A Delay-Driven Dynamic Learning Model with Cognitive Transitions and Technological Influences

A Delay-Driven Dynamic Learning Model with Cognitive Transitions and Technological Influences | 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 A Delay-Driven Dynamic Learning Model with Cognitive Transitions and Technological Influences M. A. Elfouly, Reda Abouelenien, Z. F. Elghawy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7173551/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract This study presents an educational model that effectively responds to the dynamic and time-sensitive elements of contemporary education by integrating time delays, cognitive transitions, instructional support and technological influences. The model depicts learners' transitions through three distinct cognitive states: disengaged, active learning and cognitive mastery. The analysis incorporates practical educational elements, such as delayed feedback, memory decline, distraction and the complementary influence of both human teaching and AI-powered systems. To compare the efficacy of intermittent and continuous instruction methods under various distraction and support levels, five learning scenarios were examined. The results showed that the decline in teacher influence over time can be effectively addressed by revitalizing the teacher's role every 20 days, which achieves the best results in an ideal classroom environment. This underscores the importance of conducting periodic evaluations every 20 days to enhance sustainable educational impact. The ultimate mastery level rose from 0.57 to 0.76, demonstrating how well repetition spaced improves learning results. With a mastery level of 0.75, the fully autonomous learning system that was only assisted by AI demonstrated the highest levels of efficiency and stability. The model's high resilience to small adjustments increases its suitability for use in a variety of educational settings. This framework serves as a fundamental model for creating more efficient instructional designs, assisting in the formulation of educational policies and directing the development of adaptive education systems that are enabled by technology. Educational Philosophy and Theory Applied Mathematics Educational Psychology Delay Differential Equations Cognitive Learning Dynamics Instructional Modeling Educational Technology Knowledge Propagation AI-Supported Learning Mathematical Modeling in Education Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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-7173551","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":489177753,"identity":"492ee64e-ff14-4e00-a498-9b546afdb81d","order_by":0,"name":"M. A. 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