Date of Publication
6-2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Science Education Major in Mathematics
Subject Categories
Science and Mathematics Education
College
Br. Andrew Gonzalez FSC College of Education
Department/Unit
Science Education
Thesis Advisor
Lydia S. Roleda
Defense Panel Chair
Maricar S. Prudente
Defense Panel Member
Voltaire Mallari Mistades
Minie Rose C. Lapinid
Socorro E. Aguja
Antriman V. Orleans
Abstract (English)
Persistent difficulties in mathematical proof construction continue to challenge students in higher education, particularly in flexible and technology-enhanced learning environments. Although Inquiry-Based Learning (IBL) and Artificial Intelligence (AI) have independently shown promise in supporting mathematical reasoning, there remains a lack of validated instructional frameworks that intentionally integrate these approaches for proof learning. To address this gap, this study developed, validated, and implemented the AI-FlexIBL (AI-Supported Flexible Inquiry-Based Learning) Framework for teaching mathematical proof in Flexible Technology-Enhanced Learning (FlexTEL) environments.The study employed a three-cycle action research design guided by the Plan–Do–Study–Act (PDSA) model. Cycle 1 involved a scoping review that informed the initial design of the framework. Cycle 2 focused on expert validation, examining clarity, coherence, and pedagogical relevance, and guiding iterative refinements toward the finalized framework. Cycle 3 entailed classroom implementation and evaluation. Participants were fourth-year Bachelor of Secondary Education major in Mathematics students enrolled in a Methods of Proof course. Data were collected through formative and summative assessments, analytic rubrics, student reflection journals, and teacher observation records. A convergent parallel mixed-methods design was used to analyze quantitative and qualitative data. Findings revealed that the AI-FlexIBL Framework produced substantive improvements in students’ proof reasoning across four interrelated dimensions: cognitive development, proof-writing proficiency, engagement and participation, and conceptual understanding. Structured and regulated AI integration strengthened logical organization, metacognitive monitoring, and reflective validation processes, while inquiry-based tasks deepened conceptual grounding and collaborative reasoning. Lastly, the findings affirm that the deliberate integration of AI within inquiry-based pedagogy meaningfully advances mathematical proof instruction. Rather than diminishing autonomy, AI functioned as a cognitive scaffold that amplified students’ independent reasoning and analytical precision. The AI-FlexIBL Framework therefore offers a validated and scalable instructional framework capable of addressing persistent challenges in proof education within flexible learning environments.
Keywords: Mathematical Proof, Inquiry-Based Learning, Artificial Intelligence in Education, Flexible Learning, Proof Reasoning, AI-FlexIBL Framework
Abstract Format
html
Abstract (Filipino)
Ang patuloy na kahirapan sa pagbuo ng matematikal na patunay ay nananatiling hamon sa mga mag-aaral sa mataas na edukasyon, lalo na sa mga flexible at teknolohiya-pinagyamang kapaligiran ng pagkatuto. Bagaman ang Inquiry-Based Learning (IBL) at Artificial Intelligence (AI) ay kapwa nagpakita ng potensyal sa pagsuporta sa matematikal na pangangatwiran, nananatili ang kakulangan ng mga napatunayang balangkas na instruksyonal na sadyang nag-iintegrate ng mga pamamaraang ito para sa pagkatuto ng patunay. Upang tugunan ang puwang na ito, binuo, pinagtibay, at ipinatupad sa pag-aaral na ito ang AI-FlexIBL (AI-Supported Flexible Inquiry-Based Learning) Framework para sa pagtuturo ng matematikal na patunay sa mga Flexible Technology-Enhanced Learning (FlexTEL) na kapaligiran. Gumamit ang pag-aaral ng tatlong siklong disenyo ng action research na ginabayan ng Plan–Do–Study–Act (PDSA) na modelo. Ang Cycle 1 ay nagsagawa ng scoping review na nagsilbing batayan sa paunang disenyo ng balangkas. Ang Cycle 2 ay nakatuon sa beripikasyon ng mga eksperto, na sumuri sa kalinawan, kohirensiya, at kahalagahang pedagogikal, at gumabay sa paulit-ulit na pagpapahusay tungo sa pinal na balangkas. Ang Cycle 3 ay nagsangkot ng implementasyon at ebalwasyon sa loob ng silid-aralan. Ang mga kalahok ay mga mag-aaral sa ikaapat na taon ng kursong Bachelor of Secondary Education major in Mathematics na naka-enrol sa asignaturang Methods of Proof. Nakalap ang datos sa pamamagitan ng formative at summative assessments, analytic rubrics, mga replektibong journal ng mag-aaral, at mga tala ng obserbasyon ng guro. Ginamit ang convergent parallel mixed-methods na disenyo upang suriin ang parehong kuantitatibo at kwalitatibong datos.Ipinakita ng mga natuklasan na ang AI-FlexIBL Framework ay nagdulot ng makabuluhang pag-unlad sa kakayahan ng mga mag-aaral sa proof reasoning sa apat na magkakaugnay na dimensyon: pag-unlad kognitibo, kahusayan sa pagsulat ng patunay, pakikilahok at interaksyon, at pag-unawang konseptwal. Ang istrukturado at reguladong integrasyon ng AI ay nagpalakas sa lohikal na organisasyon, metakognitibong pagmamanman, at replektibong proseso ng beripikasyon, habang ang mga gawaing nakabatay sa inquiry ay nagpalalim sa pundasyong konseptwal at kolaboratibong pangangatwiran. Higit sa lahat, pinagtitibay ng mga natuklasan na ang sinadyang integrasyon ng AI sa pedagohiyang nakabatay sa inquiry ay makabuluhang nagpapahusay sa pagtuturo ng matematikal na patunay. Sa halip na magpahina sa awtonomiya, ang AI ay nagsilbing kognitibong gabay na nagpapalakas sa independiyenteng pangangatwiran at analitikal na katumpakan ng mga mag-aaral. Samakatuwid, ang AI-FlexIBL Framework ay nag-aalok ng isang napatunayan at nasusukat na balangkas na instruksyonal na may kakayahang tugunan ang mga patuloy na hamon sa edukasyon ng matematikal na patunay sa mga flexible na kapaligiran ng pagkatuto.
Mga Susing Salita: Matematikal na Patunay, Inquiry-Based Learning, Artificial Intelligence sa Edukasyon, Flexible Learning, Proof Reasoning, AI-FlexIBL Framework
Abstract Format
html
Language
English
Format
Electronic
Keywords
Artificial intelligence—Educational applications; Mathematics—Study and teaching (Higher)—Technological innovations; Mathematics—Computer-assisted instruction
Recommended Citation
Quinto, J. D. (2026). AI-supported inquiry-based proof learning in FlexTEL (flexible technology enhanced learning) environments: A framework for integrating AI in mathematics proofs. Retrieved from https://animorepository.dlsu.edu.ph/etdd_scied/63
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Embargo Period
6-2029
