[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588188-105":59,"doc-detail-588188-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","formation-process-of-common-divisor-concept-a-study-of-realistic-mathematics-education","FORMATION PROCESS OF COMMON DIVISOR CONCEPT - A STUDY OF REALISTIC MATHEMATICS EDUCATION","","Common divisor is a key secondary-school concept that supports understanding of many later number concepts, yet students often struggle to interpret it. This case study examines how seven sixth-grade students form the concept through a Realistic Mathematics Education learning environment. Data from group and individual work and semi-structured clinical interviews are analyzed using content analysis in the APOS framework. Results show differing internalization paths, coordination with prime factorization, and students’ ability to conceptualize greatest common divisor.",{"@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/formation-process-of-common-divisor-concept-a-study-of-realistic-mathematics-education/588188/",{"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/formation-process-of-common-divisor-concept-a-study-of-realistic-mathematics-education/588188.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why is the common divisor concept important in mathematics learning?","Question",{"text":112,"@type":113},"It is a foundational idea taught in secondary school that underpins many related number concepts and operations.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the study investigate concept formation for common divisor?",{"text":117,"@type":113},"It uses a case study with seven sixth-grade students, employing a Realistic Mathematics Education learning environment and collecting data through student work and semi-structured clinical interviews.",{"name":119,"@type":110,"acceptedAnswer":120},"What does the APOS framework contribute to the analysis?",{"text":121,"@type":113},"The findings are interpreted through APOS (Action, Process, Object, Schemas) to explain how students construct and internalize mathematical concepts.","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},588188,1792546972,{"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":29,"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},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","FORMATION PROCESS OF COMMON DIVISOR CONCEPT: A STUDY OF REALISTIC MATHEMATICS EDUCATION  \nRezan YILMAZ, MerveDÜNDAR  \nAbstract: Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it.  \nThe purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we designed a learning environment based on Realistic Mathematics Education and tried to determine how students construct the concept.  \nThe data collected through group and individual study papers and semi-structured clinical interviews were analyzed with content analysis within the APOS theoretical framework. The findings showed that one student was unable to internalize the action and her thoughts depended on the contextual problem. Other students internalized all common divisors and coordinated them with prime factorization. At the end, students were able to encapsulate all the processes into object by finding the product of common prime numbers. Moreover, students were able to identify greatest common divisor among all common divisors and clarified its meaning.  \nKey words: Common divisor, Greatest common divisor, Concept formation, Realistic Mathematics Education, APOS  \n1. Introduction  \nMathematics and mathematical thinking are constructed on numbers and their properties, patterns and structures, and built on a conceptual understanding of them. Therefore operations, procedures, relationships and practices on numbers cover an important part in mathematics curriculums taught in schools. Subjects of natural numbers and operations on these numbers which are started to be taught in primary school expand with the concepts of prime number, multiple, divisor, common multiple and common divisor in secondary school (MEB, 2018; NCTM, 2000) . These concepts form the basis for the formation of other number sets and the operations on these sets and also the relations of many other concepts in the following years. On the other hand, these concepts are ideal places to learn about problem solving, reasoning, generalization, abstraction and proof, and the problems to be chosen appropriately for these concepts can provide an excellent opportunity for the development and evaluation of mathematical arguments (Selden and Selden, 2002) .  \nConsidering that the concepts of multiple, divisor, common multiple and common divisor, like many other mathematical concepts, arise from real-life needs of knowledge and relations, it is thought that teaching these concepts should be realized in a more informal and real-life context (Campbell and Zazkis, 2002; Gravemeijer, 1999) . Thus, when students learn by relating with their own lives and performing their own mathematization processes, mathematics will become meaningful for them (Gravemeijer, 1994; 1999; Gravemeijer & Terwel, 2000) . However, considering that students have difficulty in understanding and relating mathematical concepts, attention to informal meanings and familiar contexts in mathematics education should not be considered separately from the development of conceptual foundations (Campbell and Zazkis, 2002) . In this sense, it is thought that Realistic Mathematics Education (RME) which is based on the environments that the student has actively reinvented the mathematical structures by using his/her own paths and the models he/she has developed, will serve this purpose (Fauzan, Slettenhaar and Plomp, 2002; Gravemeijer, 1999; van den HeuvelPanhuizen, 2000) . There are three stages mentioned in RME (Treffers; 1991b) . These are firstly the development of operations-relations in some ordinary real-life contexts, then the realizing the same structure in other contexts, and finally, the formulation of the common structure by symbolizing it. These three steps constitute generalization and abstraction (Mitchelmore, 2002) . Considering ","cbCailLTXgRzMle1","https://ap.wps.com/l/cbCailLTXgRzMle1","pdf",328354,14,"English","# Introduction\n## Real-life contexts and realistic mathematics education\n## APOS theoretical framework and abstraction","[{\"question\":\"Why is the common divisor concept important in mathematics learning?\",\"answer\":\"It is a foundational idea taught in secondary school that underpins many related number concepts and operations.\"},{\"question\":\"How does the study investigate concept formation for common divisor?\",\"answer\":\"It uses a case study with seven sixth-grade students, employing a Realistic Mathematics Education learning environment and collecting data through student work and semi-structured clinical interviews.\"},{\"question\":\"What does the APOS framework contribute to the analysis?\",\"answer\":\"The findings are interpreted through APOS (Action, Process, Object, Schemas) to explain how students construct and internalize mathematical concepts.\"}]","FORMATION PROCESS OF COMMON DIVISOR CONCEPT - A STUDY OF REALISTIC MATHEMATICS EDUCATION | PDF",1792064716,35]