[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588848-105":59,"doc-detail-588848-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","proportional-reasoning-of-adult-students-in-a-second-chance-school-the-subconstructs-of-fractions","Proportional Reasoning of Adult Students in a Second Chance School - The Subconstructs of Fractions","","The study examines proportional reasoning difficulties among adult mathematics learners, focusing on how they understand fractions and related subconstructs. A mixed-methods approach assessed 30 adult students through 13 open-ended tasks and followed up with clinical interviews conducted with five participants to capture reasoning processes. The analysis used Kieren’s fraction subconstruct typology to categorize student approaches. Results show relatively good overall performance, while higher-level thinking tasks remain challenging.",{"@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/proportional-reasoning-of-adult-students-in-a-second-chance-school-the-subconstructs-of-fractions/588848/",{"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/proportional-reasoning-of-adult-students-in-a-second-chance-school-the-subconstructs-of-fractions/588848.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main focus of the study?","Question",{"text":112,"@type":113},"The study focuses on adult students’ proportional reasoning and examines how they use fractions in problems involving proportions and percentages.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How did the researchers assess proportional reasoning?",{"text":117,"@type":113},"They used a mixed methods approach: 13 open-ended tasks attempted by 30 adult students and clinical interviews with five participants to understand their thinking.",{"name":119,"@type":110,"acceptedAnswer":120},"What framework was used to categorize fraction-related thinking?",{"text":121,"@type":113},"The researchers used a typology of fraction subconstructs introduced by Kieren (1980) to categorize students’ approaches.","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},588848,1792209483,{"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":24,"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":36,"preview_page_count":4},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","Proportional Reasoning of Adult Students in a Second Chance School: The  \nSubconstructs of Fractions  \nAristoula Kontogianni  \nUniversity of Ioannina-Greece  \n\u003C[desmath@gmail.com](desmath@gmail.com)>  \nKonstantinos Tatsis  \nUniversity of Ioannina-Greece  \n\u003C[ktatsis@uoi.gr](ktatsis@uoi.gr)>  \nAbstract  \nOne of the subjects that constitute a problem for adult students of mathematics is the understanding of fractions and proportions. These notions are interrelated with proportional reasoning which was the focal point of our study. Using a mixed methods approach, we tried to assess the proportional reasoning of adult students during problem solving. We designed a task sheet with 13 open-ended tasks, each attempted by 30 adult students, and we conducted “clinical interviews” (Ginsburg, 2009) with five participants in order to acquire more data about their ways of thinking. For the task categorisation we used a typology of fraction subconstructs (Kieren, 1980) . The results indicate that the adult students’performance was relatively good despite their limited mathematical background. However, they had difficulties with the tasks that required a higher level of thinking.  \nKeywords: second chance school; proportional reasoning; rational numbers; fractions.  \nIntroduction – Rationale of the study  \nIn an era of rapid technological changes, the development of mathematical understanding in accordance with the contextual knowledge and skills for the use of mathematics in different settings is of great significance (FitzSimons, 2019) . One of the most important understandings of mathematics is proportional reasoning, since it is strongly connected with other areas of science and mathematics across all levels of compulsory education. Proportional reasoning refers to the ability to use ratios in situations involving comparison of quantities and it has been described as the foundation for the understanding of algebra and the transition from informal to formal mathematical thought (Doyle, Dias, Kennis, Czarnocha, & Baker, 2016) . Additionally, proportional reasoning “is one of the most commonly used applications of mathematics in everyday life”(Hilton, Hilton, Dole, & Goos, 2016, p. 194). Among the skills needed for proportional reasoning are multiplicative and relational thinking and an understanding of concepts such as rational numbers, fractions, decimals, multiplication, and division (Lamon, 2005) . The comprehension of rational numbers and fractions is of especial importance since these notions are connected with real world situations (Behr et al., 1983) .  \nWhile the importance of proportional reasoning is indisputable, many adults and students fail to reason proportionally (Lamon, 2007; 2012). This may have a serious impact for adults that have not completed compulsory education or lack basic mathematical knowledge, since they will not be able to operate in their daily lives. Based on the above assumptions we designed our study which aimed at the assessment of adults’ proportional reasoning in the setting of a Second Chance School in Greece, which offers education to adults over 18 years of age.  \nProportional reasoning presupposes the understanding of fractions. The teaching of fractions is a precondition of the teaching of rational numbers. Whilst there are many studies about children’s understanding of fractions and proportional reasoning (e.g. Charalambous & Pitta-Pantazi, 2007), few studies refer to adults. The objective of our study was to examine the ways adult students use fractionsin proportional reasoning problems. Our main research question was: To what extent do students understand the different subconstructs offractions? In order to address this, we examined how students deploy subconstructs of fractions in solving problems involving proportions and percentages.  \nIn the following sections, we review the research on how adults understand fractions in the context of proportional reasoning. Then we describe our methods and p","cbCain3Gz67xnGnL","https://ap.wps.com/l/cbCain3Gz67xnGnL","pdf",455294,16,"English","# Abstract\n# Introduction – Rationale of the study\n# Literature review","[{\"question\":\"What is the main focus of the study?\",\"answer\":\"The study focuses on adult students’ proportional reasoning and examines how they use fractions in problems involving proportions and percentages.\"},{\"question\":\"How did the researchers assess proportional reasoning?\",\"answer\":\"They used a mixed methods approach: 13 open-ended tasks attempted by 30 adult students and clinical interviews with five participants to understand their thinking.\"},{\"question\":\"What framework was used to categorize fraction-related thinking?\",\"answer\":\"The researchers used a typology of fraction subconstructs introduced by Kieren (1980) to categorize students’ approaches.\"}]","Proportional Reasoning of Adult Students in a Second Chance School - The Subconstructs of Fractions | PDF",1792066051]