An Interactive Pedagogical Framework for the Axiomatic Construction of Natural Numbers in High Achieving Groups

An Interactive Pedagogical Framework for the Axiomatic Construction of Natural Numbers in High Achieving Groups | 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 An Interactive Pedagogical Framework for the Axiomatic Construction of Natural Numbers in High Achieving Groups Asif Nabiyev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9455774/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 3 You are reading this latest preprint version Abstract Traditional pedagogical approaches in university-level mathematics often struggle to maintain student engagement during highly abstract topics. This paper presents an interactive methodology implemented within the "SABAH" excellence groups—a strategic initiative by the Ministry of Science and Education of the Republic of Azerbaijan. The curriculum for "Numerical Systems" was restructured into student-led research modules focusing on Peano axioms. By leveraging the competitive and high-potential nature of the SABAH initiative, we transformed abstract number theory into a collaborative research project. This study details the implementation of the "Four-Group Research Model," the multi-dimensional assessment matrix, and the qualitative outcomes of the project. Findings suggest that shifting the epistemological responsibility from the instructor to the students significantly enhances engagement and retention in abstract mathematical logic. Peano axioms Axiomatic construction Active learning SABAH groups Mathematics education Inquiry-based learning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 29 Apr, 2026 Submission checks completed at journal 27 Apr, 2026 First submitted to journal 27 Apr, 2026 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9455774","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":630436523,"identity":"1a193cf9-5d0a-4b31-9f7a-51a8e61db9bc","order_by":0,"name":"Asif Nabiyev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYHACNoYEIMkvAeYwk6BFcgZJWkDA4AaxWvhnNz978LDNJnHz7eZjEgwV1okN7Mcf4NUiceeYuUFiW1ritjvH0iQYzqQnNvAkJOC35kaCmURi22Fjsxs5ZhKMbYcTGxgSDuDVIX8j/RtQy39j4xn53yQY/wG18D9swKvFAGR4YtsBOQOJHDYJxgagFolk/O4yvJFTbpBwLlkO6Clji4Rj6cZtEs/wa5G7kb7t4Y8yOx5g0D288aHGWrafP/0Bfj0gwMgGZSQwwKKJIPhDnLJRMApGwSgYoQAAXUVHkNW+kGsAAAAASUVORK5CYII=","orcid":"","institution":"Baku Engineering University","correspondingAuthor":true,"prefix":"","firstName":"Asif","middleName":"","lastName":"Nabiyev","suffix":""}],"badges":[],"createdAt":"2026-04-18 09:39:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9455774/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9455774/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108068363,"identity":"654406b5-e627-4637-82c4-cb08c8125754","added_by":"auto","created_at":"2026-04-29 05:16:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":612992,"visible":true,"origin":"","legend":"","description":"","filename":"Sabah2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9455774/v1_covered_deff7842-aa13-4a1a-b606-7984ab225761.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Interactive Pedagogical Framework for the Axiomatic Construction of Natural Numbers in High Achieving Groups","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"discover-education","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"diedu","sideBox":"Learn more about [Discover Education](https://www.springer.com/journal/44217)","snPcode":"44217","submissionUrl":"https://submission.nature.com/new-submission/44217/3","title":"Discover Education","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Peano axioms, Axiomatic construction, Active learning, SABAH groups, Mathematics education, Inquiry-based learning","lastPublishedDoi":"10.21203/rs.3.rs-9455774/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9455774/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTraditional pedagogical approaches in university-level mathematics often struggle to maintain student engagement during highly abstract topics. 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