Utilizing Praxeology and the cKȼ Model to Developing Didactical Design in Derivatives: An Indonesian Mathematics Textbook Study

Utilizing Praxeology and the cKȼ Model to Developing Didactical Design in Derivatives: An Indonesian Mathematics Textbook Study | 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 Utilizing Praxeology and the cKȼ Model to Developing Didactical Design in Derivatives: An Indonesian Mathematics Textbook Study Putri Haryani Syahar, Lukman Lukman, Sufyani Prabawanto This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9126888/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 Analyses of mathematics textbooks have predominantly employed praxeological approaches to examine the organization of theory and institutional relations to knowledge. However, limited attention has been given to the epistemological foundations underlying the mathematical concepts presented. This study addresses this gap by employing the cKc model to connect textbook concepts with historical interpretations. We analyzed how the concept of ‘rate of change’ was institutionalized in Calculus: Early Transcendentals (CET) and Matematika Tingkat Lanjut (MTL) to inform didactical design for upper secondary students. The findings reveal that the concept of the derivative is transformed from an algebraic to a calculus perspective. Textbooks tend to present the rate of change and the slope of the tangent line as applications of the derivative rather than as epistemological foundations of the concept itself. Consequently, students often prioritize algebraic manipulation over a conceptual understanding of change and increment, which should serve as the central focus of calculus instruction. 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-9126888","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":609957836,"identity":"9c0f8fbb-f947-4ee0-b756-bcaaadbb773f","order_by":0,"name":"Putri Haryani Syahar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYLCCxAYIfYCxgUGOgQFIMrDhU8+MqsWYOC2MUC0gBlQ7Hi3mEvnHPjzcYZdvcPzswYM/d9xL33C7uYHhQ9lhnFosZyQzz0g8k2y54UxewmHeM8W5G+4cbGCccQ63FoMbycwMiW3MBgYHcgwOM7Yl5G64kdjAzNtGUEu9gcH5NwYHf7YlpBuAtPwlrOWwgcGNHIMDvG0JCWAtjHi0WPY8NgZqOW4geeONwWGgFsOZQL8c7DmXjlOLOXviY8afbdUGfOdzjD8CHSbPd7v94YMfZda4HQZjKByAsSSAcYpTPbIW+QYkLaNgFIyCUTAKkAEAvP5htbqXYZkAAAAASUVORK5CYII=","orcid":"","institution":"Indonesia University of Education","correspondingAuthor":true,"prefix":"","firstName":"Putri","middleName":"Haryani","lastName":"Syahar","suffix":""},{"id":609957837,"identity":"57a751a4-0a55-4d3b-be3b-9a22d04be740","order_by":1,"name":"Lukman Lukman","email":"","orcid":"","institution":"Indonesia University of Education","correspondingAuthor":false,"prefix":"","firstName":"Lukman","middleName":"","lastName":"Lukman","suffix":""},{"id":609957838,"identity":"f0d01955-24ba-493d-a1c1-e6fde639f80f","order_by":2,"name":"Sufyani Prabawanto","email":"","orcid":"","institution":"Indonesia University of Education","correspondingAuthor":false,"prefix":"","firstName":"Sufyani","middleName":"","lastName":"Prabawanto","suffix":""}],"badges":[],"createdAt":"2026-03-15 07:24:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9126888/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9126888/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107480494,"identity":"d50e174c-1a5c-4c38-b06e-334bba4cfbcd","added_by":"auto","created_at":"2026-04-22 02:11:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":524427,"visible":true,"origin":"","legend":"","description":"","filename":"anindonesianmathematicstextbookstudy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9126888/v1_covered_20898104-0302-45c5-b11a-28e07bea031f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Utilizing Praxeology and the cKȼ Model to Developing Didactical Design in Derivatives: An Indonesian Mathematics Textbook Study","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":"","lastPublishedDoi":"10.21203/rs.3.rs-9126888/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9126888/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAnalyses of mathematics textbooks have predominantly employed praxeological approaches to examine the organization of theory and institutional relations to knowledge. 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