Exploring Opportunities to Learn through Classroom Observations in Korean Middle School Geometry Lessons

Exploring Opportunities to Learn through Classroom Observations in Korean Middle School Geometry Lessons | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Exploring Opportunities to Learn through Classroom Observations in Korean Middle School Geometry Lessons Sanghee Yeo, Gooyeon Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9295263/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study investigated the opportunities to learn (OTL) in middle school geometry lessons through classroom observations. Using an integrated analytical framework that considers the cognitive demands of tasks, teacher-student interactions, and classroom contexts as mutually shaping dimensions of OTL, we observed and analyzed the geometry lessons taught by four Korean middle school mathematics teachers. The analysis revealed three patterns. First, students' predominantly observed and replicated procedural steps that teacher had already worked out. Second, classroom interactions consistently converged predetermined answers, leaving students with few opportunities to reason or construct justifications. Third, students posed questions that can be extended to mathematical ideas, in which technology could have afforded opportunities for mathematical exploration, yet inquiry was not sustained throughout the lesson. These three patterns are reinforce each other: procedural tasks give rise to interactions focused on confirming predetermined answers, which prevent further development of inquiry openings. This study contributes to the research on OTL by offering an integrated framework that can be used to examine learning opportunities in different classroom contexts. The findings also show empirical evidence that opportunities for inquiry are present, they cannot be sustained due to a combination of curriculum coverage, procedural task design, and evaluation focused on confirming correct answer. Opportunities to learn (OTL) Geometry Mathematical inquiry Teacher-student interaction Middle school mathematics mathematical task Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9295263","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627968273,"identity":"9b8d2809-7da1-436d-8b8b-2c564125902d","order_by":0,"name":"Sanghee Yeo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIie3RMYvCMBTA8SeBTpGuz8EWv0FKoCh+GbN0Ks4OWgpCnY6ufgxBEMcegXPJcWvW4xZBhTo6KGbslHrbweU/vUB+kPAAXK6/mnhg4DfOpJ3U3pD38t+QztqbiU31KglXn/JEKYrtl5TH234B/qoifGYhTE2TMUXkO50kozd1AFQTIpSNQBpzyrC/0zRm3eIDQAN5zy0kLM+GTLCzLVUc3Q0J2wjolH+vKxxsIOU/3WIOzBBhI0yfY7jmyNH8hfSLikZKLCP7w1JeizwL/FLK66XIguAgZc9GTB42BknNnlqAWVzdGLK22y6Xy/UPewITXE7/WMbyzgAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Sanghee","middleName":"","lastName":"Yeo","suffix":""},{"id":627968278,"identity":"92f80117-ffd6-466f-a737-2ff97f85b2dd","order_by":1,"name":"Gooyeon Kim","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Gooyeon","middleName":"","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2026-04-01 18:39:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9295263/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9295263/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108182952,"identity":"7cb2d7d7-af54-4539-8a71-8657d927ce3d","added_by":"auto","created_at":"2026-04-30 08:59:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":659674,"visible":true,"origin":"","legend":"","description":"","filename":"ExploringOpportunitiestoLearnthroughClassroomObservationsinKoreanMiddleSchoolGeometryLessons.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9295263/v1_covered_ac8d0f9a-181e-42ba-892f-77c79f7dca7b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exploring Opportunities to Learn through Classroom Observations in Korean Middle School Geometry Lessons","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Opportunities to learn (OTL), Geometry, Mathematical inquiry, Teacher-student interaction, Middle school mathematics, mathematical task","lastPublishedDoi":"10.21203/rs.3.rs-9295263/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9295263/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigated the opportunities to learn (OTL) in middle school geometry lessons through classroom observations. 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