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A Tang, Sui, and Wang (2003) framework is adapted to embed numeracy applications and modelling through five levels: Extension, Special Subject, Investigation Report, Paper Discussion, and Mini Scientific Research. The approach advances from teacher-set applications to independent project work, with case studies across engineering, construction, computing, and environmental science.",{"@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/integrating-real-world-numeracy-applications-and-modelling-into-vocational-courses/588584/",{"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/integrating-real-world-numeracy-applications-and-modelling-into-vocational-courses/588584.png","ImageObject",300,407,{"name":92,"@type":93},"Rizky","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","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},"What problem does the practitioner research target for vocational students?","Question",{"text":112,"@type":113},"Students often start vocational courses with limited school mathematics experience and low motivation. The project aims to improve numeracy and problem solving as an essential part of vocational training.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What framework is adapted in this paper, and what levels does it identify?",{"text":117,"@type":113},"The paper adapts a framework proposed by Tang, Sui, and Wang (2003). It identifies five levels for embedding numeracy applications and modelling: Extension, Special Subject, Investigation Report, Paper Discussion, and Mini Scientific Research.",{"name":119,"@type":110,"acceptedAnswer":120},"Which courses are included in the case studies?",{"text":121,"@type":113},"Case studies present incorporation of the five application levels in engineering, construction, computing, and environmental science courses.","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},588584,1792210106,{"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":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":36,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Hall,G.(2014).Integrating real-world numeracy applications and modelling into vocational courses.  \nAdults Learning Mathematics:An International Journal,9(1),53-67  \n# Integrating Real-World Numeracy Applications and Modelling intoVocational Courses\n\nGraham Hall  \nColeg Meirion-Dwyfor,Dolgellau,United Kingdom,LL402SW\u003Cgraham.hall@gllm.ac.uk>  \n## Abstract\n\nPractitioner research is in progress at a Further Education college to improve the motivation ofvocational students for numeracy and problem solving.A framework proposed by Tang,Sui,&Wang(2003)has been adapted for use in courses.Five levels are identified for embeddingnumeracy applications and modelling into vocational studies:Extension;Special Subject;Investigation Report;Paper Discussion;and Mini Scientific Research.These levels represent aprogression from applications set by the teacher,through increasing student involvement in thesolution of real world problems,to totally independent project work.Case studies are presentedof the incorporation of the five levels of application in engineering,construction,computing,and environmental science courses.In addition to student motivation,teaching staff observedthat improvements have occurred in:use of specialised mathematical vocabulary;the combineduse of numerical and algebraic methods in problem solving;and abstract reasoning,and adeeper level of understanding of the mathematics used in problem solving.A difficulty whichhas not yet been fully resolved is the reconciliation of a problem solving and project basedapproach to numeracy,and the requirement by some Examination Board numeracy syllabuses toassess specific mathematical methods.  \nKey words:numeracy,vocational education,modelling,applications,assessment  \n## Introduction\n\nThis paper describes practitioner research which is being carried out by tutors of vocationalcourses at a Further Education College in Wales.Students often begin vocational courses with apoor experience of school mathematics and lack enthusiasm to improve their mathematicalskills.However,they will need to develop numeracy and problem solving as an essential aspectof their vocational training,for example:in subjects such as engineering or construction.Theaim of the current project is to develop a framework of learning strategies which will interestand motivate students.It is hoped to develop students'numeracy skills within their vocationalareas;and to help them to gain transferrable skills in critical thinking,creativity,teamwork andcollaboration,and learning self-direction.  \nSchool mathematics in Britain,as in many other countries,is designed around a bottom-upacademic model.Pupils learn mathematical methods within distinct topic areas such as:number,algebra and geometry,then work on example applications still within these same topic areas.The intention of the developers of mathematics syllabuses seems that pupils will progress tostudy subjects at an advanced level,such as sciences,where they will be able to make good useof the mathematical techniques they have learned.Figure 1 highlights the components of thisbottom up academic model in Britain.  \ncontext  \napplications  \ntechniques  \nI'lgure 1.DuLUIII-up acaucIIIIC IaLiICIIauUS IUuC1  \nThis model can present problems for students who leave school at the age of 16 to study apractical vocational course.They may view mathematics as a series of unrelated topics,some ofwhich seem to have no relevance to their chosen profession.Algebra,in particular,is seen bymany school leavers as having very little practical everyday.  \n## Methodology\n\nStudents entering further education courses in engineering,construction,computing,andenvironmental science at post-16 age took part in questionnaire surveys.This allowed theresearchers to better appreciate and understand the attitudes and abilities in numeracy developedby the students during their school education.  \nClinical interviews(Ginsburg,1981)were then carried out with a total of 12 students chosenfrom the range of ","cbCais9qkHAWiYDA","https://ap.wps.com/l/cbCais9qkHAWiYDA","pdf",3149996,16,"English","# Abstract\n# Introduction\n# Methodology","[{\"question\":\"What problem does the practitioner research target for vocational students?\",\"answer\":\"Students often start vocational courses with limited school mathematics experience and low motivation. The project aims to improve numeracy and problem solving as an essential part of vocational training.\"},{\"question\":\"What framework is adapted in this paper, and what levels does it identify?\",\"answer\":\"The paper adapts a framework proposed by Tang, Sui, and Wang (2003). It identifies five levels for embedding numeracy applications and modelling: Extension, Special Subject, Investigation Report, Paper Discussion, and Mini Scientific Research.\"},{\"question\":\"Which courses are included in the case studies?\",\"answer\":\"Case studies present incorporation of the five application levels in engineering, construction, computing, and environmental science courses.\"}]","Integrating Real-World Numeracy Applications and Modelling intoVocational Courses | PDF",1792065540]