Evaluating Interdisciplinary Mathematics Teaching Quality in Senior High Schools via Distributional Comparison and Robust Ranking

Evaluating Interdisciplinary Mathematics Teaching Quality in Senior High Schools via Distributional Comparison and Robust Ranking | 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 Article Evaluating Interdisciplinary Mathematics Teaching Quality in Senior High Schools via Distributional Comparison and Robust Ranking Gaofeng Liu, Leiqiong Li, Tianqi Luo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9098924/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Against the background of ongoing curriculum reform, evaluating interdisciplinary mathematics teaching requires methods that are scalable, robust, and sensitive to multidimensional evidence. This study proposes a distributionally robust MOS-TOPSIS framework that converts repeated classroom observations into A/B/C/D grade distributions, constructs sample-driven positive and negative ideal distributions, and measures teacher–ideal similarity through MOS overlap. To enhance ranking reliability, bootstrap resampling and Dirichlet weight perturbation are introduced to produce confidence intervals, Top-k probabilities, and rank intervals. A case study covering 13 teachers, 10 indicators, six classroom observations, and ratings from three senior experts shows a clear three-tier ranking structure. The top three teachers all obtained closeness coefficients above 0.70 and Top-3 membership probabilities of 1.00. Compared with conventional TOPSIS, the proposed method achieved perfect agreement with expert ranking (Spearman’s ρ = 1.0000; Kendall’s τ = 1.0000), while better preserving distributional information and reducing rank drift. Physical sciences/Engineering Physical sciences/Mathematics and computing Interdisciplinary mathematics teaching Teaching quality evaluation Distributional comparison MOS-TOPSIS Robust ranking Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 24 Apr, 2026 Reviewers agreed at journal 08 Apr, 2026 Reviewers invited by journal 03 Apr, 2026 Editor assigned by journal 03 Apr, 2026 Editor invited by journal 20 Mar, 2026 Submission checks completed at journal 18 Mar, 2026 First submitted to journal 18 Mar, 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. 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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-9098924","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":619736762,"identity":"7ffd89ab-5f58-499e-9e25-ac104c874086","order_by":0,"name":"Gaofeng Liu","email":"data:image/png;base64,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","orcid":"","institution":"Leshan Normal University","correspondingAuthor":true,"prefix":"","firstName":"Gaofeng","middleName":"","lastName":"Liu","suffix":""},{"id":619736763,"identity":"1851fdc9-f161-4d8c-8b54-9a86167fb3b3","order_by":1,"name":"Leiqiong Li","email":"","orcid":"","institution":"Leshan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Leiqiong","middleName":"","lastName":"Li","suffix":""},{"id":619736771,"identity":"7b51c93b-465c-4184-943e-d73d27abac79","order_by":2,"name":"Tianqi Luo","email":"","orcid":"","institution":"Leshan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Tianqi","middleName":"","lastName":"Luo","suffix":""}],"badges":[],"createdAt":"2026-03-12 01:38:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9098924/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9098924/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106519067,"identity":"b3735621-3ef5-4827-9b34-a38baf9b5e58","added_by":"auto","created_at":"2026-04-09 12:27:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2327870,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptV320260318.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9098924/v1_covered_e149f790-dd88-41ef-b8a3-e26446921043.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Evaluating Interdisciplinary Mathematics Teaching Quality in Senior High Schools via Distributional Comparison and Robust Ranking","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Interdisciplinary mathematics teaching, Teaching quality evaluation, Distributional comparison, MOS-TOPSIS, Robust ranking","lastPublishedDoi":"10.21203/rs.3.rs-9098924/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9098924/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Against the background of ongoing curriculum reform, evaluating interdisciplinary mathematics teaching requires methods that are scalable, robust, and sensitive to multidimensional evidence. 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