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A non-standard open problem administered as pre- and post-test materials contained four connected questions targeting the number of solutions for a given answer. Participants included 348 third-graders and 356 fifth-graders. Fluency correlated with solving success, yet the share reporting infinitely many solutions stayed similar, and limited justifications highlight the need for attentive teacher dialogue to support understanding of infinity and core calculations.",{"@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/development-of-finnish-elementary-pupils-problem-solving-skills-in-mathematics/598889/",{"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/development-of-finnish-elementary-pupils-problem-solving-skills-in-mathematics/598889.png","ImageObject",300,407,{"name":92,"@type":93},"jay","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","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 is the study’s main purpose and grade span?","Question",{"text":112,"@type":113},"The study determines how Finnish pupils’ problem-solving skills develop from the 3rd to the 5th grade.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How was the non-standard open problem structured and used?",{"text":117,"@type":113},"The open problem was used in pre- and post-test materials with four connected questions, designed to help pupils find how many solutions exist for a particular answer.",{"name":119,"@type":110,"acceptedAnswer":120},"What did the results show about infinity-related answers and justification?",{"text":121,"@type":113},"A similar proportion of 3rd and 5th graders reported infinitely many solutions, and insufficient justifications indicate the importance of teacher listening to promote understanding of infinity and basic calculations.","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},598889,1792171126,{"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":56,"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":144},3985747858866,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Development of Finnish Elementary Pupils’ ProblemSolving Skills in Mathematics  \nAnu Laine*1, Liisa Näveri2, Maija Ahtee3 and Erkki Pehkonen4  \n• The purpose of this study is to determine how Finnish pupils’ problemsolving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre-and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other. The purpose of the formulation of the problem was to help the pupils to find how many solutions for a certain answer exist. The participants in the study were 348 third-graders and 356 fifth-graders. Pupils’ fluency, i.e. ability to develop different solutions, was found to correlate with their ability to solve the problem. However, the proportions ofthe pupils (17% of the 3rd graders and 21% of the 5th graders) who answered that there were an infinite number of solutions are of the same magnitude. Thus, the pupils’ ability to solve this kind of problem does not seem to have developed from the 3rd to the 5th grade. The lack and insufficiency of pupils’ justifications reveal the importance of the teacher carefully listening to the pupils’ ideas in order to be able to promote pupils’ understanding of the concept of infinity, as well as the basic calculations.  \nKeywords: open problem, development of problem-solving skills, infinity, Finnish elementary school, mathematics  \n1 *Corresponding Author. University of Helsinki, Finland; [anu.laine@helsinki.fi](anu.laine@helsinki.fi)  \n2 University of Helsinki, Finland  \n3 University of Helsinki, Finland  \n4 University of Helsinki, Finland  \n112 development of finnish elementary pupils’ problem-solving skills in    \nRazvoj spretnosti reševanja matematičnih problemov pri finskih osnovnošolcih  \nAnu Laine*, Liisa Näveri, Maija Ahtee in Erkki Pehkonen  \n• Namen prispevka je ugotoviti, kako se med finskimi osnovnošolci razvijajo spretnosti reševanja problemov od tretjega do petega razreda. Podatki študije so bili zbrani na podlagi enega nestandardnega problemaiz pred-in potesta v okviru triletne t. i. sledilne študije na območju Helsinkov na Finskem. Problema obeh testov sta bila sestavljena iz štirih med seboj povezanih vprašanj. Oblikovana ali pripravljena sta bila tako, da sta bila učencem v pomoč pri iskanju števila mogočih rešitev na posamezen odgovor. Vključenih je bilo 348 tretješolcev in 356 petošolcev. Fluentnost učencev, tj. sposobnost razvijanja različnih rešitev, je bilapovezana z njihovo sposobnostjo, da so problem rešili. Vendar pa jedelež učencev (17 % tretješolcev in 21 % petošolcev), ki so odgovorili, da je mogočih rešitev neskončno, ostal enak. Zdi se torej, da se sposobnost učencev za reševanje tovrstnih problemov od tretjega do petega razreda ni razvila. Pomanjkanje in nepopolnosti v utemeljitvah učencevkažejo, kako pomembno je, da učitelj pozorno posluša ideje učencev, da bi nato lahko spodbujal njihovo razumevanje koncepta neskončnosti in osnovnih izračunov.  \nKljučne besede: odprti problem, razvijanje spretnosti reševanja problemov, neskončnost, finska osnovna šola, matematika  \nIntroduction  \nAlready at the elementary level in Finland, the aim of learning mathematics is also to understand mathematical structures, not merely to learn mechanical calculations. The curriculum for the Finnish comprehensive school (NBE, 2004) has problem solving as one of the formal objectives for all school subjects. Pupils should be able to make justified conclusions, explain their actions and present their solutions via concrete models, treatments, voice and written texts (NBE, 2004) . Current thinking among researchers and reformers is that mathematical discourse involving explanation, argumentation, and that the defence of mathematical ideas should be a defining feature of a quality classroom experience (Walshaw & Anthony, 2008) . Pedagogical practices that create opportunities for students to explai","cbCaiePgts6DCZ0C","https://ap.wps.com/l/cbCaiePgts6DCZ0C","pdf",147640,"English","# Introduction\n# Problem solving","[{\"question\":\"What is the study’s main purpose and grade span?\",\"answer\":\"The study determines how Finnish pupils’ problem-solving skills develop from the 3rd to the 5th grade.\"},{\"question\":\"How was the non-standard open problem structured and used?\",\"answer\":\"The open problem was used in pre- and post-test materials with four connected questions, designed to help pupils find how many solutions exist for a particular answer.\"},{\"question\":\"What did the results show about infinity-related answers and justification?\",\"answer\":\"A similar proportion of 3rd and 5th graders reported infinitely many solutions, and insufficient justifications indicate the importance of teacher listening to promote understanding of infinity and basic calculations.\"}]","Development of Finnish Elementary Pupils’ Problem-Solving Skills in Mathematics | PDF",1792087787,48]