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Findings showed that both high- and low-achieving students could address recognized difficulty. The study explains how Knowledge Building principles and practices supported deep understanding and wide participation, using Knowledge Forum® to enable democratization of knowledge and students’ epistemic agency through evidence, justification, and multiple solutions.",{"@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/knowledge-building-and-mathematics-shifting-the-responsibility-for-knowledge-advancement-and-engagement/598516/",{"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/knowledge-building-and-mathematics-shifting-the-responsibility-for-knowledge-advancement-and-engagement/598516.png","ImageObject",300,407,{"name":92,"@type":93},"A glass of water","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What research task did the Grade 4 students complete in early algebra?","Question",{"text":112,"@type":113},"Students collaborated to solve a series of linear and quadratic generalizing problems, including the Border Problem, to predict patterns for grids of different sizes.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How did the study structure responsibility for knowledge advancement?",{"text":117,"@type":113},"After problems were posted on Knowledge Forum, the database was entirely student-managed with no teacher voice and no external answers, so students assumed responsibility to conjecture, solve, and negotiate approaches.",{"name":119,"@type":110,"acceptedAnswer":120},"What did analysis of participation reveal about knowledge building?",{"text":121,"@type":113},"Participation and written notes reflected Knowledge Building practices, including democratization of knowledge across achievement levels and epistemic agency, with students providing evidence and justifications while generating multiple solutions.","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},598516,1792171968,{"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":44,"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":145},962090760832,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Knowledge Building and Mathematics: Shifting the Responsibility for Knowledge Advancement and Engagement  \nLa coélaboration de connaissances et les mathématiques : faire basculerla responsabilité pour l’avancement des connaissances vers l’apprenant  \nJoan Moss and Ruth Beatty  \nAuthors  \nJoan Moss, Associate Professor (CSE/DPE), University of Toronto, OISE | Ontario  \nInstitute for Studies in Education. Correspondence regarding this article can be sent to:  \n[jmoss@oise.utoronto.ca](jmoss@oise.utoronto.ca)  \nRuth Beatty, Assistant Professor, Faculty of Education, Lakehead University.  \nAbstract  \nThree classrooms of Grade 4 students from different schools and diverse backgrounds collaborated in early algebra research to solve a series of linear and quadratic generalizing problems. Results revealed that high-­‐ and low-­‐achieving students were able to solve problems of recognized difficulty. We discuss Knowledge Building principles and practices that fostered deep understanding and broad participation. Students used the online Knowledge Building environment Knowledge Forum® to conduct their work and we illustrate how Knowledge Forum supported a Knowledge Building culture for mathematical learning and problem solving. Analyses of participation patterns and note content revealed practices consistent with Knowledge Building principles, specifically democratization of knowledge, with students at all achievement levels participating, and epistemic agency, with students providing evidence and justification for conjectures and generating multiple solutions to challenging problems.  \nRésumé  \nTrois classes de quatrième année issues de diverses écoles et ayant des bagages de connaissance diversifiés ont participé à une recherche en algèbre élémentaire pour résoudre une série de problèmes linéaires et quadratiques généralisés. Les résultats ont démontré que tous les élèves, tant les moins performants que les plus performants, ont été en mesure de résoudre des problèmes complexes.  \nL’article fait état des principes et des pratiques de coélaboration de connaissances qui mènent à une compréhension approfondie et à une participation élargie des élèves. Ces derniers ont utilisé l’environnement decoélaboration de connaissances en ligne Knowledge Forum® pour effectuer leur travail. Nous illustrons de quelle façon Knowledge Forum a soutenu une culture de coélaboration de connaissances dans l’apprentissage des mathématiques et  \nla résolution de problèmes. Des analyses des modèles de participation et des contributions écrites des élèves ont révélé des pratiques cohérentes avec les principes de coélaboration de connaissances, en particulier la démocratisation de la connaissance (participation d’élèves à tous les niveaux de rendement) et l’action épistémique (élèves prouvant et justifiant leurs hypothèses et générantdes solutions multiples aux défis proposés) .  \nIntroduction  \nWe start by presenting a written discussion among Grade 4 students engaged in Knowledge Building in mathematics. The students were from different urban settings, they had never met each other, and they were collaborating online to find solutions to a series of challenging mathematics generalization problems. This work was part of an ongoing study of early algebra. A special feature of the research was that once the mathematics problems were posted on Knowledge Forum, the database was entirely student-­‐managed; there was no teacher voice in the database and no answers provided from any source external to the students. Thus, it was the students who took the responsibility to offer conjectures, find solutions, and negotiate multiple approaches for mathematics problem solving. How was this possible? This report provides an overview of Knowledge Building pedagogy and technology that allowed students to assume high levels of agency for their knowledge work.  \nThe Border Problem (see Figure 1) was one of six problems posted on Knowledge Forum. In this problem students were chall","cbCaiv6eHWQQ5pbV","https://ap.wps.com/l/cbCaiv6eHWQQ5pbV","pdf",448988,33,"English","# Introduction\n# The Border Problem\n## Online Knowledge Forum Setup\n## Two Visual Strategies for Solutions","[{\"question\":\"What research task did the Grade 4 students complete in early algebra?\",\"answer\":\"Students collaborated to solve a series of linear and quadratic generalizing problems, including the Border Problem, to predict patterns for grids of different sizes.\"},{\"question\":\"How did the study structure responsibility for knowledge advancement?\",\"answer\":\"After problems were posted on Knowledge Forum, the database was entirely student-managed with no teacher voice and no external answers, so students assumed responsibility to conjecture, solve, and negotiate approaches.\"},{\"question\":\"What did analysis of participation reveal about knowledge building?\",\"answer\":\"Participation and written notes reflected Knowledge Building practices, including democratization of knowledge across achievement levels and epistemic agency, with students providing evidence and justifications while generating multiple solutions.\"}]","Knowledge Building and Mathematics - Shifting the Responsibility for Knowledge Advancement and Engagement | PDF",1792087074,83]