[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-592107-105":59,"doc-detail-592107-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","cultivating-divergent-thinking-in-mathematics-through-an-open-ended-approach-study","Cultivating Divergent Thinking in Mathematics through an - Open-Ended Approach - Study","","The study develops and evaluates a mathematics program designed to foster divergent thinking using open-ended problems. Participants included 398 seventh-grade middle school students in Seoul. Pre- and post-testing measured divergent thinking skills, focusing on fluency, flexibility, and originality. Results show the treatment group outperformed the comparison group across all components. The developed program is presented as a practical resource for teachers to strengthen students’ creative thinking and mathematical creativity through open-ended instruction.",{"@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/cultivating-divergent-thinking-in-mathematics-through-an-open-ended-approach-study/592107/",{"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/cultivating-divergent-thinking-in-mathematics-through-an-open-ended-approach-study/592107.png","ImageObject",300,407,{"name":92,"@type":93},"Grenda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","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 was the purpose of the study?","Question",{"text":112,"@type":113},"The study aimed to develop a program that cultivates divergent thinking in mathematics through open-ended problems and to investigate its effect.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How were students’ divergent thinking skills measured?",{"text":117,"@type":113},"A pre- and post-testing method was used, mainly assessing divergent thinking skills through open-ended problems.",{"name":119,"@type":110,"acceptedAnswer":120},"What were the overall results of using the open-ended program?",{"text":121,"@type":113},"The treatment group performed better than the comparison group overall on each component of divergent thinking skills, including fluency, flexibility, and originality.","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},592107,1792167038,{"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":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},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Cultivating Divergent Thinking in Mathematics through an  \nOpen-Ended Approach  \nOh Nam Kwon Jung Sook Park Jee Hyun Park  \nSeoul National University  \nKorea  \nThe purpose of this study was to develop a program to help cultivate divergent thinking in mathematics based on open-ended problems and to investigate its effect. The participants were 398 seventh grade students attending middle schools in Seoul. A method of pre- and post-testing was used to measure mainly divergent thinking skills through open-ended problems. The results indicated that the treatment group students performed better than the comparison students overall on each component of divergent thinking skills, which includes fluency, flexibility, and originality.  \nThe developed program can be a useful resource for teachers to use in enhancing their students' creative thinking skills. An open-ended approach in teaching mathematics suggested in this paper may provide a possible arena for exploring the prospects and possibilities of improving mathematical creativity.  \nKey Words : mathematical creativity, divergent thinking, open-ended approach  \nWhat is common in a lot of middle-school mathematics problems is that they are supposed to have only one solution. Pehkonen ( 1995) defined this type of problem as a closed problem. He suggested that these particular problems, which do not allow divergent thinking, are not able to enhance the quality of education, even after the introduction of new approaches such as small-group cooperative learning. If the goal of mathematics education is to realize an individual ’s potential of mathematical creativity, it is necessary to break the habit of “knowledge delivery” from the teacher to the student, which is the conventional instructor-oriented teaching method. Mathematics education should be focused on the development of creative thinking where students are free to  \nOh Nam Kwon, Jung Sook Park, and Jee Hyun Park, Department of Mathmatics Education, Seoul National University, Seoul, Korea. Support for this paper was funded by the Korea Research Foundation under grant No. KRF-2002-030-B00055 . The opinions expressed do not necessarily reflect the views of the foundation  \nCorrespondence concerning this article should be addressed to Oh Nam Kwon, Department of Mathmatics Education, Seoul National University, Gwanak-gu, Seoul, 151-742, Korea. E-mail: onkwon@ [snu.ac.kr](snu.ac.kr).  \ntry their own original possible solutions. It means avoiding the traditional teaching method that emphasizes ‘convergent thinking,’ in which a student memorizes existing mathematical rules and theorems and then applies them to problems with great adroitness in order to find one exclusive solution. Since these closed problems do not encourage students to adopt divergent thinking and reasoning, it is  \nnecessary to introduce new contexts that allow them to respond positively and participate actively in the learning process.  \nFor this reason, many new approaches have been set forth. A recently highlighted method, Realistic Mathematics Education, claims that a constructive mathematics education should provide challenging tasks and an environment in which students try to construct their own concrete and informal problem solution strategies by exploring experientially real and mathematically real context problems (Gravemeijer & Doormann, 1999) . Silver ( 1997) also tried to combine a student’s originality and problem-solving ability by giving a problem-posing assignment to them. Brown (200 1) used a “What-if-not” strategy to help students invent new ideas as possible solutions. What they have in common is  \nthat they provided challenging assignments and regarded students not as simple knowledge receivers, but as agents of knowledge creation. Therefore, what was important to them was not only the introduction of contexts that encouraged students to fully participate, but also how to lead those contexts effectively.  \nIn Japan in the 1970s, Shimada with other","cbCaicpRHF6oUAQY","https://ap.wps.com/l/cbCaicpRHF6oUAQY","pdf",448544,11,"English","# Purpose and Participants\n# Methods and Assessment\n# Results on Divergent Thinking\n# Pedagogical Rationale for Open-Ended Problems\n# Related Approaches and Definitions","[{\"question\":\"What was the purpose of the study?\",\"answer\":\"The study aimed to develop a program that cultivates divergent thinking in mathematics through open-ended problems and to investigate its effect.\"},{\"question\":\"How were students’ divergent thinking skills measured?\",\"answer\":\"A pre- and post-testing method was used, mainly assessing divergent thinking skills through open-ended problems.\"},{\"question\":\"What were the overall results of using the open-ended program?\",\"answer\":\"The treatment group performed better than the comparison group overall on each component of divergent thinking skills, including fluency, flexibility, and originality.\"}]","Cultivating Divergent Thinking in Mathematics through an - Open-Ended Approach - Study | PDF",1792073873,28]