[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-585956-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-585956-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","coordination-of-geometry-representations-in-a-textbook","COORDINATION OF GEOMETRY REPRESENTATIONS IN A TEXTBOOK","","The study investigates how common representations in a high school geometry textbook are coordinated, using semiotics and a pragmatic approach combined with descriptive statistics. Analysis targets the mechanisms that support frequent coordination patterns, identifying which representations are linked most often, comparable to written language. Findings show coordination mechanisms that may involve numbers, point names, and textbook gestures such as color, arrows, and font changes, to narrow focus onto the most prevalent representational coordinations.",{"@graph":14,"@context":72},[15,34,55],{"@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 & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/coordination-of-geometry-representations-in-a-textbook/585956/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/coordination-of-geometry-representations-in-a-textbook/585956.png","ImageObject",300,407,{"name":42,"@type":43},"Jordan Avery","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-09","2026-10-15",true,{"@type":52,"interactionType":53,"userInteractionCount":26},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What is the main goal of the study on geometry representations?","Question",{"text":62,"@type":63},"The study aims to identify how representations are presented and coordinated in a high school geometry textbook by analyzing mechanisms that support the most common coordinations.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Which analytical frameworks guide the study?",{"text":67,"@type":63},"The analysis combines semiotics tools for examining signs and representations with cognitive load theory as the learning theory guiding how geometry signs are learned.",{"name":69,"@type":60,"acceptedAnswer":70},"What are the key findings about representation coordination?",{"text":71,"@type":63},"The study exposes which representations are coordinated most often, and it highlights mechanisms using numbers, point names, and textbook gestures such as color, arrows, and font changes.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},585956,1792056436,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":26,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":115,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":143,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","COORDINATION OF GEOMETRY REPRESENTATIONS IN A TEXTBOOK  \nWaldemar Stepnowski  \nTemple University  \n[wstepnowski@temple.edu](wstepnowski@temple.edu)  \nThe study describes how the common representations are coordinated. I analyzed a popular geometry textbook using semiotics and a pragmatic approach to capture the variety of representations into categories and to use descriptive statistics to narrow the focus to the most common representations and coordinations. The major findings are: (1) exposing which representations are most often coordinated like written language; (2) some of the mechanisms in coordination use numbers, point names, and textbook gestures, which include color, arrows, font changes, etc.  \nKeywords: Geometry and Spatial Reasoning, High School Education  \nIntroduction  \nSome representations are ideal in certain situations, while some are not. Teachers, students, and seasoned mathematicians must make choices in how they represent a mathematical object so that it helps them attain their goal. To be able to make choices in the use of geometry representations, teachers, students, and mathematicians need to know which representations are available and how to use them. That is precisely the goal of my research, i.e., to identify how they are presented and coordinated in a high school geometry textbook, Larson and Boswell’s (2015) Geometry: A Common Core Curriculum. I do that by analyzing the mechanisms that aid in the most common coordinations.  \nBesides the above, there are a few more reasons why studying representations is valuable. First, we all want students to solve problems with a high degree of accuracy and efficiency, and representations help us manage mathematical information. Students who coordinate different mathematical representations well solve mathematical problem better than those who do not (Gagatsis & Shiakalli, 2004) . Second, there is a difference between changing within one representation and changing or coordinating between different representations. While students have difficulty changing representations (conversion), they have less difficulty in manipulating (treatment) a given representation (Duval, 2006). Therefore, studying which representations appear to be coordinated most often and what are some ways that they are coordinated may help geometry teachers, publishers, and researchers devise strategies that aid students with those conversions. Third, to solve problems students need to use aids or tools like representations to reduce the complexity of a problem. We use representations as a kind of external memory, where we can offload some of the information from our working memory (Scaife & Rogers, 1996) . Chandler and Sweller’s (1991) seminal work on cognitive load theory shows via experiments that integrated diagrams with text, in contrast to a diagram with text below it, reduced the cognitive load, and reducing cognitive load improves learning. Fourth, we are beginning to develop digital textbooks, online environments, etc., where the choice of representations is important (Presmeg etal., 2016) .  \nFramework  \nI take the formalist tradition as to the ontology of what mathematics is, and the pragmatist tradition as to the epistemology of this study. Cognitive Load theory was the learning theory that guided how I analyzed how the signs of geometry could be learned. According to cognitive load  \nLamberg, T., & Moss, D. (2023). Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2). University of Nevada, Reno.  \n698  \nArticles published in the Proceedings are copyrighted by the authors.  \ntheory, students make use of all three components of working memory, namely central executive, visual-spatial sketchpad and an auditory loop (Sweller, Ayres, & Kalyga, 2011) . Our working memory is limited to a sentence, maybe two, an equation or two, a small diagram, a few ordered pairs, etc. As we will see i","cbCaiatagVyyll0i","https://ap.wps.com/l/cbCaiatagVyyll0i","pdf",393048,"English","# Introduction\n# Framework\n# Methods","[{\"question\":\"What is the main goal of the study on geometry representations?\",\"answer\":\"The study aims to identify how representations are presented and coordinated in a high school geometry textbook by analyzing mechanisms that support the most common coordinations.\"},{\"question\":\"Which analytical frameworks guide the study?\",\"answer\":\"The analysis combines semiotics tools for examining signs and representations with cognitive load theory as the learning theory guiding how geometry signs are learned.\"},{\"question\":\"What are the key findings about representation coordination?\",\"answer\":\"The study exposes which representations are coordinated most often, and it highlights mechanisms using numbers, point names, and textbook gestures such as color, arrows, and font changes.\"}]","COORDINATION OF GEOMETRY REPRESENTATIONS IN A TEXTBOOK | PDF",23]