are new to the students. According to Aydın (2009) since the students encounter special difficulties in making sense of the concepts of linear algebra it differs from other mathematics courses.. Many of the concepts students encounter in linear algebra are new to them, leading to difficulties in relating concepts to one another (Akyıldız ve Çınar, 2016) . Carlson, Johnson, Lay, and Porter (1993) reported that students’ being unable to associate even the simple concepts to each other reduces the motivation of teachers in teaching linear algebra.  \nMoreover, in a study by Ençerman (2008) it has been articulated that a teaching without concretizing the concepts of linear algebra drives students to memorize the definitions and the techniques. In Turgut (2010), it has been determined that the technology assisted linear algebra instructions increase the pre-service mathematics teachers’ success in linear algebra. In a study conducted by Aydın (2009), researches on teaching linear algebra were discussed in three main topics. The first is the difficulties in teaching linear algebra and the appropriate curriculum development, the second is the use of geometry in linear algebra, the cognitive flexibility research focusing on topics such as formal structure of the algebra, and the third is focusing on the evaluation of software programs and linear algebra. This  \nresearch is in the third research group because it aims to teach Linear Algebra with GeoGebra software.  \nSierpinska (2000) suggested that students have three different ways of thinking in learning linear algebra. The first of these was named as a synt","cbCaibm5LTKxBDhr","https://ap.wps.com/l/cbCaibm5LTKxBDhr","pdf",876216,22,"English","# Introduction\n# Conceptual Difficulties and Misconceptions in Linear Algebra\n# Technology-Supported Teaching and Concretization\n# Thinking Forms: Synthetic-Geometric, Analytical-Arithmetic, Analytical-Structural\n# Teaching Languages: Geometric, Algebraic, Abstract Language","[{\"question\":\"Why is linear algebra harder to teach than other mathematics courses?\",\"answer\":\"Because students often face special difficulties in understanding the concepts, which can result in misconceptions and reliance on memorizing definitions and rules.\"},{\"question\":\"Which linear algebra concepts were linked with visual equivalents in the study?\",\"answer\":\"The study focused on linear combination, linear dependency/independency, and spanning, relating each to visual representations in R2 and R3.\"},{\"question\":\"How was GeoGebra used in the research?\",\"answer\":\"Interviews were conducted using GeoGebra-prepared activities, and the participants used the concepts flexibly while quickly relating visualization to definitions.\"}]","Teaching Linear Algebra Supported by GeoGebra Visualization Environment - Research Summary | PDF",1792064612,55]