From Problem Solving to Algebraic Thinking: The Power of Mathematical Modelling in Equations and Equalities

From Problem Solving to Algebraic Thinking: The Power of Mathematical Modelling in Equations and Equalities | 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 From Problem Solving to Algebraic Thinking: The Power of Mathematical Modelling in Equations and Equalities Çağla ÇAĞLAYAN SÜNNETÇİ, Hasan ÜNAL This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7964404/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 The objective of the present study is to examine the impact of a mathematical modelling approach supported by instruction on problem-solving skills, with a particular focus on the levels of algebraic thinking and mathematisation skills of middle school seventh grade students in the subject of equality and equation in mathematics. The study was conducted with a total of 60 seventh-grade students, 27 in the experimental group and 33 in the control group, in the 2024 2025 academic year. The study adopted a mixed method approach, employing a convergent parallel design. The quantitative dimension of the study incorporated a quasi-experimental design, with a pretest-posttest control group. In the qualitative dimension, document analysis was utilised. The mathematical modelling activities were designed within the framework of Blum and Leiss's (2007) modelling cycle. The findings demonstrate that the implementation of mathematical modelling activities within the experimental group in the quantitative dimension resulted in a statistically significant increase in students' algebraic thinking levels and problem solving skills (p < .05). In the qualitative dimension, it is evident that students enhanced their mathematical thinking by refining their mathematisation processes. Furthermore, it was determined that problem understanding and simplification skills had a direct impact on the mathematisation and model building processes. The findings indicate that modelling-based instruction is an effective approach in the development of algebraic thinking, problem solving and mathematisation skills, and highlight the importance of integrating mathematical modelling into curricula for the development of concept teaching, problem solving and algebraic thinking. Educational Philosophy and Theory Algebra Applied Mathematics mathematical modelling algebraic thinking level problem-solving skills mathematical modelling activity equation and equality Full Text Additional Declarations The authors declare no competing interests. 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-7964404","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":535967765,"identity":"fe1c2a88-bf77-4585-af83-fa5267564d78","order_by":0,"name":"Çağla ÇAĞLAYAN SÜNNETÇİ","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABM0lEQVRIie2PP0vDQBiHLwQuDm+99SSln+EkIEJDOvhFUgLJckJdQsFCM6WDFdf4LQJ+gZRAskRxERqy2KUu2VwKVjAJCAppcHS4Z/jxuz8P7x1CAsH/RIrqPG76VB9gxasKO+90GgU3NbM1AvWa0T8qkh+P7wOzrocVskifo93MMHwlO32/8mMpzN9ewt2EVkc3ZptCMz5ZLRPL8oFravDkyKzgbr6sHkazx7BNYYibUc+TLYw4U8Ed4kqx11ApjF62K6Q0V5/e3MKk1D4Ay8DyzM73XQp1orjnxQam/EwF/4KeBEpSdE2h6xLF/SQ1Md26Q8hsRoDjos8oHPoLuXM2m3J2PSLEeihgqs99Jd3m5V4fkMVtq4IQsDrHHjpiv3ag/XqN8lrn6LugH0UgEAgEDV+Jc2adLC6PMgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0005-7090-6451","institution":"Yıldız Technical University","correspondingAuthor":true,"prefix":"","firstName":"Çağla","middleName":"ÇAĞLAYAN","lastName":"SÜNNETÇİ","suffix":""},{"id":535967816,"identity":"389411ef-eca3-4d1c-a4fd-ba7876048634","order_by":1,"name":"Hasan ÜNAL","email":"","orcid":"","institution":"Yıldız Technical University","correspondingAuthor":false,"prefix":"","firstName":"Hasan","middleName":"","lastName":"ÜNAL","suffix":""}],"badges":[],"createdAt":"2025-10-28 08:39:10","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7964404/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7964404/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94640856,"identity":"7df3c6f4-2e06-4e84-ab9e-9247b17c538a","added_by":"auto","created_at":"2025-10-29 07:50:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":719488,"visible":true,"origin":"","legend":"","description":"","filename":"CaglayanSunnetciModellingAlgebraIJSMESubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7964404/v1_covered_486f4ea3-2cd4-4c44-8934-b16297f4955a.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eFrom Problem Solving to Algebraic Thinking: The Power of Mathematical Modelling in Equations and Equalities\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"YILDIZ TECHNICAL UNIVERSITY","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 modelling, algebraic thinking level, problem-solving skills, mathematical modelling activity, equation and equality ","lastPublishedDoi":"10.21203/rs.3.rs-7964404/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7964404/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe objective of the present study is to examine the impact of a mathematical modelling \u0026nbsp;approach supported by instruction on problem-solving skills, with a particular focus on the levels \u0026nbsp;of algebraic thinking and mathematisation skills of middle school seventh grade students in the \u0026nbsp;subject of equality and equation in mathematics. The study was conducted with a total of 60 \u0026nbsp;seventh-grade students, 27 in the experimental group and 33 in the control group, in the 2024 2025 academic year. The study adopted a mixed method approach, employing a convergent \u0026nbsp;parallel design. The quantitative dimension of the study incorporated a quasi-experimental \u0026nbsp;design, with a pretest-posttest control group. In the qualitative dimension, document analysis was \u0026nbsp;utilised. The mathematical modelling activities were designed within the framework of Blum and \u0026nbsp;Leiss's (2007) modelling cycle. The findings demonstrate that the implementation of \u0026nbsp;mathematical modelling activities within the experimental group in the quantitative dimension \u0026nbsp;resulted in a statistically significant increase in students' algebraic thinking levels and problem solving skills (p \u0026lt; .05). In the qualitative dimension, it is evident that students enhanced their \u0026nbsp;mathematical thinking by refining their mathematisation processes. Furthermore, it was \u0026nbsp;determined that problem understanding and simplification skills had a direct impact on the \u0026nbsp;mathematisation and model building processes. The findings indicate that modelling-based \u0026nbsp;instruction is an effective approach in the development of algebraic thinking, problem solving \u0026nbsp;and mathematisation skills, and highlight the importance of integrating mathematical modelling \u0026nbsp;into curricula for the development of concept teaching, problem solving and algebraic thinking.\u003c/p\u003e","manuscriptTitle":"From Problem Solving to Algebraic Thinking: The Power of Mathematical Modelling in Equations and Equalities","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-29 04:54:14","doi":"10.21203/rs.3.rs-7964404/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"6bea1f3c-4733-4bdb-9f44-40fed201429e","owner":[],"postedDate":"October 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":56983556,"name":"Educational Philosophy and Theory"},{"id":56983557,"name":"Algebra"},{"id":56983558,"name":"Applied Mathematics"}],"tags":[],"updatedAt":"2025-10-29T04:54:14+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-29 04:54:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7964404","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7964404","identity":"rs-7964404","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}