[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588715-105":59,"doc-detail-588715-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","creativity-and-technology-in-mathematics-from-story-telling-to-algorithmic-with-opart","CREATIVITY AND TECHNOLOGY IN MATHEMATICS - FROM STORY TELLING TO ALGORITHMIC WITH OP'ART","","This article presents results from the European mcSquared project on using Op'Art and optical-illusion pieces to foster modeling and creative mathematical thinking in students. It outlines the c-book technology, describing how narrative and programming can support geometry understanding from early storytelling to algorithmic generative art. Op'Art is framed as a resource that objectifies creative choices by identifying variables, describing their relationships, and exploring configuration spaces, enabling the question “what if…” through controlled creation and reproducible descriptions.",{"@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/creativity-and-technology-in-mathematics-from-story-telling-to-algorithmic-with-opart/588715/",{"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/creativity-and-technology-in-mathematics-from-story-telling-to-algorithmic-with-opart/588715.png","ImageObject",300,407,{"name":92,"@type":93},"Rizky","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-09","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does the article connect Op’Art to creative mathematical thinking?","Question",{"text":112,"@type":113},"It argues that Op’Art and optical illusions can model geometric ideas, using narratives and algorithms so learners explore variables, relationships, and configurations in a controlled way.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the role of the c-book technology mentioned in the article?",{"text":117,"@type":113},"The c-book technology is described as an infrastructure that blends hyper-text, images, and widgets into a single interactive narrative where students can create and share mathematical-art productions.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the approach aim to improve geometry learning in curricula?",{"text":121,"@type":113},"The article discusses a transition from perceptive to axiomatic geometry and proposes narration plus programming as a pathway to help learners describe figures so others can reproduce similar constructions.","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},588715,1792065798,{"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":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":46,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","CREATIVITY AND TECHNOLOGY IN MATHEMATICS: FROM STORY TELLING TO ALGORITHMIC WITH OP'ART  \nChristian Mercat, Pedro Lealdino Filho, Mohamed El-Demerdash  \nAbstract: This article describes some of the results of the European project mcSquared ([http://mc2-project.eu/](http://mc2-project.eu/)) regarding the use of Op'Art and optical illusion pieces as a tool to foster modeling and creative mathematical thinking in students. We present briefly the c-book technology and some results we got experimenting it. The Op'Art movement, with artists such as Victor Vasarely, Julio Le Parc or Bridget Riley, uses algorithms to create geometric patterns. It is agoldmine for mathematical thinking, from early ages, with the use of narratives to describe the paintings and produce new ones in a controlled way, up to higher education with generative art produced by the implementation of algorithm. The outcome is that technology, far from hindering the creative process actually can be used to help putting it on firm grounds, narrowing the diverging phase into a converging one by giving means to objectify the description and creation of the artwork itself and making explicit the choices made, allowing for the creative exploration of new original ways: “what if…”. This objectivation is done differently by different audiences but comprises the same phases of identifying the relevant variables (disks, squares, colors, position), describing their relationships (the color of the disks depends on their position in such a way) and exploring the space of configurations the modeling gives rise to.  \nKeywords: Mathematics Education, Creativity, Creative Mathematical Thinking, Digital Resources, Technology Enhanced Learning, Op Art  \n1. Introduction  \nIf mathematics is the queen of science, geometry is the queen of mathematics. Unfortunately, this paramount subject has not been well treated in recent curricula reforms in Europe. However, the appearance of algorithmic and programming therein allow for practical rather than theoretical geometry. A great divide between geometry approaches in primary and secondary schools is the change from a perceptive to an axiomatic geometry, from touched and seen objects to relations between concepts. In primary school mathematics, using the ruler is enough to prove that three points are aligned. This article describes an attempt at finding a pathway to ease this process through narration, from early personal and subjective storytelling to programming, and relates how Art and Technology come as perfect tools for this objective. Understanding the need for axiomatization can be fostered by description of figures with the explicit goal that someone else can, out of this description, reproduce a similar one. Optical Illusions are very interesting in that respect because what is seen isnot exactly what is actually drawn. For example lines are parallel while they don’t look so in Figure. 1. As a construction protocol, it makes explicit the difference between a figure and a drawing (Parzysz, Duval, Laborde-Capponi), paving the way for an axiomatic approach to geometry. In this article we focus our attention to simple series and sequences, not individual elaborate drawings: the complexity does not rely on many degrees of freedom but on an algorithm. Therefore the complexity can be reduced, the underlying scheme can be described, the figure wants to tell you a story, something begs to be understood, and the user knows when he has understood it.  \nFigure 1. The Railway Illusion. Notice the two dots allowing for exploration: Unlike a static reproduction, the distance between segments, their length and orientation can be modified and the configuration space explored.  \nDeconstruction of complex figures has been used to study many aspects of cognition such as perception and memory (Rey, 1941, Osterrieth 1944), stereotype threat between girls and boys (Huguet-Régner, 2007) visualization and perception (Duval, 2005), geometric paradigms (Houdem","cbCaifHGFlBob272","https://ap.wps.com/l/cbCaifHGFlBob272","pdf",1341912,"English","# Introduction\n## The Op’Art Movement","[{\"question\":\"How does the article connect Op’Art to creative mathematical thinking?\",\"answer\":\"It argues that Op’Art and optical illusions can model geometric ideas, using narratives and algorithms so learners explore variables, relationships, and configurations in a controlled way.\"},{\"question\":\"What is the role of the c-book technology mentioned in the article?\",\"answer\":\"The c-book technology is described as an infrastructure that blends hyper-text, images, and widgets into a single interactive narrative where students can create and share mathematical-art productions.\"},{\"question\":\"How does the approach aim to improve geometry learning in curricula?\",\"answer\":\"The article discusses a transition from perceptive to axiomatic geometry and proposes narration plus programming as a pathway to help learners describe figures so others can reproduce similar constructions.\"}]","CREATIVITY AND TECHNOLOGY IN MATHEMATICS - FROM STORY TELLING TO ALGORITHMIC WITH OP'ART | PDF"]