1 
 
Guide  to  the  use  of  generative 
artificial  intelligence  in  education 
and research 
 
Perez  Verástegui,  Jhon  Francisco;  Ortega 
Rojas, Yesmi  Katia;  Casazola Cruz, Oswaldo 
Daniel; Morales Chalco, Osmart Raúl; Zapata 
Villar,  Loyo  Pepe;  Castro  Chiroque,  Roberto 
Javier; Rojas Orbegoso, Jorge Luis  
 
©  Perez  Verástegui,  Jhon  Francisco;  Ortega 
Rojas, Yesmi  Katia;  Casazola Cruz, Oswaldo 
Daniel; Morales Chalco, Osmart Raúl; Zapata 
Villar,  Loyo  Pepe;  Castro  Chiroque,  Roberto 
Javier; Rojas Orbegoso, Jorge Luis, 2025  
 
First edition (1st ed.): December, 2025 
 
Edited by:   
 
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Editorial Mar Caribe

Guide to the use of generative artificial

intelligence in education and research

Colonia, Uruguay


 
Index 
Introduction .............................................................................................................. 8 
Chapter I. ................................................................................................................ 10 
Generative AI and the Epistemological Reconfiguration of Research in Mathematics 
Education ................................................................................................................ 10 
The Algorithmic Turn in Mathematical Knowledge Production ....................... 10 
Theoretical Frameworks: Revisiting Constructivism and the Networked Mind 12 
1 The Disruption of Social Constructivism and the "Synthetic ZPD" .............. 12 
2 Connectivism and the Node of "Surrogate Knowing" ................................. 13 
3 Critical Pedagogy and the Hidden Curriculum ........................................... 14 
Table 1: Comparative Analysis of Theoretical Frameworks in the AI Era ......... 15 
The Ontological Status of Mathematical Objects in the AI Era .......................... 16 
1 Digital Irreducibility and the "Thinghood" of AI Math ................................ 16 
2 Innate vs. Generated Knowledge: The Meno Paradox ................................. 17 
3 The Homogenization of Mathematical Reality ............................................ 17 
Reconfiguring Research Methodologies in Mathematics Education ................. 18 
1 Automated Qualitative Analysis and the Coding Crisis .............................. 18 
2 Quantitative Shifts: Synthetic Data and Circular Validation ........................ 19 
3 The Crisis of Authorship and Scientific Integrity ........................................ 20 
Table 2: Risks to Scientific Integrity in AI-Mediated Research .......................... 21 
Pedagogical Epistemologies: Teaching, Learning, and the Nature of Proficiency
 ............................................................................................................................ 22 
1 The Obsolescence of the "Math Wars" ......................................................... 22 
2 Cognitive Offloading vs. Adaptive Reasoning: The PNAS Study ................ 22 
3 Redefining Mathematical Understanding ................................................... 23 
The Political Economy of Math Knowledge: Curriculum as Cultural Politics ... 24 
1 South Korea's "Digital Citizenship" as a Case Study .................................... 24 
2 Equity, Access, and the Digital Divide 2.0 ................................................... 25 
Teacher Knowledge and the Transformation of Expertise ................................ 26 
1 TPACK and the Need for "Critical AI Literacy" ........................................... 26 
2 The Displacement of Authority and "Epistemic Guiding" ........................... 26 
Human-AI Collaboration and Hybrid Intelligence ........................................... 27 


 
1 Symbiotic Learning Systems ....................................................................... 27 
2 The Human-in-the-Loop in Research .......................................................... 28 
Future Directions and the "Special Issue" Landscape ........................................ 29 
1 Emerging Research Agendas ...................................................................... 29 
2 Key Venues for Discourse ........................................................................... 29 
Towards a Critical AI Literacy ........................................................................ 30 
Chapter II. ............................................................................................................... 32 
Comprehensive Guide to the Use of Generative Artificial Intelligence in Education 
and Research ........................................................................................................... 32 
The Epistemic Shift in Knowledge Systems ...................................................... 32 
Global Governance and the Regulatory Landscape .......................................... 33 
1 UNESCO’s Human-Centered Framework ................................................... 33 
2 The European Union AI Act: The High-Risk Classification ......................... 35 
Table 3: High-Risk Domain .............................................................................. 35 
Institutional Policy Frameworks in Higher Education ...................................... 36 
1 Divergent Approaches to Academic Integrity ............................................. 37 
2 The Data Privacy "Red Line." ...................................................................... 38 
Pedagogical Applications: Transforming the Classroom .................................. 39 
1 Intelligent Tutoring Systems (ITS): The Case of Khanmigo ......................... 39 
2 Automated Assessment and Feedback: The Gradescope Model .................. 40 
3 Curriculum Design and Resource Generation ............................................. 41 
The Research Revolution: Methodologies, Tools, and Risks ............................. 41 
1 Literature Review: The Battle for Accuracy ................................................. 42 
Table 4: The Battle for Accuracy ....................................................................... 42 
2 Qualitative Data Analysis (QDA): The Hybrid Workflow ........................... 43 
3 Code Generation and Data Science ............................................................. 44 
4 Grant Writing: The Stanford "10 Rules." ...................................................... 45 
Ethics, Integrity, and the Arms Race ................................................................ 45 
1 The Failure of Plagiarism Detection ............................................................ 45 
2 Bias and Representation .............................................................................. 46 
Prompt Engineering: A Technical Guide for Academics ................................... 47 


 
1 The Prompt Library Concept ...................................................................... 47 
2 High-Utility Academic Prompts ................................................................. 47 
3 Advanced Techniques: Few-Shot and Chain-of-Thought ............................ 48 
Future Outlook: The Integrated Academy ........................................................ 49 
1 The Skill Shift .............................................................................................. 49 
2 The Infrastructure Divide ........................................................................... 49 
Chapter III. .............................................................................................................. 51 
The Age of the Synthetic Sociologist: Generative AI and the Epistemological 
Reconfiguration of Social Science Research ............................................................. 51 
The Arrival of Adaptive Epistemology ........................................................ 51 
1 The Crisis of Expertise and Disciplinary Anxiety ........................................ 52 
2 The Concept of "In Silico" Social Science ..................................................... 53 
Qualitative Research Transformation: The Automated Hermeneutic ............... 54 
1 The Evolution of Thematic Analysis: From Grounded Theory to "Prompted 
Theory." ........................................................................................................... 54 
2 Reliability Wars: Human vs. Synthetic Coders ............................................ 56 
Table 5: Comparative Analysis of Human vs. LLM Coders in Qualitative 
Research ........................................................................................................... 56 
3 The Tooling Landscape: NVivo, MAXQDA, and ATLAS.ti ......................... 57 
Quantitative Frontiers: In Silico Sociology and Synthetic Data ......................... 59 
1 Silicon Subjects: Simulating the Survey Respondent ................................... 59 
2 Social Simulacra: The Petri Dish of Society .................................................. 60 
3 Prediction-Powered Inference (PPI): The Statistical Bridge ......................... 61 
Autonomous Research Agents: The "AI Scientist." ........................................... 62 
1 The "Team of AI Scientists" (TAIS) Framework ........................................... 62 
2 The "AI Scientist" and Automated Publication ............................................ 63 
Measuring the Machine: Validity as a Social Science Challenge ....................... 64 
1 Wallach’s Four-Level Measurement Framework ......................................... 64 
2 Validity Lenses for AI ................................................................................. 65 
Ethics, Policy, and the Future of Authorship .................................................... 66 
1 The "Non-Author" Consensus ..................................................................... 66 
Table 6: Publisher Policy Comparison on GenAI .............................................. 66 


 
2 Data Privacy: The "Upload" Trap ................................................................ 67 
Future Trajectories: The Horizon of 2030 .......................................................... 67 
1 The contraction of "Knowledge Extent." ...................................................... 68 
2 From "In Silico" to "Robotic Sociology." ....................................................... 68 
3 The Hybrid Researcher ............................................................................... 68 
Chapter IV. .............................................................................................................. 70 
Generative AI and Statistics Education: A Comprehensive Report on Pedagogical 
Transformation, Research Outcomes, and Policy Frameworks (2023–2025) ............. 70 
Introduction: The Disruption of Statistical Pedagogy ....................................... 71 
The Institutional Response and Academic Discourse ....................................... 72 
1 The International Association for Statistical Education (IASE) .................... 72 
2 eCOTS 2024: A Barometer of Pedagogical Change ...................................... 74 
3 Professional Society Positions (ASA, RSS, ISI) ............................................. 75 
Pedagogical Transformations: The "Coding Without Code" Debate ................. 76 
1 The "Prompt-Based" Paradigm.................................................................... 76 
2 The "Black Box" and Cognitive Offloading Risks ......................................... 78 
3 The Hybrid Approach: "Code Critique." ..................................................... 78 
The Synthetic Data Ecosystem .......................................................................... 79 
1 Methodologies for Generation .................................................................... 79 
Table 7: Research identifies several tiers of synthetic data generation used in 
educational contexts ......................................................................................... 79 
2 Pedagogical Benefits ................................................................................... 80 
3 Limitations and "Hyper-Realism" ............................................................... 80 
Empirical Evidence: RCTs and Classroom Studies ........................................... 81 
1 The Khan Academy/UPenn Study .............................................................. 81 
2 The Corvinus University Study ................................................................... 82 
3 ChatGPT vs. Human Tutors ........................................................................ 82 
Advanced Statistical Domains: Bayesian Inference ........................................... 83 
1 Generative AI for Bayesian Computation.................................................... 83 
2 Pedagogical Applications............................................................................ 83 
Curriculum, Assessment, and Policy ................................................................ 84 
1 Assessment Redesign: The "AI-Resilient" Classroom .................................. 84 


 
2 Syllabus Policies and Academic Integrity .................................................... 85 
3 GAISE Guidelines and Future Standards .................................................... 85 
AI Literacy: A New Core Competency ............................................................. 85 
1 The AI Literacy Framework ........................................................................ 86 
Table 8: Application in Statistics ....................................................................... 86 
2 Integrating AI Literacy into Statistics .......................................................... 86 
Ethical and Societal Implications ...................................................................... 87 
1 The AI Divide ............................................................................................. 87 
2 The "Bot-Enshittification" of Data................................................................ 87 
3 The Human Element ................................................................................... 87 
Conclusion .............................................................................................................. 89 
Bibliography ........................................................................................................... 91

Introduction

The history of education and science is marked by technological milestones

that irrevocably transformed the way we access and create knowledge: the printing

press, the personal computer, and the Internet. Today, we are facing a new threshold,

the most dizzying of all: Generative Artificial Intelligence (AGI).

This book, "Guide to the use of generative artificial intelligence in education and

research", was born from an urgent need. In classrooms and laboratories around the

world, the emergence of tools capable of generating text, code, images, and complex

analysis has generated a mixture of fascination and uncertainty. How do we integrate

these tools without sacrificing critical thinking? How do we harness its potential to

accelerate scientific discovery without compromising academic integrity?

The aim of this book is not simply to explain what AI is, but how to use it

effectively, ethically, and rigorously. It is not a question of replacing the educator or

the researcher, but of enhancing their human capacities through intelligent human-

machine collaboration.

Over the course of four chapters, we will explore:

• In Education: The transition from a standardized teaching model to a

personalized one. We will see how AI can act as a Socratic tutor, generator of

didactic resources, and assistant in formative assessment.

• In Research: The optimization of processes, from the review of literature and

the synthesis of large volumes of data, to assistance in the writing and

correction of manuscripts, always under the expert supervision of the

researcher.

• The Ethical Compass: An in-depth analysis of algorithmic biases, data

"hallucination", intellectual property, and the redefinition of plagiarism in the

synthetic age.

This guide is designed for teachers, students, administrators, and scientists

who want to move from passive spectators to competent users. The fundamental

premise is that generative AI is a co-pilot, a powerful tool that requires a human pilot

with judgment, curiosity, and a solid one.

We live in an era where science fiction has become intertwined with our

everyday reality. Generative Artificial Intelligence has ceased to be a futuristic

promise to become a tangible presence in our educational institutions and research

centers. However, with their arrival, fundamental questions arise about the nature of

learning and human creation. Therefore, the authors invite us to look beyond the

media noise and apocalyptic predictions. It is a proposal to understand AI not as an

oracle with all the answers, but as a cognitive scaffold that helps us reach higher.

So, we face the challenge of educating a generation that will coexist with

synthetic intelligences and of conducting research in an environment where the speed

of data processing exceeds traditional human capacity. It is expected that, in the short

term, governments will establish verification protocols to ensure that speed does not

destroy the truth, seeking that these tools close educational gaps rather than widening

them, and that, by automating the routine, researchers can dedicate themselves to the

creative and the empathetic.

Chapter I.

Generative AI and the Epistemological

Reconfiguration of Research in

Mathematics Education

1. The Algorithmic Turn in Mathematical

Knowledge Production

The integration of Generative Artificial Intelligence (GenAI) into the landscape

of mathematics education constitutes a seismic shift that transcends mere

technological accretion. It represents a profound epistemological reconfiguration of

the field, fundamentally altering the mechanisms by which mathematical knowledge

is produced, validated, consumed, and disseminated. We are currently witnessing the

"algorithmic turn," a transition where the boundaries between human cognition and

machine processing are becoming increasingly porous, necessitating a rigorous re-

examination of the foundational axioms of educational research and practice.

Historically, the domain of mathematics education has been predicated on the

understanding of learning as a human-centric endeavor—a process of co-construction

rooted in social interaction, dialogue, and the struggle for meaning within a

community of practice.1 The classroom and the research laboratory have served as the

primary loci for this epistemic work, governed by established authorities such as the

teacher, the textbook, and the peer-reviewed journal. However, the emergence and

rapid proliferation of Large Language Models (LLMs) such as ChatGPT, Claude,

Gemini, and specialized solvers like Photomath have introduced a "surrogate knower"

into this ecosystem.1 These entities, capable of producing fluent, instantaneous, and

confident mathematical outputs, challenge traditional epistemic hierarchies and force

a renegotiation of what counts as mathematical understanding.

The scale of this transformation is evident in the widespread adoption of these

tools across the scientific and educational communities. A 2023 study involving 1,600

scientists revealed that nearly 30% were already engaging GenAI to assist with their

work, a figure that signals the transition of AI from a novelty to an infrastructural

component of research.3 In the context of mathematics education, this adoption was

accelerated by the remote teaching imperatives of the COVID-19 pandemic, which

normalized digital mediation.4 Yet, the implications extend far beyond the logistical

or functional; they strike at the core of epistemic agency. As AI systems begin to

mediate the generation of hypotheses, the coding of qualitative data, and the

scaffolding of student problem-solving, they influence not only the dissemination of

information but the very ontology of mathematical truth.5

This report provides an exhaustive analysis of these dynamics, structured to

interrogate the redefinition of theoretical frameworks, the ontological status of

mathematical objects in the AI era, the transformation of research methodologies, and

the reshaping of pedagogical epistemologies. It argues that the field is navigating a

critical tension between the functionalist utility of AI—its ability to optimize

performance and automate labor—and the foundational risks it poses to critical

thinking, authorship, and the "productive struggle" essential for deep learning.6 By

synthesizing empirical data, philosophical inquiry, and case studies of curriculum

reform, this report posits that the integration of GenAI requires a new "critical AI

literacy" that centers human epistemic agency against the tide of automation bias.

2. Theoretical Frameworks: Revisiting

Constructivism and the Networked Mind

The introduction of GenAI into mathematics education necessitates a rigorous

revisiting of the dominant theoretical frameworks that have guided the field for

decades. Theories such as social constructivism, connectivism, and critical pedagogy

are being stretched to accommodate non-human actors that simulate social interaction

and knowledge construction. The traditional dyads of teacher-student and researcher-

participant are being complicated by the insertion of an algorithmic intermediary that

possesses a fluid, albeit synthetic, form of agency.

2.1 The Disruption of Social Constructivism and the "Synthetic

ZPD"

Social constructivism, which frames learning as the growth of diverse

networks of information and connections formed through social interaction, faces a

unique challenge in the age of GenAI. Traditionally, this theory presupposes human

interlocutors who co-construct meaning through dialogue, negotiation, and the use of

shared cultural tools.3 The Vygotskian concept of the Zone of Proximal Development

(ZPD) relies on a "more knowledgeable other"—typically a teacher or peer—who

possesses not just superior content knowledge but an empathetic understanding of

the learner's cognitive state.

GenAI disrupts this dynamic by inserting an agent that mimics the "social"

aspects of interaction—conversational fluency, turn-taking, and responsiveness—but

lacks the "constructivist" capacity for genuine meaning-making. When a student

interacts with a GenAI chatbot to solve a complex problem, such as a differential

equation or a geometric proof, the interaction superficially resembles the scaffolding

process within the ZPD.9 However, unlike a human tutor, the AI's responses are not

grounded in a lived understanding of the student's misconceptions or the pedagogical

trajectory. Instead, they are probabilistic generations based on pattern matching

within vast datasets.

Recent research utilizing Plato’s Meno to analyze ChatGPT's mathematical

knowledge highlights this distinction. In the Meno, Socrates guides an uneducated

secondary device boy to solve a geometry problem through questioning, arguing that

the knowledge was innate and "recollected" (anamnesis).9 When researchers replicated

this dialogic approach with ChatGPT, the AI demonstrated the capacity to function

within what can be termed a "Chat's ZPD." The AI could not solve certain complex

problems independently, but could do so when prompted by a knowledgeable user

who provided the necessary scaffolding.9 This inversion—where the human scaffolds

the AI—suggests the emergence of a Synthetic ZPD, a space where knowledge is

emergent from the interaction between human intent and algorithmic probability.

This forces a recalibration of social constructivism to account for "machine creativity,"

which stems from high-throughput generation, versus "human creativity," which

involves the formation of mental models and conceptual abstraction.10

2.2 Connectivism and the Node of "Surrogate Knowing"

Connectivism offers a potentially more compatible framework for

understanding GenAI, viewing knowledge as distributed across a network of non-

human and human nodes.3 In this view, learning is the process of connecting

specialized nodes or information sources. The GenAI tool becomes a high-weight

node in the learner's Personal Learning Network (PLN). The epistemological

reconfiguration here lies in this node. Unlike a static textbook or a calculator, the

GenAI node is dynamic, interactive, and generative.

Research indicates that the integration of AI into these networks can enhance

self-directed learning by providing instant access to information and personalized

tutoring, effectively removing structural and economic barriers to knowledge.2

However, this "democratization" comes with the risk of epistemic pollution.

Connectivist theory must now grapple with the phenomenon of "hallucination"—

where the AI node generates plausible but false information—and "echo chambers,"

where the AI reinforces misconceptions or biases present in its training data.11 The

"networked mind" in the age of AI is thus a hybrid entity, relying on a symbiosis of

biological cognition and silicon processing, raising fundamental questions about

where the "knowing" actually resides. If a student can instantly retrieve a proof from

an AI, is that knowledge "connected" to them, or merely "accessed" by them?

2.3 Critical Pedagogy and the Hidden Curriculum

Critical pedagogy, which draws attention to cultural biases, power

imbalances, and the need to address inequities, provides a vital lens for analyzing the

"hidden curriculum" of GenAI.1 AI systems are not neutral tools; they are cultural

artifacts encoded with the epistemological assumptions and biases of their creators

and training data.

The "hidden curriculum" of AI in mathematics education often prioritizes a

specific form of knowledge: procedural, text-based, and standardized. Research

suggests that while GenAI bots are successful at writing lesson plans, they often differ

significantly in their understanding of teaching strategies, sometimes defaulting to

didactic or instructionist methods that may not align with contemporary pedagogical

goals.12 Furthermore, the opaque nature of these systems—the "black box"—obscures

the source of their authority. A critical pedagogical approach demands that we

interrogate why an AI suggests a particular method or solution and whose knowledge

is being prioritized (See Table 1). This perspective reveals that the rise of AI is not just

a technical shift but a shift in the political economy of knowledge, where "truth" is

increasingly defined by algorithmic consensus rather than human consensus.1

Table 1: Comparative Analysis of Theoretical Frameworks in the

AI Era

Theoretical

Framework

Traditional Focus

Impact of Generative

Epistemological

Challenge

Social

Constructivism

Knowledge is co-

constructed through

human social

interaction

(Vygotsky).

AI acts as a "synthetic

partner" mimicking

social interaction.

Distinguishing

between genuine

scaffolding and

"simulated empathy":

the risk of the

"Synthetic ZPD."

Connectivism

Knowledge is

distributed across

networks of

human/non-human

nodes.

AI becomes a

dynamic, generative

node capable of

independent output.

Validating the

accuracy of the AI

node; defining

"knowledge

possession" vs.

"access."

Critical Pedagogy

Power dynamics,

equity, and cultural

bias in education.

AI as a carrier of

"hidden curriculum"

and algorithmic bias.

Interrogating the

"black box" of

authority, addressing

the displacement of

human judgment.

TPACK

Integration of

Technology,

Pedagogy, and

Content Knowledge.

AI mediates content

generation and

pedagogical strategy

simultaneously.

Developing "Critical

AI Literacy" within

TPACK; managing the

opaque derivation of

content.

3. The Ontological Status of Mathematical Objects

in the AI Era

The reconfiguration of research in mathematics education extends to the very

ontology of mathematical objects. The debate over whether mathematical truths are

discovered (Platonism) or invented (Formalism/Constructivism) is reignited by the

presence of machines that can "generate" mathematical proofs and objects without

human intervention.

3.1 Digital Irreducibility and the "Thinghood" of AI Math

The ontological status of AI-generated mathematics touches on the concept of

"digital irreducibility." Mathematical objects have traditionally been viewed either as

abstractions derived from the physical world or as pure rational concepts accessible

only to the conscious mind.14 GenAI systems, however, operate on "digital things"—

abstractions that are discrete, distinct, and manipulate symbols without necessary

reference to physical reality or conscious intent.

This raises a profound question: Does a proof generated by an AI, which no

human has verified step-by-step, possess the same ontological status as a human-

derived proof? Functionalist accounts of intelligence argue that if the system behaves

intelligently (i.e., produces the correct proof), it is intelligent.15 However, critics argue

that true intelligence requires a mode of being—a sustaining of identity through time

and a coordination of reasons—that AI lacks. The AI generates "structures" but does

not "understand" them in a phenomenological sense. 15

For mathematics education research, this distinction is critical. If we accept AI-

generated explanations as valid educational content, we are implicitly accepting a

functionalist ontology where "performance" equates to "understanding." This shift

legitimizes the use of AI as a "surrogate knower," potentially displacing the human

teacher's authority, which is grounded in experiential and ethical judgment.1 The risk

is an "ontological inflation," where we ascribe understanding to systems that merely

simulate the statistical correlates of understanding, leading to a degradation of the

concept of "meaning" in mathematics.

3.2 Innate vs. Generated Knowledge: The Meno Paradox

The replication of Plato's slave-boy experiment with ChatGPT serves as a

pivotal case study for this ontological tension. In the original dialogue, Socrates argues

that the boy's ability to solve the geometry problem proves that knowledge is innate

and recalled. When ChatGPT solves the same problem, it does so not through

recollection of a Platonic form, but through the probabilistic assembly of tokens based

on its training on millions of texts.9

However, the "Chat's ZPD" finding—that the AI could solve the problem only

with specific prompting—suggests that the knowledge is neither fully innate to the

model nor fully external. It is emergent. This challenges the binary of innate versus

generated knowledge. In the educational context, this implies that "knowledge" is not

a static object transferred from teacher to student, nor solely constructed by the

student, but a dynamic state achieved through the tuning of the human-AI interface.

The mathematical object (the solution to doubling the square) exists in a state of

potentiality within the model, collapsed into reality only through the agency of the

human prompter.

3.3 The Homogenization of Mathematical Reality

Another ontological risk is the potential for GenAI to homogenize

mathematical thought. LLMs are trained on vast but finite datasets, primarily from

the internet, which are dominated by Western, English-language mathematical

conventions. When they generate mathematical tasks or explanations, they tend to

converge on the most statistically probable patterns. This could lead to a narrowing

of the "mathematical reality" presented to students, privileging standard, text-based

mathematical conventions over alternative or diverse mathematical practices.16

Research on the discourse of STEM education in different national contexts,

such as the comparison between the U.S. and China, reveals distinct "regularities" or

orders of statements.16 The universalizing tendency of large language models

threatens to flatten these cultural distinctions, imposing a "standardized" algorithmic

ontology that may obscure the rich, pluralistic nature of mathematical heritage. This

"algorithmic mediation" creates new logics for validating knowledge, where the

"truth" is what the model can most consistently reproduce, rather than what is most

mathematically profound or culturally relevant.17

4. Reconfiguring Research Methodologies in

Mathematics Education

The most tangible impact of GenAI on the field is the transformation of

research methodologies. From the formulation of hypotheses to the analysis of

qualitative data, GenAI is altering the mechanics of how research is conducted,

introducing efficiencies while simultaneously creating new vectors for error and

ethical compromise.

4.1 Automated Qualitative Analysis and the Coding Crisis

Qualitative research in mathematics education often involves the labor-

intensive coding of transcripts from classroom observations, interviews, and student

work. GenAI tools are increasingly being used to automate this process. LLMs can

identify themes, patterns, and sentiments in text data with a speed that human

researchers cannot match.3

For instance, studies have employed tools like ChatGPT and NVivo's AI

integration to analyze preservice teachers' perceptions and student problem-solving

strategies.18 Researchers have used these tools to classify open-ended survey

responses and generate initial coding schemes. While this increases efficiency and

removes barriers for researchers with limited resources, 3 it introduces significant

epistemological risks:

1. Loss of Interpretive Nuance: AI coding relies on semantic pattern matching

rather than interpretive understanding. It may miss the subtle, contextual cues—

sarcasm, hesitation, cultural references—that a human researcher immersed in

the field would catch.

2. Homogenization of Interpretation: If multiple researchers use the same

foundation models (e.g., GPT-4) to code their data, there is a risk of converging

on similar, generic interpretations. This reduces the diversity of theoretical lenses

applied to data, leading to a "scientific monoculture". .20

3. The "Black Box" of Analysis: The "reasoning" behind an AI's coding decision is

often opaque. Unlike a human coder who maintains a memo log of their

interpretive choices, an LLM operates as a black box. This makes the "audit trail"

of the research difficult to establish, challenging the criterion of trustworthiness

in qualitative inquiry.3

4.2 Quantitative Shifts: Synthetic Data and Circular Validation

In quantitative research, GenAI is opening new frontiers in data cleaning,

transformation, and even the generation of synthetic data for modeling.3 The ability

of LLMs to write Python or R scripts allows researchers to perform complex statistical

analyses without deep programming expertise, democratizing access to advanced

quantitative methods.3

However, the use of AI to evaluate student performance introduces a

dangerous circularity. If AI is used to grade student work (which may itself be AI-

assisted), and then AI is used to analyze the aggregate data, the entire research loop

becomes detached from human cognition. We risk measuring the "alignment"

between two algorithms rather than the mathematical proficiency of the student.

Furthermore, the reliance on AI for hypothesis generation could lead to research

questions driven by what is computationally convenient for the model to answer

rather than what is pedagogically vital.20 The use of synthetic data—generated by AI

to train or test other models—must be handled with extreme rigor, "provenance

information" to avoid contaminating the scientific record with fabricated

observations. 21

4.3 The Crisis of Authorship and Scientific Integrity

The widespread availability of GenAI has precipitated a crisis in scientific

authorship and integrity. The ease with which these tools can generate literature

reviews, summarize findings, and even draft manuscripts challenges the definition of

a "researcher.".22

The concept of "autopoietic authorship" suggests that the authorial role is

shifting from "producer" to "system manager" or "curator," responsible for the

integrity of the human-machine system.23 This shift necessitates new ethical

guidelines. Publishers and funding bodies are increasingly requiring strict disclosure

of AI use, demanding that researchers clearly distinguish between human-generated

and AI-generated content (See Table 2).21 The risk of "hallucination"—where the AI

fabricates citations or data—is a persistent threat to the integrity of the literature base.3

Table 2: Risks to Scientific Integrity in AI-Mediated Research

Risk Factor

Description

Implication for Math

Ed Research

Mitigation Strategy

Hallucination

AI generation of

plausible but false

citations, data, or

mathematical proofs.3

Corruption of the

literature base;

dissemination of false

pedagogical theories

or invalid proofs.

Mandatory

verification of all AI

outputs; "human-in-

the-loop" protocols.

Plagiarism/Attributio

Re-hashing of existing

texts without clear

provenance; lack of

citation for training

data sources. 24

Erosion of intellectual

property; difficulty in

tracing the genealogy

of ideas.

Strict citation

standards for AI use;

requirement for

"provenance

information".21

Authorial

Authenticity

Difficulty

distinguishing human

vs. AI text; loss of

"voice".23

"The author" becomes

a curator rather than a

creator; devaluation of

scholarly writing.

Redefining

authorship to include

"prompt engineering"

and "system

management"; an

autopoietic

perspective.

Bias Amplification

Reproduction of

stereotypes in

generated content

(e.g., gender roles in

math word problems).

.11

Reinforcement of

gender/racial biases in

math education

research narratives

and materials.

Critical auditing of AI

outputs for bias; use of

diverse training data

where possible.

5. Pedagogical Epistemologies: Teaching,

Learning, and the Nature of Proficiency

The capabilities of GenAI force a re-evaluation of what constitutes

mathematical proficiency. If a machine can perform procedural tasks perfectly and

solve standard word problems instantly, what is left for the human student to learn?

This question strikes at the heart of the pedagogical enterprise.

5.1 The Obsolescence of the "Math Wars"

The "Math Wars" between proponents of procedural fluency (the ability to

carry out mathematical procedures flexibly, accurately, and efficiently) and

conceptual understanding (comprehension of mathematical concepts, operations, and

relations) have long defined the politics of mathematics education.25 GenAI renders

this binary obsolete. Tools like Photomath and ChatGPT can now automate both the

procedure and the explanation of the concept, providing step-by-step "reasoning" on

demand.19

This technological reality suggests that "procedural fluency" as a terminal goal

of education is a dead end. However, research emphasizes that procedural fluency

and conceptual understanding are intertwined; one builds upon the other.27 The

danger lies in cognitive offloading—the tendency for students to rely on the AI to

perform the cognitive labor, bypassing the "productive struggle" necessary for

building neural schemas.7

5.2 Cognitive Offloading vs. Adaptive Reasoning: The PNAS

Study

A landmark study published in PNAS provides critical empirical evidence on

this tension. The study compared students using a standard GPT-based tool ("GPT

Base") with those using a specialized tutor ("GPT Tutor") and those with no AI access.

The results revealed a complex trade-off:

1. Short-Term Performance: Both GPT Base and GPT Tutor significantly reduced

grade dispersion, effectively closing the "skill gap" by providing the largest

benefits to the weakest students during the assisted practice sessions.30

2. Long-Term Learning: However, the study found no significant effect on grade

dispersion for the unassisted exam. The reduction in the skill gap did not persist

when access to the AI was removed. More alarmingly, the results suggested that

access to generative AI tools could degrade human learning, particularly when

appropriate safeguards were absent.30

This confirms the risk of cognitive offloading: students may perform better

with the tool but learn less from the task. The AI acts as a crutch rather than a scaffold.

In contrast, other studies focusing on adaptive reasoning—the capacity for logical

thought, reflection, explanation, and justification—show more promise. For example,

in solving differential equations, students using AI tools (like MatGPT) demonstrated

significantly different adaptive reasoning patterns compared to those using

traditional methods or MATLAB.31 The AI acted as a dialogic partner that could

scaffold complex reasoning tasks, provided the students engaged in "structured

prompting" rather than passive consumption.32

5.3 Redefining Mathematical Understanding

The presence of GenAI compels a redefinition of "mathematical

understanding" itself. It is no longer sufficient to define understanding as the ability

to produce a correct answer. Understanding in the AI era must include:

1. Evaluative Judgment: The ability to discern correct from incorrect AI outputs

(handling hallucinations).33

2. Epistemic Agency: The capacity to take responsibility for the mathematical

claim, regardless of its source.34

3. Integration: The ability to synthesize AI-generated components into a coherent

mathematical argument.

4. Prompt Engineering: The skill to formulate mathematical queries that elicit high-

quality, conceptually rich responses from the AI.35

This aligns with a move toward "human-centered" authority, where the

teacher and student remain the ultimate arbiters of truth, using AI as a subservient

tool for exploration.1

6. The Political Economy of Math Knowledge:

Curriculum as Cultural Politics

The epistemological reconfiguration cannot be separated from its ethical and

political dimensions. The integration of AI into national curricula is not merely a

technical upgrade; it is a political project that defines the "ideal subject" of the future.

6.1 South Korea's "Digital Citizenship" as a Case Study

South Korea's 2022 national curriculum reform offers a potent case study of

this phenomenon. The reform emphasizes "digital citizenship" and "data-driven

scientific decision-making," positioning teachers' "data literacy" as a core

competency.13 This represents a fundamental transformation, like educational

judgment.

The curriculum's focus on "AI-based personalized learning support systems"

presupposes that educational reality can be captured through data and that

algorithmic pattern detection can provide meaningful educational insights.13 This is

an epistemological shift that redefines the teacher's expertise from "pedagogical

judgment" to "data management." Critics argue that this normalizes specific forms of

citizenship compliant with the needs of the digital economy, producing new forms of

social classification and differentiation under the guise of "customization".13 It reduces

the complexity of the learning process to measurable variables, potentially ignoring

the unquantifiable aspects of mathematical development such as creativity, intuition,

and aesthetic appreciation.

6.2 Equity, Access, and the Digital Divide 2.0

The "democratization" narrative of AI—that it provides every student with a

personal tutor—masks deeper equity issues. There is a risk of a new "digital divide"

based not just on access to hardware, but on access to superior models. High-quality,

personalized AI tutoring systems (e.g., GPT-4-based tutors with advanced reasoning

capabilities) may become the province of well-funded schools or paid subscriptions,

while under-resourced schools and students rely on generic, less capable, or ad-

supported free versions 36

Furthermore, if "weak" students become dependent on AI to perform at the

same level as "strong" students (as suggested by the PNAS study findings on skill gap

reduction), they remain epistemologically disadvantaged when the tool is removed.

True equity requires that AI be used to build capacity, not just mask incapacity. The

"hidden curriculum" of these tools also poses a threat; if AI tutors are trained on biased

data, they may reinforce stereotypes—for example, by associating advanced

mathematics with male pronouns or Western contexts.11

7. Teacher Knowledge and the Transformation of

Expertise

The role of the mathematics teacher is undergoing a fundamental

transformation. The traditional "sage on the stage" model, already eroded by the

internet, is further dismantled by AI systems that can explain concepts in multiple

ways, tirelessly and instantaneously.

7.1 TPACK and the Need for "Critical AI Literacy"

The Technological Pedagogical Content Knowledge (TPACK) framework is

being updated to include AI literacy. However, this literacy must go beyond

functional skills. Teachers need to understand not just how to use the technology, but

how it mediates the content and pedagogy.4

Teachers must possess the "didactical knowledge" to recognize the limitations

and biases of AI tools. Research shows that while GenAI bots are successful at writing

lesson plans, they differ significantly in their awareness of teaching means, often

struggling to distinguish between teaching methods, strategies, and techniques.12 A

teacher with high "Critical AI Literacy" would use the AI to generate a draft lesson

plan but would then critique and refine it, identifying where the AI's suggested

approach might lack pedagogical depth or cultural relevance.

7.2 The Displacement of Authority and "Epistemic Guiding"

The rise of AI subtly reconfigures where authority resides in the classroom.

Historically, the teacher's authority rested on content expertise and pedagogical

judgment.1 When students can query an AI for an immediate, confident answer, the

teacher's role as the primary source of information is challenged.

To maintain relevance and authority, teachers must pivot to roles that AI

cannot fulfill:

1. Epistemic Guide: Teaching students how to know, rather than what to know. This

involves guiding students in the verification of AI outputs and the construction

of valid arguments.1

2. Social Facilitator: Managing the human discourse and collaboration that AI can

simulate but not replicate. Learning is a social process, and the teacher

orchestrates the community of practice.38

3. Emotional Support: Addressing math anxiety and building confidence. Research

suggests AI can provide some emotional support, but the human connection

remains vital for fostering resilience.39

Preservice teachers are acutely aware of this shift. Surveys indicate that they

view GenAI tools like Photomath as both opportunities for engagement and threats

to traditional instruction, creating a tension that teacher education programs must

address.19

8. Human-AI Collaboration and Hybrid

Intelligence

The future of mathematics education research and practice lies not in the

replacement of humans by AI, but in human-AI collaboration. The goal is to create

"hybrid intelligence" systems where the strengths of both parties are leveraged.

8.1 Symbiotic Learning Systems

AI systems excel at processing vast amounts of data, identifying patterns, and

providing consistent feedback. Humans excel at emotional intelligence, ethical

reasoning, and contextual understanding. Effective educational environments will

integrate these distinct capabilities.38

For example, "Pedagogical AI Tools" can support broad instructional goals

(personalized learning paths, interactive engagement), while "Generative AI Tools"

provide specific, on-demand problem-solving.40 The synergy between these tools can

create a learning environment that is both efficient and deeply human. In a "symbiotic"

system, the AI might handle the routine grading and initial error diagnosis, freeing

the teacher to engage in high-leverage one-on-one interventions that address the root

cause of the misunderstanding, which is often conceptual or emotional rather than

procedural.

8.2 The Human-in-the-Loop in Research

In research, the "human-in-the-loop" is essential for ensuring validity. While

AI can generate literature reviews or analyze data, human oversight is required to

check for hallucinations, interpret nuanced findings, and ensure ethical standards are

met.41

Experimental studies have shown that "unguided human-AI collaboration"

often fails to outperform autonomous AI output, as users tend to passively accept the

AI's suggestions (a manifestation of automation bias). However, structured human-

AI collaboration—where users are guided to critically engage with the tool through

specific protocols—results in significantly higher reasoning quality.32 This suggests

that the protocol of interaction is as important as the tool itself.

9. Future Directions and the "Special Issue"

Landscape

The academic community is actively responding to these challenges,

attempting to formalize the new epistemological reality through dedicated research

avenues. The proliferation of special issues in leading journals signals the

crystallization of a new research agenda.

9.1 Emerging Research Agendas

1. Longitudinal Impact Studies: There is a critical need for long-term research to

assess the impacts of AI on retention, motivation, and equity. Studies like the

PNAS experiment 30 need to be replicated over semesters and years to

understand the cumulative effect of cognitive offloading.

2. AI-Specific Didactics: Developing and validating teaching methods that

specifically leverage AI for conceptual understanding. This includes "AI-assisted

problem posing," where students use AI to generate problems that test specific

concepts, shifting their role from solver to creator.6

3. Epistemic Agency Assessment: Creating metrics to measure "epistemic agency"

and "critical AI literacy" in students. How do we test if a student is "critically

engaging" with an AI rather than passively consuming its output?.34

4. The Ethics of Synthetic Data: Establishing protocols for the use of AI-generated

data in research. What are the reporting standards? How do we validate

synthetic findings against empirical reality?.21

9.2 Key Venues for Discourse

● Journal for Research in Mathematics Education (JRME) and Educational

Studies in Mathematics (ESM) are publishing calls for papers that address the

"critical mathematical competences" needed in the age of AI.42

● ZDM – Mathematics Education is focusing on "AI-based personalized learning"

and "AI in support of equitable mathematics education," highlighting the

sociopolitical dimensions.43

● The Annals of Applied Statistics is seeking work on the intersection of statistics

and AI, highlighting the methodological convergence and the need for rigorous

statistical evaluation of AI models.45

10. Towards a Critical AI Literacy

The integration of Generative AI into mathematics education constitutes a

profound epistemological reconfiguration. It challenges the nature of mathematical

objects, the methodology of research, and the authority of the teacher. It forces us to

ask not just "How can we use AI to teach math?" but "What is math when it can be

done by an AI?"

The analysis reveals that while AI offers the promise of personalized, efficient,

and "democratized" learning, it carries substantial risks: cognitive offloading,

epistemic displacement, automation bias, and the homogenization of mathematical

thought. The "Math Wars" of the past are over, replaced by a struggle for epistemic

agency.

The path forward requires a rejection of both uncritical techno-optimism and

reactionary prohibition. Instead, the field must embrace a critical AI literacy that

centers human agency. We must instruct students and researchers not just to use AI,

but to know with AI—to treat the algorithm not as an oracle, but as an interlocutor

whose outputs must be rigorously verified, contextualized, and, when necessary,

challenged.

The future of research in mathematics education will not be defined by the

capabilities of the machines we build, but by the wisdom with which we integrate

them into the human project of making meaning. Only by reclaiming the "productive

struggle" of meaning-making can we ensure that the algorithmic turn enhances, rather

than diminishes, the human capacity for mathematical thought.

Chapter II.

Comprehensive Guide to the Use of

Generative Artificial Intelligence in

Education and Research

1. The Epistemic Shift in Knowledge Systems

The advent of Generative Artificial Intelligence (GenAI) constitutes a

structural transformation in the architecture of knowledge creation, dissemination,

and assessment. Unlike previous technological inflections in academia—such as the

digitization of archives or the introduction of Learning Management Systems (LMS)—

GenAI does not merely store or transmit information; it synthesizes it. This capacity

for synthesis, simulation, and generation presents a paradox that defines the current

educational and research landscape: the technology offers unprecedented

mechanisms for personalized learning and scientific acceleration while

simultaneously destabilizing the traditional pillars of academic integrity, copyright,

and verification.

This report provides an exhaustive analysis of the integration of GenAI into

education and research ecosystems. It moves beyond the initial reactionary phase of

2023—characterized by bans and panic over plagiarism—into the mature "Integration

Phase" of 2025. This phase is defined by the development of robust governance

frameworks, such as UNESCO’s human-centered guidance and the European Union’s

legislative strictures, as well as the emergence of sophisticated pedagogical and

methodological applications.

The analysis synthesizes data from global policy documents, institutional case

studies (including Harvard, UCL, and the University of Edinburgh), and empirical

research on tool efficacy (comparing ChatGPT, Bing, and specialized academic

agents). It explores the granular realities of implementing "Intelligent Tutoring

Systems" like Khanmigo, the workflow revolution in "Qualitative Data Analysis"

using Large Language Models (LLMs), and the complex ethical "arms race" between

text generation and detection. The findings suggest that the successful integration of

GenAI requires a fundamental re-skilling of the academic workforce, shifting the

focus from information retrieval to "critical AI literacy," prompt engineering, and the

rigorous verification of algorithmic outputs.

2. Global Governance and the Regulatory

Landscape

The integration of GenAI is occurring within a rapidly solidifying global

regulatory framework. The laissez-faire approach of the early deployment phase is

being replaced by structured governance that seeks to balance the utility of AI with

the protection of fundamental human rights, data privacy, and intellectual property.

2.1 UNESCO’s Human-Centered Framework

The United Nations Educational, Scientific, and Cultural Organization

(UNESCO) has established the normative baseline for GenAI in education. Its 2023

"Guidance for generative AI in education and research" is predicated on a "human-

centered approach," which asserts that the deployment of these technologies must

serve to enhance human agency rather than replace it.1

2.1.1 The Imperative of Human Agency

UNESCO’s guidance explicitly warns against the "automation of the teacher."

It posits that while AI can manage content delivery and assessment, the "pedagogical

relationship" is irreducibly human. The guidance suggests that the deployment of

GenAI must be accompanied by a massive capacity-building effort for teachers.

Educators must not only learn how to use the tools but must also understand their

underlying mechanisms to maintain authority in the classroom. This includes the

ability to audit AI outputs for bias and to decide when not to use AI.1

2.1.2 Age Limits and Developmental Appropriateness

A critical and often overlooked recommendation in the UNESCO framework

is the imposition of strict age limits. The guidance suggests a minimum age of 13 for

any engagement with GenAI tools in a classroom setting, with a recommendation to

raise this threshold to 16 for independent, unsupervised use. This recommendation is

driven by two primary concerns:

1. Data Privacy of Minors: GenAI models are data-hungry systems that harvest

user interactions to refine their algorithms. Minors are less capable of providing

informed consent for this data extraction.

2. Cognitive Development: There is a concern that early exposure to "oracle-like"

AI systems may inhibit the development of critical thinking and epistemic

resilience, leading to a dependency on algorithmic answers.2

2.1.3 The Digital Divide and Equity

UNESCO highlights that GenAI is likely to exacerbate existing educational

inequalities. The "premiumization" of AI—where the most capable models (e.g., GPT-

4, Claude 3 Opus) are behind paywalls while free versions are less capable and more

prone to hallucination—creates a two-tier system.