AI-ENABLED MATHEMATICS EDUCATION: THEORETICAL RECONSTRUCTION, PRACTICAL PATHWAYS, AND INNOVATIVE TRANSFORMATION OF NORMAL UNIVERSITIES

Danish Scientific Journal No102, 2025 53 PEDAGOGICAL SCIENCES AI-ENABLED MATHEMATICS EDUCATION: THEORETICAL RECONSTRUCTION, PRACTICAL PATHWAYS, AND INNOVATIVE TRANSFORMATION OF NORMAL UNIVERSITIES He Yongfeng JiNing Normal University, School of Mathematics and statistic, Ulanqab, Inner Mongolia, P. R. China https://doi.org/10.5281/zenodo.17740988 Abstract The rapid advancement of artificial intelligence (AI) technology is profoundly transforming the teaching ecology of mathematics education, offering novel pathways to address traditional pain points such as inadequate personalized instruction, difficulties in translating abstract knowledge into practical application, and low efficiency in thinking cultivation. Based on the three-stage learning theory of "Acquisition-Practice-Insight" and the PIE cycle framework, this study systematically analyzes the application value and limitations of AI in mathematics teaching by integrating domestic and international practical cases of "AI + Mathematics Education." From three dimensions—teaching model reconstruction, content innovation, and evaluation upgrading—this paper proposes an intelligent transformation pathway for mathematics education featuring "human-machine collaboration, precise empowerment, and thinking guidance." Furthermore, aiming at the talent cultivation mission of normal universities, a trinity training system of "Discipline + AI + Education" is constructed. The research concludes that as an auxiliary tool rather than a substitute for mathematics education, the core value of AI lies in liberating teachers from repetitive work and realizing large-scale personalized teaching. Normal universities should take AI technology as a key driver to promote the transformation of mathematics education from "knowledge transmission" to "competency development," thereby providing basic education with outstanding teachers equipped with digital literacy and innovative teaching capabilities. Keywords: Artificial Intelligence; Mathematics Education; Human-Machine Collaboration; Normal Universities; Teaching Transformation; Core Competencies 1 Introduction 1.1 Research Background As the cornerstone of the development of science and technology, mathematics derives its core value not only from its knowledge system itself but also from the cultivation of thinking skills and problem-solving abilities. However, traditional mathematics education has long been confronted with three major dilemmas: first, it is difficult to accommodate individual differences in students' cognitive levels and learning styles, making large-scale personalized teaching challenging to promote; second, abstract mathematical concepts are disconnected from practical applications, leading to students' lack of knowledge transfer capabilities; third, teachers are occupied with substantial energy by repetitive tasks such as lesson preparation and homework correction, making it hard to focus on the core link of thinking guidance. Driven by the national education digitalization strategy, the in-depth integration of artificial intelligence (AI) technology and education has become a key breakthrough in building a powerful education nation. Endowed with advantages such as big data analysis, adaptive push, and multimodal presentation, AI provides technical support for improving the quality and efficiency of mathematics education. As the main front for training basic education teachers, normal universities not only shoulder the task of reforming their own mathematics teaching but also assume the mission of cultivating innovative mathematics teachers adaptable to the AI era. Their transformation path directly influences the intelligent development level of regional mathematics education. 1.2 Research Significance 1.2.1 Theoretical Significance This study constructs a theoretical framework for the in-depth integration of AI and mathematics education, improves the trinity integration logic of "Technology-Education-Discipline," enriches the academic research system of mathematics education intellectualization, and provides a theoretical reference for subsequent related studies. 1.2.2 Practical Significance It proposes operable practical schemes for "AI + Mathematics Teaching," offering specific guidance for the reform of mathematics courses in normal universities; clarifies the cultivation path of pre-service teachers' digital literacy, facilitating the modernization transformation of the basic education mathematics teacher workforce; and provides a practical model for local normal universities to serve the digitalization of regional basic education. 2 Theoretical Basis and Core Value of "AI + Mathematics Education" 2.1 Core Theoretical Support 2.1.1 The Three-Stage Learning Theory of "Xue (Acquisition)-Xi (Practice)-Wu (Insight)" Derived from Confucian learning thought, this theory defines the learning process as three progressive stages: "Xue" (Acquisition) refers to the initial contact and perception of new knowledge; "Xi" (Practice) denotes consolidating knowledge through exercises to achieve internalization and transfer; "Wu" (Insight) represents a profound understanding of the essence of knowledge and its innovative application, serving as the core goal of mathematics education. AI technology 54 Danish Scientific Journal No102, 2025 can provide precise support for each stage: in the "Xue" (Acquisition) stage, multimodal presentation simplifies abstract concepts; in the "Xi" (Practice) stage, adaptive exercises enable personalized consolidation; in the "Wu" (Insight) stage, problem chain guidance and thinking visualization facilitate in-depth understanding. 2.1.2 The PIE Cycle Collaborative Framework The closed-loop process of Plan-Implement-Evaluate provides an operational framework for "AI + Mathematics Teaching." In the planning phase, AI assists teachers in accurately identifying the starting point of teaching and personalized goals through data analysis; in the implementation phase, AI acts as a "data assistant" to collect learning process data, while teachers take the lead in thinking guidance and situational creation; in the evaluation phase, AI enables automatic grading of objective questions and visualization of learning situation data, with teachers focusing on higher-order competence assessment and teaching strategy optimization. 2.2 Core Values of AI in Mathematics Education 2.2.1 Realizing Large-Scale Personalized Teaching AI adaptive learning platforms can dynamically adjust content difficulty and learning pathways based on students' learning performance, generating customized learning plans for each student. For instance, the "Shenhang Zhishu" (Shenyang Aerospace University Intelligent Mathematics) system leverages knowledge graphs and learning situation analysis to implement hierarchical learning task recommendation and targeted homework practice, enabling students at different proficiency levels to achieve optimal learning outcomes within their zone of proximal development. 2.2.2 Addressing the Dilemma of Teaching Abstract Knowledge Through technologies such as virtual simulation and dynamic calculation, AI can visualize abstract mathematical content including concepts and formula derivations. In teaching the area calculation of irregular shapes, students drag and splice graphics via AI courseware to intuitively grasp the transformation thinking; the "virtual ruler" tool allows students to independently adjust scale divisions, establishing the intrinsic connection between decimals and fractions and lowering the threshold for understanding abstract knowledge. 2.2.3 Constructing a Data-Driven Teaching Closed Loop AI can collect multi-dimensional data throughout the entire process, including students' preview performance, classroom interaction, and homework completion, generating learning situation reports and knowledge gap maps. By leveraging these data, teachers can accurately identify common class-wide problems and individual students' weak points, optimize teaching strategies, and realize a closed-loop optimization of "data collection - diagnostic analysis - intervention and improvement," thereby enhancing the scientific nature of teaching decisions. 2.2.4 Freeing Up Teachers to Focus on Core Teaching Tasks AI can efficiently complete repetitive tasks such as lesson plan generation, courseware development, and objective question grading, freeing teachers from tedious work. For example, intelligent teaching assistant systems can automatically classify and count problem types such as "calculation errors" and "thinking errors," enabling teachers to concentrate on high-order teaching activities including thinking guidance, group inquiry, and personalized tutoring. 3 Reconstruction of Practical Pathways for "AI + Mathematics Education" 3.1 Teaching Model: Reconstruction of HumanMachine Collaborative Blended Teaching 3.1.1 Optimization of the Three-Stage Teaching Process In the pre-class stage, AI learning companions guide students to complete the preview of basic knowledge points, identify cognitive gaps through pretests, and provide teachers with learning situation diagnostic reports; in the in-class stage, teachers focus on in-depth explanation of key and difficult points as well as thinking guidance, while AI assists in conducting interactive inquiry, real-time answer feedback and other activities, and creates real problem scenarios through virtual simulation tools; in the post-class stage, AI generates customized review plans and extended exercises, teachers provide centralized Q&A for common problems, and offer precise tutoring for individual differences. 3.1.2 Design of Interdisciplinary Project-Based Learning Anchored in real-world problems, project-based learning is carried out by integrating AI tools and interdisciplinary knowledge. For example, in the project "Class Sports Venue Planning," students need to apply mathematical parameter calculation and spatial optimization thinking, combined with sports rules and safety standards, to complete scheme design, verification, and iteration through an AI simulation platform. In the process of collaboration, they achieve in-depth integration and application of knowledge. 3.2 Teaching Content: Knowledge System Innovation Empowered by AI 3.2.1 Integration of Fragmented Knowledge With the help of AI knowledge graph technology, the isolated presentation mode of traditional mathematical knowledge points is broken, and an interconnected network of "Concept-Method-Application" is constructed. For instance, in advanced mathematics teaching, knowledge points such as derivatives and integrals are associated with practical engineering problems, and their application scenarios are dynamically demonstrated through AI, helping students understand the inherent logic and practical value of knowledge. 3.2.2 Visualization of Thinking Training AI tools are utilized to achieve the visualized presentation and comparative analysis of mathematical thinking processes. In the teaching of classic problems such as "Chicken and Rabbit in the Same Cage," AI guides students to independently derive problem-solving ideas through problem chains, while displaying the thinking paths of different problem-solving methods. Danish Scientific Journal No102, 2025 55 This helps students understand the essence of mathematical thinking and improve their logical reasoning abilities. 3.3 Teaching Evaluation: A Data-Driven Multidimensional Evaluation System 3.3.1 Full Coverage of Process-Oriented Evaluation AI collects behavioral and achievement data throughout students' learning processes, including answer speed, error types, inquiry paths, and collaborative performance, to construct multidimensional learning portfolios. This breaks the limitation of traditional evaluation that "emphasizes results over processes." 3.3.2 Precision of Evaluation Feedback AI can not only quickly complete the grading of objective questions but also analyze and score complex problem-solving steps, pushing personalized error correction suggestions targeting specific mistakes. Combining AI feedback, teachers conduct qualitative evaluations from dimensions such as thinking methods and innovative awareness, forming a collaborative model of "AI quantitative evaluation + teacher qualitative evaluation." 4 AI Transformation Pathways for Mathematics Education in Normal Universities 4.1 Upgrade of Talent Training Objectives Normal universities need to upgrade the training objective of pre-service mathematics teachers from "mastering subject knowledge and teaching skills" to "compound talents with AI literacy, subject intelligence, and educational innovation capabilities." Specifically, it includes: first, the ability to operate and apply AI-based mathematics teaching tools; second, the practical ability to use AI technology for learning situation analysis, teaching design, and precise tutoring; third, the thinking guidance ability to guide students in the rational use of AI and avoid technical dependence; fourth, the research and innovation capabilities for mathematics education reform in the AI era. 4.2 Curriculum System Reconstruction 4.2.1 Construction of a "Trinity" Curriculum Framework A integrated curriculum system of "Mathematical Discipline Foundation + AI Technology Application + Educational Teaching Methods" is established. Core courses such as "Introduction to AI in Mathematics Education" and "Data Analysis for Mathematics Teaching" are offered, with AI ethics and critical thinking training integrated into the curriculum content to strengthen pre-service teachers' technical application capabilities and value guidance competence. 4.2.2 Development of an "X + AI" Interdisciplinary Curriculum Group On one hand, promote "Mathematical Discipline + AI" courses, such as "Mathematical Modeling and AI Simulation" and "Statistical Analysis and Big Data Processing," to enhance pre-service teachers' subject intelligence; on the other hand, strengthen "Teacher Education + AI" courses, such as "AI-Assisted Teaching Design" and "Practice of Intelligent Teaching Evaluation," to cultivate pre-service teachers' digital teaching capabilities. 4.3 Practical Teaching Innovation 4.3.1 Construction of an AI Teaching Practice Platform Collaborate with AI technology enterprises and primary and secondary schools to establish practice bases, introducing intelligent teaching systems and simulated teaching tools. This enables pre-service teachers to practice AI-assisted teaching methods and skills in real teaching scenarios, accumulating practical experience. 4.3.2 Conducting Collaborative Teaching and Research Activities Organize pre-service teachers to participate in project-based teaching and research on "AI + Mathematics Teaching." Centering on themes such as abstract knowledge visualization, personalized teaching design, and interdisciplinary practice, collaborative research is carried out jointly with in-service teachers from primary and secondary schools and AI technical personnel to enhance educational innovation capabilities. 4.4 Faculty Development 4.4.1 Strengthening Teachers' Digital Literacy Training Through special training, workshop exchanges, and other approaches, the AI technology application capabilities and intelligent teaching design proficiency of existing mathematics teachers are enhanced, fostering a compound faculty team integrating "mathematical discipline + AI + education." 4.4.2 Promoting Industry-Education Integration for Collaborative Talent Cultivation Introduce professional talents in the AI field to form interdisciplinary teaching teams with mathematics education teachers; cooperate with technology enterprises to conduct research projects, transforming the latest AI technological achievements into teaching resources to enhance the cutting-edge nature and practicality of teaching content. 5 Challenges and Countermeasures of "AI + Mathematics Education" 5.1 Key Challenges 5.1.1 Limitations of Technology Application Current AI systems have limited capabilities in understanding the profound connotations of mathematical concepts, fostering students' mathematical intuition, and cultivating innovative thinking. Most feedback is based on preset rules, making it difficult to achieve the heuristic guidance effect of teachers. Over-reliance on AI may weaken students' independent thinking abilities and resilience in the face of setbacks. 5.1.2 Data Security Risks There is a risk of leakage of students' personal information and learning data generated during the learning process. Potential biases in AI algorithms may lead to educational inequity, affecting the fairness of personalized teaching. 5.1.3 Teachers' Transformation Dilemmas Some teachers face issues such as insufficient digital literacy and lack of confidence in technology application. They have an inadequate understanding of the concept of "AI + Mathematics Education," making it difficult to effectively achieve the teaching effect of human-machine collaboration. 56 Danish Scientific Journal No102, 2025 5.1.4 Inadequate Adaptation of Teacher Education The existing curriculum system and teaching models are struggling to meet the talent training needs of the AI era. Practical teaching is disconnected from the reality of basic education, and the cultivation of preservice teachers' digital teaching capabilities lags behind. 5.2 Countermeasures 5.2.1 Constructing a Human-Machine Collaborative Thinking Guidance Model Clarify AI's auxiliary positioning: teachers focus on core links such as thinking training and value guidance, and make up for AI's deficiencies in higher-order thinking cultivation through problem design, inquiry guidance, and method summarization. A collaborative model of "AI-assisted knowledge transmission + teacher-led thinking cultivation" is thus formed. 5.2.2 Establishing a Data Security and Ethical Norms System Formulate norms for the collection, storage, and use of AI teaching data, and adopt encryption technologies to ensure data security; strengthen AI ethics education to guide teachers and students to view AI technology rationally, fostering awareness of data privacy protection and capabilities in critical use. 5.2.3 Improving the Teacher Professional Development Support System Construct a teacher development pathway of "hierarchical training + practical research + teaching and research leadership," providing customized training based on the needs of teachers of different age groups; establish a case library and resource platform for "AI + Mathematics Teaching," promoting the transformation of teachers' teaching concepts and skills through exemplary leadership. 5.2.4 Strengthening the Practical Orientation of Teacher Education Optimize pre-service teacher training programs and increase the class hour ratio of AI teaching practice; establish a regular cooperation mechanism with local primary and secondary schools, conducting joint teaching and research as well as internship practices on "AI + Mathematics Teaching" to enhance pre-service teachers' practical capabilities. 6 Conclusion AI technology has brought unprecedented development opportunities to mathematics education. Its advantages in realizing personalized teaching, visualizing abstract knowledge, and improving teaching efficiency are driving the transformation of mathematics education from "standardization" to "precision" and "personalization." However, AI has always been an auxiliary tool in mathematics education and cannot replace teachers' core roles in thinking guidance, value leadership, and emotional care. As the main position for cultivating basic education teachers, the AI transformation of mathematics education in normal universities holds dual significance: on the one hand, it is necessary to promote their own teaching reform and enhance the intelligence level of mathematics teaching; on the other hand, it is essential to construct a talent training system adapting to the needs of the AI era, cultivating outstanding teachers with digital literacy, subject intelligence, and educational innovation capabilities. In the future, normal universities should adhere to the principles of "human-machine collaboration, thinking leadership, and practical orientation," continuously deepen the integrated innovation of "discipline + AI + education," seek a balance between technological application and the essence of education, and provide solid support for the high-quality development of mathematics education in basic education. AI empowerment in mathematics education is not a simple superposition of technologies, but a systematic reform of educational concepts, teaching models, and talent training systems. Only by adhering to the core goals of mathematics education and rationally exerting the auxiliary value of AI technology can mathematics education truly achieve "student-centeredness" in the intelligent era and cultivate new-generation talents with logical thinking, innovative capabilities, and social responsibility. References: 1. Gu, X. Q., & Li, S. J. (2024). 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