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The author discusses skepticism toward brain-based approaches, then describes classroom and small-group experience using a selected problem originally used in a closed form. The article explains theoretical ideas about open problems, open-ended goals, and how problem structure affects solution paths, supported by reflections on teaching style and students’ activity.",{"@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/teaching-mathematical-problem-solving-with-the-brain-in-mind-how-can-opening-a-closed-problem-help/598878/",{"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/teaching-mathematical-problem-solving-with-the-brain-in-mind-how-can-opening-a-closed-problem-help/598878.png","ImageObject",300,407,{"name":92,"@type":93},"jay","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What question does the article address about brain-based mathematics teaching?","Question",{"text":112,"@type":113},"It investigates whether opening a closed mathematical problem can help more students solve it individually or with limited assistance.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the article define an “open problem”?",{"text":117,"@type":113},"An open problem is one where at least one of the initial state, transformation steps, or goal state is not exactly determined.",{"name":119,"@type":110,"acceptedAnswer":120},"What theoretical perspectives on mathematics does the author present for teachers?",{"text":121,"@type":113},"The author outlines Platonist, Formalist, and Intuitionist perspectives, explaining how each views mathematics and its relationship to reality and the mind.","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},598878,1792171583,{"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":39,"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},3985747858866,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Teaching Mathematical Problem-Solving with the Brainin Mind: How can opening a closed problem help?  \nAndrás Ambrus1  \n• In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. Fora long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have attempted to implement some ideas in my teaching. In this article, I will report on my experience with a selected mathematical problem in mathematics lessons and group study sessions; I will demonstrate how I modified the problem, based on my experience with the students, and I will reflect on my studies of brain-based mathematics teaching and learning.  \nKeywords: problem solving, brain based learning, working memory, open problems, representations, students’ activity  \n1 Eötvös Lóránd University Budapest, Hungary; [ambrus@cs.elte.hu](ambrus@cs.elte.hu)  \nUčenje reševanja matematičnih problemov zupoštevanjem možganov: kako lahko pomaga odpiranje zaprtega problema?  \nAndrás Ambrus  \n• V mednarodni literaturi narašča število objavljenih člankov in knjig opoučevanju in učenju, ki upoštevata delovanje možganov. Dolgo časa sem bil skeptičen do tega vprašanja. Vendar pa sem ob opažanju veliko nerešenih težav pri poučevanju in učenju matematike počasi začelanalizirati relevantno literaturo in skušal vpeljati nekaj idej v svojepoučevanje. V prispevku bom predstavil svoje izkušnje z izbranim matematičnim problemom pri urah matematike in skupinskih študijskihsrečanjih. Pokazal bom, kako sem na podlagi svojih izkušenj s študenti problem modificiral, reflektiral pa bom tudi svoj študij poučevanja inučenja matematike ob upoštevanju delovanja možganov.  \nKljučne besede: reševanje problemov, učenje na podlagi možganov, delovni spomin, odprti problemi, prikazi, aktivnost učencev  \nIntroduction  \nFor a long time in the Hungarian teaching practices of mathematics, the scientific aspect of mathematics dominated, while the psychological, pedagogical, social, biological aspects were mostly neglected. It is not surprising that in Hungarian mathematics curricula and in the mathematics textbooks (including in lower grades) there is a chapter with the title ‘Sets. Logic’, which cannot be found in other European and American curricula and mathematics textbooks. In short, in Hungarian mathematics teaching, the symbolic, abstract and verbal aspects are dominant.  \nRegarding mathematical problems and tasks, the so-called closed problems are predominantly used. I can characterise our mathematics teaching by quoting the opinion of Laurinda Brown, who, after numerous visits to Hungarian secondary schools, summarised her experiences in the following way: ‘You in Hungary are teaching mathematics; we in England children’.  \nAnother main characteristic of Hungarian mathematics teaching is the fostering of talented pupils, which is in the centre of mathematics teaching. Hungary is a small country from which many world famous mathematicians come. The idea is that such a small country must honour its talent, because they can contribute in a great manner to the development of our country. A direct consequence of focusing mainly on fostering talented students is that 90% of the students suffer from this situation. Teaching not only the rather talented but also average students, I slowly started to seek some possibilities to help the average pupils. Many books and articles have been published recently on the topic of learning with a specific focus on how the brain works, which can be also applied for mathematics education. Based on my studies, I started to change my mathematics teaching style.  \nIn this article, I will report about my experience with a selected problem, which was formulated and used in Hungarian mathematics teaching in a closed form. However, seeing the immense difficulties my students had, I op","cbCaitz0fZmdytYr","https://ap.wps.com/l/cbCaitz0fZmdytYr","pdf",139759,16,"English","# Introduction\n# Some theoretical considerations\n## Open problem and open-ended problem\n# How can the teacher think about mathematics?\n## Platonist perspective\n## Formalist perspective\n## Intuitionist perspective","[{\"question\":\"What question does the article address about brain-based mathematics teaching?\",\"answer\":\"It investigates whether opening a closed mathematical problem can help more students solve it individually or with limited assistance.\"},{\"question\":\"How does the article define an “open problem”?\",\"answer\":\"An open problem is one where at least one of the initial state, transformation steps, or goal state is not exactly determined.\"},{\"question\":\"What theoretical perspectives on mathematics does the author present for teachers?\",\"answer\":\"The author outlines Platonist, Formalist, and Intuitionist perspectives, explaining how each views mathematics and its relationship to reality and the mind.\"}]","Teaching Mathematical Problem-Solving with the Brain in Mind - How can opening a closed problem help? | PDF",1792087766]