Mathematical Modeling of Teaching and Learning: Assessing the Influence of Learner-Centric Factors Versus Fixed Parameters of Content and Resources

Mathematical Modeling of Teaching and Learning: Assessing the Influence of Learner-Centric Factors Versus Fixed Parameters of Content and Resources | 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 Systematic Review Mathematical Modeling of Teaching and Learning: Assessing the Influence of Learner-Centric Factors Versus Fixed Parameters of Content and Resources Shadrack Mwakalinga This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6860003/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 uses mathematical modeling to quantify the impact of learners' needs, motivation, and readiness on teaching effectiveness. It found that active engagement with resources and information leads to meaningful teaching. Teachers used formal assessments and had over ten years of experience. The biggest obstacles were lack of resources and class size. Students recognized their learning demands and evaluated instructional strategies as effective. The study introduced two mathematical models: a linear model and a differential model. The linear model depicts instruction as a function of needs, content, learners, and resources, while the differential model records changes over time. Key terms: Mathematical Modeling, Teaching and Learning and Learners’ needs, readiness and desire Where: Teaching effectiveness (T) is modeled as a function of learner factors (L), needs (N), and a constant factor (C) representing fixed resources and content, such that: T=C⋅L⋅NT = C \cdot L \cdot NT=C⋅L⋅N where C accounts for infrastructure and teaching materials assumed constant in the analysis. While Learning is a function of readiness, content, resources and desire (Conrad & Donaldson, 2011). Taking content and resources constant, then F (L) is proportional to readiness (R) and desire (D) F (L) = C x R x D ……………………………….ii Where C refers to the constant factors (content and resources) Then combining the teaching and learning equation i and ii: then F (T and L) = C x L x N x R x D This can be interpreted as: C (Bolded) = Factors kept constant (resources and the content) are supposed to be considered in bold, that means they should be as many times as required because of their fundamental roles they play in the process of the teaching and learning. The study has discovered that teaching and learning needs carefully attention from planning to evaluation of educational attainment as it involves complex processes through which some are taken for granted, yet without them the teaching will not be effective. For example content and resources of teaching should always be available according to the learning needs and not focusing to the learners only. Educational planners, curriculum developers and implementers should always take into consideration of reliability of the content, resources and then move to the needs of the learners before executing the teaching and learning. Mathematical Modeling Teaching and Learning and Learners’ needs readiness and desire 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. 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-6860003","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Systematic Review","associatedPublications":[],"authors":[{"id":511676031,"identity":"c224b3d7-47fe-4f76-b832-e90733ed6b6a","order_by":0,"name":"Shadrack Mwakalinga","email":"data:image/png;base64,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","orcid":"","institution":"Catholic University of Mbeya","correspondingAuthor":true,"prefix":"","firstName":"Shadrack","middleName":"","lastName":"Mwakalinga","suffix":""}],"badges":[],"createdAt":"2025-06-10 07:08:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6860003/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6860003/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103218941,"identity":"eece46a2-3a15-4843-bb16-479bba5a02c4","added_by":"auto","created_at":"2026-02-23 09:57:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":668889,"visible":true,"origin":"","legend":"","description":"","filename":"TherrevisedMathematicalmodelingofteaching.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6860003/v1_covered_98975a15-5afb-43fe-b0f0-50b92b8a02ae.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical Modeling of Teaching and Learning: Assessing the Influence of Learner-Centric Factors Versus Fixed Parameters of Content and Resources","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":"Mathematical Modeling, Teaching and Learning and Learners’ needs, readiness and desire","lastPublishedDoi":"10.21203/rs.3.rs-6860003/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6860003/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eThis study uses mathematical modeling to quantify the impact of learners' needs, motivation, and readiness on teaching effectiveness. 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While Learning is a function of readiness, content, resources and desire (Conrad \u0026amp; Donaldson, 2011). Taking content and resources constant, then F (L) is proportional to readiness (R) and desire (D) F (L) = C x R x D ……………………………….ii Where C refers to the constant factors (content and resources) Then combining the teaching and learning equation i and ii: then F (T and L) = C x L x N x R x D This can be interpreted as: C (Bolded) = Factors kept constant (resources and the content) are supposed to be considered in bold, that means they should be as many times as required because of their fundamental roles they play in the process of the teaching and learning. The study has discovered that teaching and learning needs carefully attention from planning to evaluation of educational attainment as it involves complex processes through which some are taken for granted, yet without them the teaching will not be effective. 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