Intelligent Tutoring System (ITS) for Mathematics using Computational Engines

Stanley, Jason Neville

Intelligent Tutoring System (ITS) for Mathematics using Computational Engines

Stanley, Jason Neville

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Publication Type:: Thesis
Issue Date:: 2025

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Field	Value	Language
dc.contributor.author	Stanley, Jason Neville
dc.date.accessioned	2026-03-03T04:10:45Z
dc.date.available	2026-03-03T04:10:45Z
dc.date.issued	2025
dc.identifier.uri	http://hdl.handle.net/10453/193760
dc.description	University of Technology Sydney. Faculty of Science.	en_US.UTF-8
dc.description.abstract	This thesis addresses a persistent challenge in mathematics education: the epistemological and pedagogical disconnect between secondary and tertiary learning. While secondary instruction often emphasises procedural fluency and examination performance, tertiary mathematics demands abstraction, symbolic reasoning, and conceptual understanding. This mis-alignment contributes to student underpreparedness, disengagement, and attrition in mathematically intensive disciplines. To bridge this gap, the research explores the potential of Intelligent Tutoring Systems (ITSs) grounded in constructivist learning theories and powered by symbolic computation. The study positions curriculum intuition—a student’s capacity to recognise structure, pattern, and mathematical form—as central to successful transition. It conceptualises learning as a dynamic, perturbation-sensitive process, where moments of cognitive disequilibrium indicate readiness for conceptual growth. The thesis develops and evaluates a prototype Intelligent Tutoring System (ITS) that incorporates a symbolic reasoning engine (Mathematica® ) to interpret student input, recognise mathematical equivalence, and provide adaptive feedback. This system is implemented using modular, LMS-compatible web technologies (notably Extensibility), supporting scalable deployment while retaining responsiveness to individual learners. A design-based research (DBR) methodology underpins the project, integrating iterative development with theoretical inquiry. Findings from classroom trials demonstrate the system’s capacity to scaffold conceptual understanding, detect meaningful perturbations, and support learners in transitioning from procedural to relational mathematical thinking. The research contributes a novel hybrid Student Model sensitive to conceptual dynamics, proposes diagnostic uses of perturbation for feedback, and advances the integration of symbolic engines within ITS design. Future work is outlined, including the prospective augmentation of ITSs with large language models to combine conversational flexibility with formal mathematical rigour. The study affirms the importance of theoretically informed, technologically enabled interventions in addressing systemic challenges in mathematics transition pedagogy.	en_US.UTF-8
dc.format	Thesis (PhD)
dc.language.iso	en_US	en_US.UTF-8
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/193760/1/thesis.pdf
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.rights	© 2025 Jason Neville Stanley
dc.rights	au.edu.uts.lib/cph
dc.title	Intelligent Tutoring System (ITS) for Mathematics using Computational Engines	en_US.UTF-8
dc.type	Thesis
utslib.copyright.status	open_access	*

Abstract:

This thesis addresses a persistent challenge in mathematics education: the epistemological and pedagogical disconnect between secondary and tertiary learning. While secondary instruction often emphasises procedural fluency and examination performance, tertiary mathematics demands abstraction, symbolic reasoning, and conceptual understanding. This mis-alignment contributes to student underpreparedness, disengagement, and attrition in mathematically intensive disciplines. To bridge this gap, the research explores the potential of Intelligent Tutoring Systems (ITSs) grounded in constructivist learning theories and powered by symbolic computation. The study positions curriculum intuition—a student’s capacity to recognise structure, pattern, and mathematical form—as central to successful transition. It conceptualises learning as a dynamic, perturbation-sensitive process, where moments of cognitive disequilibrium indicate readiness for conceptual growth. The thesis develops and evaluates a prototype Intelligent Tutoring System (ITS) that incorporates a symbolic reasoning engine (Mathematica® ) to interpret student input, recognise mathematical equivalence, and provide adaptive feedback. This system is implemented using modular, LMS-compatible web technologies (notably Extensibility), supporting scalable deployment while retaining responsiveness to individual learners. A design-based research (DBR) methodology underpins the project, integrating iterative development with theoretical inquiry. Findings from classroom trials demonstrate the system’s capacity to scaffold conceptual understanding, detect meaningful perturbations, and support learners in transitioning from procedural to relational mathematical thinking. The research contributes a novel hybrid Student Model sensitive to conceptual dynamics, proposes diagnostic uses of perturbation for feedback, and advances the integration of symbolic engines within ITS design. Future work is outlined, including the prospective augmentation of ITSs with large language models to combine conversational flexibility with formal mathematical rigour. The study affirms the importance of theoretically informed, technologically enabled interventions in addressing systemic challenges in mathematics transition pedagogy.

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