[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588564-105":59,"doc-detail-588564-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","visual-representations-in-mathematics-teaching-an-experiment-with-students","VISUAL REPRESENTATIONS IN MATHEMATICS TEACHING - AN EXPERIMENT WITH STUDENTS","","General problem-solving skills are central to school mathematics achievement, and word problems support learning and understanding in mathematics as well as general education. The paper argues that assigning new word problems forces students to determine solution steps and algorithms. Prior research in mathematics didactics highlights the essential role of visual representations in word-problem solving and improved mathematical reasoning. An experiment with university students compares paper-and-pencil work with model-based solving.",{"@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/visual-representations-in-mathematics-teaching-an-experiment-with-students/588564/",{"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/visual-representations-in-mathematics-teaching-an-experiment-with-students/588564.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":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why are word problems important in mathematics education?","Question",{"text":112,"@type":113},"Word problems strengthen mathematical learning by requiring students to build understanding and solution steps, and they support comprehension, text interpretation, and related skills in the mathematical competence model.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What was the purpose of the experiment described in the paper?",{"text":117,"@type":113},"The study examined whether problem solving is more efficient using the traditional paper-and-pencil method or using a model, with university students divided into three experimental groups.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the paper connect visual representations with problem-solving outcomes?",{"text":121,"@type":113},"Visual representations help students understand problems, improve special mathematical reasoning, and play an essential role in word-problem solving according to didactics research cited by the paper.","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},588564,1792959950,{"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":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":143,"read_time":46,"preview_page_count":4},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","VISUAL REPRESENTATIONS IN MATHEMATICS TEACHING: AN EXPERIMENT WITH STUDENTS  \nEdith Debrenti  \nAbstract: General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In order to efficiently enhance students’ problem solving skills they should be assigned world problems which are new to them and to which they themselves have to find the steps to the solution, the algorithm. A number of researches, experiments and scientific papers in the didactics of mathematics prove that the role of visual representations in word problem solving is essential.  \nVisual representation often helps in understanding a problem. Using visual representations  \nleads to a better understanding and to improving special mathematical reasoning. The present paper presents an experiment involving university students who have been asked to solve a logical problem. There were three experimental groups. The aim was to find out whether problem solving is more efficient when using the traditional method (working on paper, with pencil) or when using a model.  \nKey words: mathematical competence, problem-solving skills, word problems, comprehension, representations, mathematical model.  \n1. Introduction  \nMathematical competence encompasses the development and use of skills and abilities related to mathematical reasoning. The OECD PISA mentions the following eight components of mathematical competence. [15]  \n1. reasoning, making deductions  \n2. argument and elaborating a proof  \n3. communication  \n4. modelling  \n5. finding solutions  \n6. representation  \n7. using symbolic, formal and technical language and operations  \n8. using mathematical tools  \nThe mathematical competence model based on factor and content analysis contains a detailed list of abilities and skills of mathematical competence [2], see Table 1 for details.  \nTable 1. Mathematical competence model [2, 6]  \n\n| Skills | counting, calculation, quantitative reasoning, estimation, measuring, measurement conversion, word problem solving |\n| --- | --- |\n| Reasoning skills | systematization, combinatorial reasoning, deductive and inductive reasoning, calculating probabilities, argumentation |\n| Communication skills | relation terminology, comprehension, text interpretation, spatial visualization, visual-spatial representation, presentation |\n| Acquisition skills | problem receptivity, problem representation, originality, creativity, problem solving, metacognition |\n| Learning skills | concentration, part-whole awareness, memorization, problem solving speed |\n\nWord problem solving as well as comprehension and text interpretation are present among the skills in the mathematical competence model. Problem solving is one of the acquisition skills.  \nRepresentation and presentation are also components of mathematical competence belonging to acquisition and communication skills respectively.  \nThe Mathematics Programmes of Study effective in Romania does not present the objectives for word problem solving for school grades 1 to 8. There are no details concerning the steps or levels attaching them to grades or age groups.  \nThe performance standards for the end of elementary education state as an objective “using arithmetic reasoning in solving word problems” as well as “solving problems that require three operations at most.” [14]  \nAs concerns secondary school only the 5th grade curriculum contains as an objective “solving word problems with the help of equations and inequalities ” When it comes to higher grades solving word problems is mentioned only in a general context, e.g. “solving practical problems using operations with real numbers.” [14]  \nOne can raise the question what about the different types of word problems which can","cbCaioaZw1m4qSRk","https://ap.wps.com/l/cbCaioaZw1m4qSRk","pdf",350275,"English","# Introduction\n# Reading, word problems, representations","[{\"question\":\"Why are word problems important in mathematics education?\",\"answer\":\"Word problems strengthen mathematical learning by requiring students to build understanding and solution steps, and they support comprehension, text interpretation, and related skills in the mathematical competence model.\"},{\"question\":\"What was the purpose of the experiment described in the paper?\",\"answer\":\"The study examined whether problem solving is more efficient using the traditional paper-and-pencil method or using a model, with university students divided into three experimental groups.\"},{\"question\":\"How does the paper connect visual representations with problem-solving outcomes?\",\"answer\":\"Visual representations help students understand problems, improve special mathematical reasoning, and play an essential role in word-problem solving according to didactics research cited by the paper.\"}]","VISUAL REPRESENTATIONS IN MATHEMATICS TEACHING - AN EXPERIMENT WITH STUDENTS | PDF",1792065502]