# On The Potential of Using Generative Artificial Intelligence for Geometry Educational Activities

Eleni Dimitriadou, Andreas Lanitis

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# On The Potential of Using Generative Artificial Intelligence for Geometry Educational Activities

Eleni Dimitriadou[0000-0001-9257-0999] Andreas Lanitis[0000-0001-6841-8065]

Visual Media Technologies Co-Lab

Department of Multimedia and Graphic Arts

Cyprus University of Technology, Limassol, Cyprus.

CYENS Centre of Excellence, Nicosia, Cyprus

ela.dimitriadou@edu.cut.ac.cy, andreas.lanitis@cut.ac.cy

## Abstract

Generative Artificial Intelligence (Gen-AI) is able of generating text, images, videos or other data, often in response to educator and student prompts. The opportunities offered by Gen-AI in synthesizing multimodal responses can be highly useful for topics where advanced visualization techniques can be beneficial, such as the delivery of Geometry classes. So far, several studies have been published highlighting the potential of Large Language Models and Gen-AI in the field of education. However, there are only a few studies focusing on Gen-AI in the dedicated field of Geometry. Unlike the existing studies on the use of Gen-AI models in education, the current survey focuses on discussing the impact, and limitations of Gen-AI models from the perspective of teachers and students allowing the reader to understand the potential and advantages of adopting Gen-AI for delivering Geometry classes, but at the same time readers are informed about the disadvantages, and risks of adopting this technology in education activity.

**Keywords:** Educators, Generative AI, Geometry, Mathematics, Students.

## 1. Introduction

From education to journalism and the arts, there is every reason to believe that Artificial Intelligence (AI) technologies, and specifically, AI generative models, are changing the ways that subject-specific content is created. An AI generative model, trained on data and powered by machine learning algorithms, is an example of something that can automatically create content ranging from text to images, movies, code, music, and other forms of media. In the
context of education, Generative AI (Gen-AI) models serve as a tool that boosts the experience of teaching and learning through the seamless generation of engaging educational content.

Generative artificial intelligence, or Gen-AI, is a kind of AI that is capable of generating text, images, videos or other data, often in response to human prompts. With the recent advances in Deep Learning and the emergence of chatbots like ChatGPT, which are based on a technology called large language models (LLMs), a significant interest has been sparked towards applying such technologies in various domains, including education. Gen-AI includes artificially intelligent systems that create various content types, including texts, images, and videos, generated from vast data learning. In education, Gen-AI technologies support the development of innovative learning tools, customize learning activities for students, and aid educators in various office tasks. Typical Gen-AI applications in education include the following: (a) Systems that learn behavior and patterns to tailor education materials depending on individual needs that enhance involvement and outcomes., (b) Generated AI materials such as instructional that follow the school curriculum and students’ unique needs, help teachers work with the students., (c) Intelligent tutoring systems that offer immediate, individualized tutoring through explanations and (d) Automated performance assessment of teachers and students.

This study focuses on the use of Gen-AI in the field of Geometry by students and teachers, as well as the opportunities and threats arising from the use of Gen-AI in Geometry. So far, there are limited studies regarding the use of Gen-AI in the field of Mathematics and Geometry. Plevris et al. (2023) conducted a comparison of three chatbots, ChatGPT-3.5, ChatGPT-4, and Google Bard, regarding the ability of such tools to provide correct answers to mathematical and logic problems. The results showed that in the test conducted ChatGPT-4 outperforms ChatGPT-3.5. Gao et al. (2023) focused on solving geometric problems using image input in a LLM (e.g., ChatGPT). More specifically, the authors use the Geometry characteristic to construct a new dataset for solving geometric problems based on GeoQA+ and Geometry3K. Recently, Parra et al. (2024), analyzed answers to high school Geometry problems in Spanish using various chatbots such as OpenAI ChatGPT, Microsoft Bing Chat (BingChat), and Google Bard. The results of their study showed that the use of chatbots to solve Geometry problems is not appropriate without the critical analysis by teachers and students, suggesting that collaboration between chatbots and students in teaching is required. Compared to the above studies, in our study we focus on the use of Gen-AI models in the field of Geometry through an analysis of the relevant literature. Furthermore, we provide a detailed analysis of the impact, advantages, disadvantages, and limitations/treats of adopting Gen-AI in Geometry-related educational activities.
In the remaining sections, we present a literature review on Gen-AI in Education (Section 2) and describe the main Gen-AI models used in Education, along with typical uses such as technologies by Educators and Students (Section 3 and Section 4 respectively). In Section 5, we analyze the impact of Gen-AI in Geometry (Section 5). Conclusions and plans for future work are presented in Section 6.

# 2. Literature Review

In this section, the use of Gen-AI in education, the use of Gen-AI for teaching mathematics, and more specifically the use of Gen-AI for assisting the delivery of Geometry lessons are presented.

## 2.1 Gen-AI in Education

So far, several literature reviews on the integrations of Gen-AI have already been published. Such studies indicate an increasing attention to the potential educational opportunities and current issues of implementing Gen-AI in learning and assessment processes. The existing literature reviews aim to summarize the main efforts and results made by many authors and targeted on the potential possibilities, challenges, and ethical considerations of introducing generative artificial intelligence into teaching activities.

Bahroon et al. (2024) present a comprehensive analysis based on bibliometric and content analysis. The researchers used a range of 207 research papers to overview Gen-AI in such segments of education as medical and engineering education. The authors highlight that there is exponential growth in the Gen-AI sector from 2018 to 2023. Also, the authors emphasize that the use of Gen-AI tools in educational programs is important, even as these tools raise concerns about data privacy, algorithmic bias, and the replacement of human instructors by intelligent systems. Olga et al. (2023) provides several examples of the implications of technologies like large language models on education. Specifically, the authors explored how C-LLMs (Comprehensive Large Language Models) could be used to review and assess complex student work; while they acknowledged many promising applications, there were intrinsic limitations based on the Gen-AI's reliance on language corpora and the ultimate expression of that representation through binary notation. Overall, while the authors supported many of the possible applications, they noted the significant hole in the understanding of the long-term impacts of Gen-AI on education, arguing for further empirical research and policy development.
Abunaseer et al. (2023) focused on the potential and efficacy of Gen-AI technologies. The authors further reviewed the available literature to identify other studies conducted on this subject. Abunaseer et al. (2023) discuss the impact, limitations, challenges, and concerns of Gen-AI in education. Their study states that Gen-AI can improve learning efficiency, provide personalized learning support and automate administrative tasks. However, the collection and analysis of large amounts of student data, along with student privacy, are issues that need to be carefully considered when implementing Gen-AI in education in which educators, parents, and policy makers should be actively engaged.

These studies generally point to the growing recognition of the potential of Gen-AI in education. The authors in the reviewed articles, however, note the reality of the challenges these technologies present. As such, the continued research and consultations between educators, policy makers, and technologists remain paramount as the Gen-AI technologies continue to develop. The reviewed literature consistently reflects the significant participation of these stakeholders, especially on the making of guidelines that ensure AI technologies' ethical use to advance, rather than limit educational quality and equity.

## 2.2 Gen-AI in Mathematics

In this subsection, Gen-AI techniques targeting the delivery of mathematical concepts are described. Barana et al. (2023) used mathematical problem-solving activities with ChatGPT. Specifically, their study involved 40 university students who were asked to solve six math problems in groups using ChatGPT. Through the analysis of ChatGPT solutions and tutors' questionnaires, the results of this study showed that the use of ChatGPT supported students' critical thinking process, complementing their collective reasoning. Therefore, Barana et al. (2024) emphasize the innovation and potential of such tools in solving mathematical problems.

Pelton et al. (2024) investigate the role of ChatGPT-4 in education of mathematics teachers. The authors state that ChatGPT-4's answers are improved in the field of mathematics thus gaining users' trust in ChatGPT-4's functions. Pelton et al. (2024) emphasize the potential of ChatGPT-4 as a collaborative teaching tool rather than a replacement for human educators.

Dahal et al. (2024) examines the effectiveness of Gen-AI chatbots in solving mathematical problems by students to teachers at all levels. Generative Chatbots like ChatGPT, Google Bard, Bing Chat, and Wolfram Alpha can solve mathematical problems with a satisfactory degree of accuracy. Although these tools can provide step-by-step solutions to students, Dahal et al. (2024) state that human intelligence still surpasses artificial intelligence. The authors also
emphasize that students should continue to interact with their teachers to develop their
cognitive skills in mathematics.

Zhao et al. (2022) investigate the use of GPT-3 in the elementary math curriculum offered by Khan Academy and develop a prototype system MathyAI. The results showed that their method compared to GPT-3 achieved higher accuracy in providing hints. Zhao et al. (2022) focused mainly on the potential educational application of the MathyAI tool.

Based on the finding from the literature review in this subsection, the use of AI models has brought about a significant breakthrough in various mathematical areas, such as proof generation, complex equation solving, and confirming previously unknown theorems. Such information can only be known through machine learning and deep learning-based models. Furthermore, Gen-AI helps improve mathematics education by allowing personalized pathways as it is capable of understanding students well enough so that it creates individualized problems targeting specific weaknesses for optimal learning situations to be enhanced and to help students become more successful on their tasks at school. However, doubts revolve around the dependability of mathematics results that AI yields, how there might be too much trust in AI, and even the biases from the data that it operates on seeping through into the final product that could undermine the integrity of mathematical research and education.

## 2.3 Gen-AI models in Geometry

It is important to note that Geometry is never independent and self-contained within the mathematics field when it comes to education. Unlike the other branches of mathematics, Geometry has a very strong visual and spatial component (Zawacki-Richter et al., 2019), therefore it can be analyzed very well through Gen-AI models so as to train students and help teachers and this is the main reason that this study presents the field of Geometry as a different part from mathematics.

Driven by the revolutionary capabilities of Gen-AI, the field of Geometry is currently experiencing a remarkable metamorphosis. This state-of-the-art technology not only provides solutions to intricate geometric problems but also leads to groundbreaking innovations in design. So far, only few attempts regarding the use of Gen-AI in the field of Geometry are reported in the literature. Parra et al. (2023) perform an analysis of the answers provided by three chatbots (OpenAI ChatGPT, Microsoft Bing Chat (BingChat), and Google Bard) in the case of solving a high school Geometry problem. This study focuses on Spanish to investigate their abilities of chatbots in the Geometry lesson. DeepMind's AlphaGeometry system serves as a remarkable demonstration of its broader potential, combining language models with
symbolic thinking. This groundbreaking system achieved extraordinary results by successfully solving 25 out of 30 Geometry problems at the level of the International Mathematical Olympiad, surpassing previous methods by a wide margin (Sinha et al., 2024).

So far, there are Tool-augmented Large Language Models (TALMs) that have explored solving mathematical problems such as ART (Paranjape et al., 2023), OlaGPT (Xie et al., 2023), however these models focus on mathematical problems like arithmetic and algebra. Das et al. (2024), present the MATHSENSEI which is a TALM that provides support and solutions to various mathematical problems including Algebra, Geometry, Probability and more. The results of their study showed that MATHSENSEI achieves a 13.5% improvement compared to GPT-3.5-turbo in mathematics.

Since in literature only a few reported attempts on the use of Gen-AI tools in the field of Geometry exist, there is need for systematic efforts to promote the delivery of AI-based Geometry lessons through development of specialized platforms which integrate Gen-AI tools explicitly designed for Geometry education. Other factors that need to be further investigated in relation to the delivery of Gen-AI-based Geometry lessons are the effectiveness in improving learning outcomes, that need to be well documented and reported so as to help drive further developments on this area and offer valuable insights for educators and researchers on how to use and scale the use of Gen-AI in Geometry-related educational activities.

### 3. Gen-AI models in Education

A comprehensive list of current Gen-AI models that are significantly impacting the field of education are presented in Table 1, along with the main features, advantages and disadvantages of each model. Among the models presented in Table 1, the ones that have been used extensively for Mathematics, and Geometry education are clearly marked. The landscape of Gen-AI in education is dynamic and constantly evolving, with researchers continually developing and exploring new models. As this field progresses, the capabilities and applications of these models are expected to expand further, offering even more transformative potential in educational contexts.
<table><caption>**Table 1.** Overview of Gen-AI Models in Education</caption><thead><tr><td>Gen-AI Model</td><td>Purpose</td><td>Advantages</td><td>Disadvantages</td></tr></thead><tbody><tr><td>GPT-4*</td><td>Enhance learning through personalized tutoring and content generation.</td><td>Personalized learning, scalable support, diverse applications (e.g., writing help) (Fidaus et al., 2023).</td><td>Potential bias in responses (Fidaus et al. 2023), deficiency in deep comprehension of concepts (e.g., lack of consciousness, lack of intuition) (Shahri et al., 2024)</td></tr><tr><td>GPT-3**</td><td>Provides immediate diagnosis of students' weaknesses and helps automate routine tasks.</td><td>High-quality text generation, versatile applications, scalable to many tasks (Brown et al., 2020), rapid diagnoses of the students' deficiencies (Prieto-Andreu et al., 2023)</td><td>High computational cost, potential for biased or incorrect outputs (Bender et al., 2021), biases related to race, gender (Prieto-Andreu et al., 2023)</td></tr><tr><td>BERT*</td><td>Improve comprehension tasks and language understanding.</td><td>Superior comprehension and context understanding, high accuracy in retrieval tasks (Devlin et al., 2018).</td><td>Limited capabilities, not suitable for all generative tasks (Wang et al., 2024).</td></tr><tr><td>T5**</td><td>Convert various text-based inputs into desired textual outputs for educational tasks.</td><td>High versatility, strong performance on diverse tasks, ease of fine-tuning for specific needs (Raffel et al., 2020). Provides question answering, summarization, translation (Fox 2022).</td><td>Data efficiency, high resource usage for training, potential inaccuracies in nuanced contexts (Fox 2022).</td></tr><tr><td>UniLM</td><td>Combine capabilities for natural language understanding and generation.</td><td>Effective for both generation and comprehension tasks, high performance (Dong et al., 2019).</td><td>Complex training process, high resource requirements (Dong et al., 2019).</td></tr><tr><td>BART**</td><td>Improve comprehension and generate coherent text for summaries and translations.</td><td>Strong performance on text generation and summarization, versatile (Lewis et al., 2020).</td><td>Computationally intensive, requires fine-tuning for specific tasks (Liu et al., 2019).</td></tr><tr><td>Deep Speech</td><td>Facilitate language learning and</td><td>Improves accessibility, aids</td><td>Requires large datasets for training, performance may vary</td></tr></tbody></table>
<table><thead><tr><td>Gen-AI Model</td><td>Purpose</td><td>Advantages</td><td>Disadvantages</td></tr></thead><tbody><tr><td></td><td>accessibility through speech recognition and synthesis.</td><td>language learning, (Hannun et al., 2014).</td><td>with background noise (Amodei et al., 2016).</td></tr><tr><td>WaveNet</td><td>Generate natural and high-quality speech for educational content.</td><td>Superior audio quality, adaptable to various languages and styles (van den Oord et al., 2016).</td><td>Requires significant computational resources, time-complexity (Rethage et al., 2018)</td></tr><tr><td>DALL-E**</td><td>Aid in visual learning and creative assignments through image generation from textual descriptions.</td><td>Stimulates creativity, visual aid for complex concepts, enhances engagement, generalize for zero-shot image generation (Ramesh et al., 2021).</td><td>Ethical concerns regarding image content, not providing realistic images, requires large datasets (Singh et al., 2022).</td></tr><tr><td>CLIP**</td><td>Enhance visual learning by linking textual descriptions to images.</td><td>High versatility in linking images and text, effective for a wide range of tasks (Radford et al., 2021) and understands the multimodal hate speech (Arya et al., 2024)</td><td>Requires extensive training data, potential biases from training data.</td></tr><tr><td>OpenAI Codex*</td><td>Facilitate coding education and automation through natural language programming.</td><td>Simplifies coding for beginners, enhances productivity, supports code completion (Finnie-Ansley et al., 2022).</td><td>Limited to supported languages, potential for incorrect or inefficient code (Brown et al., 2020).</td></tr></tbody></table>

* Gen-AI models used for Mathematics, ** Gen-AI models used for Geometry.

Among the Gen-AI models mentioned in Table 1, ChatGPT is the most known example Chat Generative Pre-trained Transformer (ChatGPT) was released by OpenAI and has the potential to be an effective tool in education. ChatGPT has the ability to generate human-like texts, it's fast, and the generated text cannot be detected as plagiarism (Adheshola et al., 2023). There are concerns about the students' efficient assessment based on traditional methods on writing and theory. Furthermore, the predecessor to ChatGPT, GPT-3, has been used in the development of tutoring systems, learning modules, and even the simulation of conversations with figures. In addition to ChatGPT, other AI models have furthered the knowledge of advanced education in some distinct abilities (Ijaz 2023). For example, Jasper is primarily an intelligent assistant for content marketing, but it has been altered to assist students in terms of
writing assignments, generating ideas for projects, and learning languages. EduBirdie is a company that uses AI to help students in their writing through giving tools that check for grammar, syntax etc. Furthermore, Socratic is an AI tool introduced by Google. It was designed for providing assistance with students' homework or study questions. It uses intelligence in analyzing questions and even aiding in their stepwise explanation as well as aiding in solving problems. These examples demonstrate the potential that Gen-AI models hold in transforming the realm of education. The advantages of employing AI models using customizable settings are that they can personalize the learning experience in the sense of changing content in order to suit the students' individual needs so that they can achieve their optimum potential. This way of learning would fit the varied learning styles and would lead to better involvement and understanding among the students.

In mathematics and Geometry, AI models such as GPT-4 have been consistently utilized to offer personalized teaching and provide detailed, step-by-step solutions to complex problems. So far, the AI tools which have been used extensively in mathematics education is the BERT (Zhang et al., 2022; Shen et al., 2021). Zhang et al. (2022) examine the problem of automatic grading of short answers regarding the students' answers to mathematical questions. Their methodology was based on the MathBERT model which is a variant of the BERT tool and an in-context learning method that provides examples as input to the language model to promote generalization to new questions. The results of their study showed that the in-context learning method have improved scoring accuracy compared to existing studies. Similarly, Shen et al. (2021) used MathBERT created by pretraining the BASE BERT model for prekindergarten to college graduate level. The results of their study showed that MathBERT pretrained with 'mathVocab' outperforms existing methods as well as MathBERT trained with BASE BERT vocabulary. In addition, the models T5, ChatGPT 3.5 -Turbo, BART (Maity et al., 2023), OpenAI Codex (Drori et al., 2022), DALL-E and CLIP have been used in mathematics and Geometry education. DALL-E is focused more on image generation and has been used to visualize geometric shapes for understanding geometrical figures. Also, CLIP can be used to generate and interpret Geometric images too.
# 4. Uses of Gen-AI models in Education

Gen-AI solutions have been employed both by educators and students as part of educational activities as described in the following sections.

## 4.1 Gen-AI Uses for Educators

Gen-AI tools have been used to assist the teacher in tedious and time-consuming tasks such as generating learning objectives (Sridhar et al., 2023), or in the case of online courses, to manage the possibly high volume of questions posted on the discussion forum. Table 2 presents the main Gen-AI tools uses for Educators, while subsequent sections elaborate on those uses.

<table><caption>**Table 2.** Gen-AI Uses for Educators.</caption><thead><tr><td>Gen-AI Uses for Educators</td><td>Related Work</td></tr></thead><tbody><tr><td>Creating Quizzes.</td><td>Lee et al. (2023), Bhat et al. (2022), Blobstein et al. (2023), Dijkstra et al. (2023), Hwang et al. (2023).</td></tr><tr><td>Student Work Assessment.</td><td>Mizumoto et al. (2023), Moore et al. (2022), Pinto et al. (2023).</td></tr><tr><td>Teacher training.</td><td>Lee, Lee et al. (2023), Markel et al. (2023), Sailer et al. (2023).</td></tr><tr><td>Generation/Retrieval of Educational Content.</td><td>Sridhar et al. (2023), Roy et al. (2023)</td></tr><tr><td>Facilitating the use of other educational tools Improving the efficiency of using Gen-AI tools.</td><td>Bulusu et al. (2023).</td></tr><tr><td>Generation of answers to exercises as prompt for teacher-student discussion.</td><td>Pinto et al. (2023), Sarsa et al. (2022).</td></tr></tbody></table>

### 4.1.1 Creating quizzes

Lee et al. (2023) and Bhat et al. (2022) present examples of Automatic Question Generation (AQG). Lee et al. (2023) presents a prompt engineering protocol to produce valid questions with ChatGPT. Bhat et al. (2022) applied a multilingual model to generate questions for a data science course. Solutions such as the above have the potential to provide feedback and also to increase engagement during the learning phase by enhancing textbooks with assessments. Blobstein et al. (2023) focus on generating question – answer pairs of various difficulty while targeting higher cognitive levels, as measured by a well-known educational
theory, the Bloom taxonomy (Forehand, 2010). The researchers use the GPT-3 model and give
as inputs a textbook extract, the aforementioned taxonomy and some prompting extras, such as
an explicit instruction to the model to additionally offer the sequential thought process for its
answer, as well as to create questions that address higher Bloom taxonomy learning objectives
aiming at enhancing skills such as analysis and evaluation.

Another automatic solution for the generation of relevant quizzes for educational texts is the EduQuiz application, which generates reasonable multiple-choice question (MCQ) based on the GPT-3 technology (Dijkstra et al., 2023). In addition, Feng et al. (2024) explore the MCQ, where they focused on generating distractors (incorrect options) of good quality (i.e., distractors that target common errors or misconceptions among students). This task is particularly labor and time-intensive for teachers. Feng et al. (2024) experimented with ChatGPT and other LLM-based approaches on a real-world mathematics-related dataset and found that selecting a few example MCQs as input to ChatGPT and teaching it to generate outputs for a new task by learning from these examples was the most effective method. Finding good distractors for mathematics-related content is considered a difficult task, so while the distractors generated where valid, the methods used were not so adept at anticipating common errors or misconceptions among students. Finally, Hwang et al. (2023) use GPT-3.5 to create MCQs in introductory chemistry and biology, incorporating Bloom's taxonomy in the prompts.

4.1.2 Student Work Assessment

Mizumoto et al. (2023) used the GPT-3 model for the task of automated essay scoring (AES) to score 12,100 essays of the Non-Native Written English (TOEFL11) exam and results have shown a certain level of accuracy and reliability, such that it can be assumed that this model can be used as a supporting tool for human evaluators. The same model has also been used experimentally in Moore et al. (2022) to evaluate the answers of chemistry students and it has been shown that the model matched the human-expert evaluation in 32% of answers. However, Pinto et al. (2023) used the ChatGPT to automate the correction of free-format answers of software professionals in a training process, in questions such as “*Explain in your words what you understand about caching in REST applications*”. The optimal prompt to ChatGPT included the question, the answer of a human expert, the student’s response and instructions to ChatGPT that included some very basic grading instructions and also a request to provide an explanation for the grading. The tool gave feedback with which subject experts tended to agree.
### 4.1.3 Teacher Training

Gen-AI can also assist in teacher training programs, which often face criticisms for placing greater emphasis on theoretical knowledge rather than practical experiences. Lee, Lee et al. (2023) provide a simulation of a problematic scenario, on the basis of student agents (simulated students). The answers of the simulated students consider that a student has a persona, which is created using GPT-4. Markel et al. (2023) presents another similar application, named GPTeach. This tool is based on a GPT model that can create simulated students, allowing simulated teacher-student interactions. The GPTeach interface provides the teacher with information such as a session description and learning goals and connects with GPT-3 via an API call to generate student responses following the teacher's messages. The descriptions of various student personas can be inserted in the prompt. Similarly, Sailer et al. (2023), that proposes using a Gen-AI tool to provide pre-service teachers with simulation-based training to learn to deal with diversity and heterogeneity in classrooms.

### 4.1.4 Generation/Retrieval of Educational Content

Gen-AI tools have been used to assist teachers in tedious and time-consuming tasks such as generating learning objectives (Sridhar et al., 2023), or identifying education content within online videos. For example, Roy et al. (2023) use video analysis algorithms, leveraging both visual and audio cues, to identify if a video contains educational content and to describe the nature of the content (for example, if it is age-appropriate and if it is about a specific topic of interest).

### 4.1.5 Other Uses

Since the task is challenging, such tools incorporate automatic caption generation tools, which fall into the category of Gen-AI. Sometimes, Gen-AI-based solutions make it easier for teachers to use other pedagogical tools, reducing the overhead. For example, Bulusu et al. (2023), uses GPT-4 to produce graphs from natural language commands for mathematical pedagogy.

The LLM formulates a query that is appropriate to be passed into a mathematical solver, then based on the solver's output creates both an explanation and a graphing expression to be passed into a graphing tool that outputs the graph. Also, Pinto et al. (2023) and Sarsa et al. (2022) investigate the use of code generation tools, such as OpenAI Codex in enhancing the quality of computer programming courses and the computational thinking skills of students.
OpenAI Codex can be used not only to generate novel introductory programming exercises but also in providing comprehensive and accurate explanations of the code, which is very useful as a prompt for a discussion between a teaching assistant and a student.

## 4.2 Gen-AI Uses for Students

Gen-AI solutions have been employed and tested for the purpose of assisting students, both by automatically providing questions and problems to solve and by providing feedback regarding their answers (See Table 3).

<table><caption>**Table 3.** Gen-AI Uses for Students.</caption><thead><tr><td>Gen-AI Uses for Students</td><td>Related Work</td></tr></thead><tbody><tr><td>Personalized learning.</td><td>Pesovski et al. (2024), Pataranutaporn et al. (2022), Xu et al. (2024), Leong et al. (2024),</td></tr><tr><td>Tutoring</td><td>Jahanbakhsh et al. (2023), Kiesler et al. (2023), Savelka et al. (2023).</td></tr><tr><td>Generation of summarized revisions.</td><td>Asthana et al. (2023), Rahman et al. (2024), Wilis et al. (2016).</td></tr><tr><td>Prompt engineering as a learning activity.</td><td>Knoth et al. (2024), Denny et al. (2023), Walter (2024).</td></tr></tbody></table>

### 4.2.1 Personalized Learning

Online courses platforms such as Khan Academy and portable educational applications such as Duolingo make use of Gen-AI to create personalized experiences, allowing students to learn at their own pace and providing, among others, personalized learning plans (Mello et al., 2023).

Towards the goal of achieving more personalized learning, Pesovski et al. (2024) presents a tool that generates accompanying learning materials for different style and related multiple-choice questions with the use of OpenAI's API, as part of a Learning Management System (LMS). The inputs of this module are the basic class materials uploaded by the professor, as well as the content covered and the learning outcomes. The style of writing of the additional text is selected by the student, who chooses between a variant that resembles a computer science teacher and some variants inspired by pop-culture characters. The approach attempts to increase motivation, based on each students' preferences and analysis of its usage indicates that utilizing several versions of educational resources enhances students' study time. In a similar scope, a virtual instructor that resembles a person one likes or admires can be generated
by Gen-AI methods (in particular, text-to-audio, audio-to-video and video-to-video techniques)
to narrate educational videos (Pataranutaporn et al., 2022).

According to Xu et al. (2024), Gen-AI gives learners through an online language learning
application the ability to explicitly request personalized exercises. The concept is called
learner-initiated personalization and is associated with self-directed learning. The learner might
input the topic of interest, or the grammar concept he wants to train on, or even the learning
process (such as “words that are hard to spell” or “sentences for first-year students”). Leong et
al. (2024) investigate the effect of using LLMs for personalized content creation, specifically
for providing individualized examples to learn new vocabulary in the context of an online
language learning app, was measured. Contrary to the related aforementioned work, the
researchers have found no significant improvement regarding learning performance.

4.2.2 Tutoring

Gen-AI can also be used for tutoring services by providing answering students’ questions,
usually in the context of online learning. Jahanbakhsh et al. (2023) present the design and
implementation of a GPT-powered question answering system used at Course Hero. Emphasis
was given to the presence of step-by-step explanations in the generated answers, since this is a
critical feature according to the users of the app. Explanations generated by GPT lead to 75%
lift in users’ approval of the answer. Another finding was that GPT tended to provide shorter
answers to MCQ questions, so for this kind of questions an explicit instruction was given when
prompting the model, to provide step-by-step explanations.

Similarly, Kiesler et al. (2023) found that responses of GPT to students seeking help with
their introductory programming tasks contained textual explanations most of the time. In this
case, the model was fed with erroneous student solutions to programming tasks and the prompt
“what’s wrong with my code”. An improved version of the code was offered in 2/3 of the cases,
but in 2/3 cases the model’s answer also contained some misleading aspects.

As a step towards providing better answers to students’ questions, those can be annotated
by an LLM (either GPT-4 or GPT 3.5) as falling to several question classes. Savelka et al.
(2023) focused on questions of students in a programming course. The questions were
annotated as (a) debugging-related, (b) queries for code implementation, or (c) of an
understanding nature. The questions of the students were real questions asked in another Gen-
AI-based tool created by the authors (which they have presented in previous work), named
CodeHelp.
### 4.2.3 Generating Summarized Revisions

A different dimension regarding the possible uses of Gen-AI to enhance student learning is presented by Asthana et al. (2023). Asthana et al. (2023) focus on online courses and argue that segmenting lectures in topically coherent parts, which is done using GPT-4, and extracting for each segment (which they call “moment”) metadata such as a summary, key definitions, examples, questions, can result in high-quality summarized revisions, which can also be self-paced, for the whole course. However, the latter stages of their conceptualized pipeline are not yet implemented. Similarly, Rahman et al. (2024), examine the creation of AI-generated visual and textual summaries from the lecture video segments to facilitate the lecture video navigation for students and instructors. A visual summary includes a set of images that represent the content in the video segment while a textual summary includes a set of keywords in the video segment. The results of their study showed that the proposed methodology is acceptable by the users as it has facilitated their navigation in the video lectures and learning for the students. On the other hand, Wilis et al. (2016) examines the automatically generating educational question-answer using key phrases extraction techniques. The authors evaluated their Gen-AI model by comparing it to questions-and-answers created by education experts. The results of their study showed that their generative AI model can better generalize key phrases created by education experts than traditional ones.

### 4.2.4 Prompt Engineering as a Learning Activity

AI model uses a prompt serves as an instruction to generate the intended outcome. The role of prompt engineering is important as their goal is to improve the quality of responses without many changes in parameter. Giving examples helps the model find answers close to the examples thereby improving the quality of the answers (Chen et al. 2024). Knoth et al. (2024) examine the role of non-experts (students) on the use of LLM artificial intelligence systems in their prompt engineering skills. The results of their study demonstrate that higher-quality prompt engineering abilities have an impact on the quality of LLM output, thus emphasizing that prompt engineering is a required skill for using Gen-AI tools. Also, the results of their study indicated that some aspects of AI literacy can be crucial for both the successful integration of LLMs into education and for faster, higher-quality engineering. Denny et al. (2023) investigates the capability of Copilot, which is a tool for automatically generating source code from natural language problem explanations to enhance the computational thinking skills of students. They propose that prompt engineering, especially iteratively prompting the
tool when it initially fails, is a way of interaction that constitutes a potentially useful learning activity. Walter (2024) explores the role of artificial intelligence in higher education focusing on an in-depth understanding of prompt engineering methodologies, critical thinking skills, AI literacy, challenges, implications and opportunities. The author focuses on the benefits of prompt engineering in the learning process. In particular, Walter (2024) states that the lack of comprehensive training in the capabilities of AI for students can lead to misuse of the tools as they cannot recognize how to integrate these technologies in their academic work. Prompt engineering can act as a pedagogical tool as it has the ability to turn artificial intelligence into an interactive tool that helps students gain a deeper understanding of learning. Furthermore, it enables students not only to engage but also to improve their critical thinking. Students can become more aware of the limits of artificial intelligence which can enhance their AI literacy.

## 5. Analyzing the Impact of Gen-AI in Geometry Education: A SWOT Analysis

Gen-AI is one of today's significant issues, raising the question of whether it is useful to use AI tools in a school classroom. Specifically, the goal is to understand the strengths, weaknesses, opportunities and threats of using Gen-AI for geometry education. Based on the literature survey presented in the previous subsections, it is clear that the using Gen-AI in Geometry education has several advantages, but at the same time it involves risks that may jeopardise the learning efficiency and experience. In this section, a SWOT analysis was carried out by analyzing observations from the literature, along with the analysis of experiences derived by using Gen-AI in Geometry education. These observations are presented in a SWOT analysis in Table 4, followed by a discussion that focuses on Geometry education.

<table><caption>**Table 4.** SWOT Analysis for Gen-AI in Geometry.</caption><thead><tr><th>Strengths</th><th>Weaknesses</th></tr></thead><tbody><tr><td><ul><li>I. Always accessible by everyone/Instant feedback.</li><li>II. Teaching Material Generation.</li><li>III. Support Critical Thinking.</li><li>IV. Multi-media Responses.</li><li>V. Performance Evaluation.</li></ul></td><td><ul><li>I. Cheating/Plagiarism.</li><li>II. May provide wrong material/responses.</li><li>III. Not comparable to average humans in terms of mathematical reasoning.</li><li>IV. Subscription cost.</li></ul></td></tr><tr><th>Opportunities</th><th>Threats</th></tr><tr><td><ul><li>I. Support Remote teaching.</li><li>II. Improved 3D Visualization.</li><li>III. Personalized Content.</li><li>IV. Improving Teaching Practises.</li></ul></td><td><ul><li>I. Replacing teachers.</li><li>II. Students work in isolation.</li><li>III. Teachers/Students rely too much on it.</li><li>IV. Privacy issues.</li></ul></td></tr></tbody></table>
# 5.1 Strengths

## I. Always accessible and Instant feedback.

AI models can create geometric shapes, prove theories and even discover new properties. For example, Convolutional Neural Networks (CNNs) have shown promise for recognizing and classifying geometric patterns which also has applications in areas such as computer vision or even robotics (Schneider & Weil, 2008). Gen-AI has great future prospects in teaching Geometry. Interactive models created on AI-driven platforms enable students to explore various aspects of Geometry and make them more concrete. Dynamic Geometric Constructions Tools allow students to test properties as well as theorems thus enhancing their understanding. Moreover, one can note that these processes individualize education through such activities as task generation and provision of customized feedback (See Figure 1) that help develop retention skills in Geometry (Luckin et al., 2016). Gen-AI tools are always accessible, providing instant feedback to students, which helps them continually practice and improve at their own pace and in a way appropriate with their learning style (Kadaruddin 2023).

<figure><img src="image_3.png" /><figcaption>**Figure 1:** Gemini model provides instant feedback in Geometry. (a) Primary education., (b) Secondary education., (c) Tertiary education. We observe that for simple questions in primary, secondary, and tertiary education, the Gen-AI tool Gemini provides correct answers.</figcaption></figure>
## II. Teaching Material Generation

ChatGPT was employed for the preparation of teaching materials, specifically using ChatGPT-3.5 for the generation of quizzes (Jauhiainen et al., 2023). One of the remarkable strengths of Gen-AI in Geometry education is its capability to generate tailored teaching materials. Through advanced algorithms, Gen-AI can create customized worksheets, visual aids, and interactive simulations that align with the curriculum. This ability not only saves educators time but also ensures that materials are relevant to the specific needs of their students. For example, Gen-AI can produce varied geometric problems based on different difficulty levels, allowing teachers to provide differentiated instruction. Consequently, this promotes a more effective learning experience and helps students grasp complex geometric concepts more efficiently.

## III. Support Critical Thinking

The effectively utilizing Gen-AI, students can progress through Bloom's taxonomy. Students can start by remembering and understanding essential curriculum concepts, then move on to applying, analyzing, and evaluating complex learning scenarios. This leads to creating new knowledge through critical thinking and deep learning (Jauhiainen et al., 2023).

However, it should be highlighted that based on the interaction with these tools, it is possible to draw the conclusion that it is inappropriate to use chatbots to answer geometry problems without critical analysis from educators and pupils. More specifically, the use of Gen-AI tools in geometry lessons can give rise to three different types of errors. The first type is construction errors, which involve a mismatch between the textual response and the actual geometric figures including their graphical representation. The second type is conceptual errors, which relate to incorrect definitions (e.g., mixing units of length with units of angle measurement). The third type is contradiction errors (Parra et al., 2023). As a result, systematic assessments of Gen-AI performance support the ongoing development of more advanced and effective Gen-AI systems, which can be seamlessly integrated into educational practices in the future to enhance learning outcomes.

## V. Multi-media Responses

Gen-AI can support multi-media responses, such as visual, text, and animated formats, enhancing the learning experience when is effectively incorporated into the curriculum by making the students more engaged in the learning process (Wood et al., 2024).
Gen-AI is designed to be useful for many fields, with the optimization on Geometry and it could help revolutionize not just the practical, but also theoretical grounds and tackle complex human-unachievable or impossible Geometry problems without assistance. There are several examples as AI models can create and examine multi-dimensional visual intuition on higher dimensions' spaces, a capability to visualize geometric shapes etc, vital in fields such as physics, and engineering (Schneider & Weil, 2008). A further benefit of Gen-AI can be observed on the field of geometric design and architectural tasks, where AI is able to produce novel Geometry patterns which certainly enhance creativity in related areas (Luckin et al., 2016). All those solutions can help both teachers and students when striving with the solutions of problems that exist in Geometry, and one may also consider that in the future, AI may also help students with disabilities.

The use of Gen-AI tools in the classroom has potentially valuable applications. One such application could be critically enhanced analysis, supported by educators. This would allow pupils to discuss and study Geometry concepts (characteristics, properties, etc.) in a practical way (Parra, V et al., 2023). Additionally, using Gen-AI models, more specifically image generative models, the visualization of geometry problems may be illustrated by figures (See Figure 2) or even a short animation. This will be easier for learners to comprehend than previous pure-text responses (Li, H. et al., 2024).

<figure><img src="image_4.png" /><figcaption>**Figure 2:** A simple example of images generated by ChatGPT-4 model.</figcaption></figure>

## V. Performance Evaluation

Shin et al. (2022) highlights the use of artificial intelligence for automated assessment of students on learning outcomes through computerized formative assessments. For example, the authors state that the use of computerized formative assessments enables educators to evaluate
students more frequently, and more accurately as traditionally the majority of educators rely on their judgment which can be subjective. Baguio et al. (2021) mentions that using the Kahoot! for formative assessment, has a positive impact on students' performance and motivation in Geometry in grade 8 learners'. Studies show that using the Gen-AI tools for mathematic word problem-solving exerted a positive effect on the Geometry learning performance of the students, suggesting that the proposed system can help in improving students' learning efficiency (Hwang and Utami, 2024). Given the multimodal capabilities of some Gen-AI models, the generated learning materials for subjects such as Geometry can also include figures that act as visual aids (Li et al, 2024).

Gen-AI facilitates automatic performance evaluation in Geometry, offering immediate feedback that is essential for student growth. Traditional assessment methods often delay feedback, which can hinder learning. In contrast, AI-driven evaluation systems provide real-time insights into student performance, identifying areas of strength and weakness (Zhang & Jia, 2017). This immediate feedback loop enables educators to tailor their instruction based on student needs, fostering a more responsive teaching approach. Moreover, Gen-AI can analyze patterns in student responses, offering educators valuable data that informs instructional strategies and enhances overall teaching effectiveness.

## 5.2 Weaknesses

### I. Cheating and Plagiarism

There is concern about cheating and plagiarism from students using Gen-AI tools. With easy access to Gen-AI systems, students may be tempted to use them to submit work that they have not created themselves. As a result, ethical issues are created for the end users and the development of these technologies (Akkaş et al., 2024). According to previous studies it is not yet clear whether Gen-AI tools can assist solve mathematical problems or create personalized problems as they can be effective in solving mathematical problems but there is still a concern regarding the level of authenticity (Beauchamp et al., 2024). This can hinder their development of problem-solving skills and lead to a lack of deep understanding of mathematical problems. These risks highlight the need for careful integration of Gen-AI in the Geometry course.
## II. May provide wrong material/responses.

Gen-AI presents enormous possibilities such as the creation of 3D shapes, interactive learning environments but on the other hand there are significant risks that need to be addressed. One of the main concerns about Gen-AI in Geometry is automated content generation which can lead to incorrect answers (See Figure 3). Nevertheless, when students ask Gen-AI models to provide two contradictory answers for solving mathematical problems, this can help them understand that Gen-AI may lead to wrong questions and therefore enhance students' critical thinking (Youn et al., 2024).

<figure><img src="image_5.png" /><figcaption>**Figure 3.** A simple example of that the DALL-E model fails to produce a correct answer. In the above image, we observe that DALL-E chooses a complex approach for such a simple question and provides a wrong result.</figcaption></figure>

An important problem is trust and accuracy of AI produced geometric answers. Often AI models generate “black-box” outputs without any transparency on how they have come to a solution. This type of lack of visibility can lead to mistakes or undesirable outcomes in fields like engineering or architecture that are highly critical (Doshi-Velez & Kim, 2017). Therefore, an important matter to be considered is the enhancement of interpretability and transparency in AI models (Rudin 2019).

Moreover, there is also a worry over erosion of basic geometric instincts and knowledge among students and professionals. If Gen-AI tools continue to proliferate within instructional and occupational settings, there may be excessive dependence on them leading to only surface apprehension of geometrical concepts. In addition, this overreliance could displace critical thinking skills while degrading learning Geometry's educational worthiness. The emergence
AI generated geometrical patterns and shapes may result into disputes concerning ownership and originality especially when models have been trained using copyrighted works.

Recently released testing datasets also enable analysis on the kind of mathematical problems where Gen-AI solutions such as LLMs struggle (Frieder et al., 2024). In addition, the geometrical problems in the dataset released by Wang et al. (2024) are also annotated with their difficulty levels. Recent studies such as Trinh et al. (2024) show promising results regarding the combination of Gen-AI models with other AI domains such as symbolic engines to solve difficult geometrical problems such as theorem proofing at Olympiad level. The outputs of their method were highly interpretable and human-readable.

### III. Not comparable to average humans in terms of mathematical reasoning

In addition, there is a tendency to 'hallucinate' objects or points, which complicates their spatial reasoning process (Mouselinos et al., 2024). In a similar fashion, Wang et al. (2024) conclude that current top-tier LMMs are not yet comparable to average humans in terms of mathematical reasoning in visual contexts. LLMs such as ChatGPT struggle in solving problems where the reasoning is predominantly geometric or where an insight is obtained geometrically (Frieder et al., 2024). High-quality data is important for improving the geometric capabilities of multi-modal models, however available open-source datasets and correlated efforts are either excessively complex for direct model learning or suffer from misalignment between text and images (Cai et al., 2024). Currently, the performance of both LLMs and MMs declines as the problem length and complexity of the problem increases (Zhang et al., 2024). For example, GPT-4 can be used for undergraduate-level mathematics but fails on graduate-level difficulty (Frieder et al., 2024).

### IV. Subscription cost

Students and teachers need a subscription to access all the features of Gen-AI models in geometry. As a result, depending on the financial status of student families, the use of advanced tools may not be accessible to all students, causing a discrimination effect. More specifically, the non-Open Educational Resources (OERs) contribute to non-social inclusion, non-improvement of gender equality and non-promotion of lifelong learning (Bulathwela et al., 2024).
## 5.3 Opportunities

### I. Support Remote teaching

Gen-AI is well suited for delivering remote classes that require advanced visualization and interactivity. This can support the delivery of geometry classes when physical access is restricted. For example, when access is restricted due to pandemic, due to weather conditions or due to student mobility issues. Furthermore, the Virtual teaching assistants, driven by AI, answer questions, provide resources, and provide emotional support, resulting in an interactive learning environment (Ufomba et al., 2024). Gen-AI models can provide students with personalized math instruction tailored to their level of understanding (Chen et al., 2020) and can support online learning in geometry through engaging visual presentations, virtual assistants, online learning assessments chatbots, and assignment correction. However, the full exploiting of the potential of Gen-AI in geometry during online courses will be possible when the digital divide that exists among students in low-income or rural areas due to access to an internet connection or the required technological equipment is resolved. In conclusion, Gen-AI models can facilitate remote teaching by providing automated feedback, personalized lessons, and interactive problem-solving support, making geometry education more accessible.

### II. Improved 3D Visualization

Gen-AI presents significant opportunities for improved visualization in Geometry, especially through immersive and interactive 3D modeling. By integrating Gen-AI with emerging technologies like extended reality (XR), educators can create more engaging learning experiences that transcend traditional teaching methods. XR technologies allow students to interact with geometric concepts in a tangible way, enhancing their spatial reasoning skills. Studies demonstrate that immersive environments foster deeper understanding and retention of geometric concepts, as students can visualize and manipulate 3D shapes, leading to enhanced conceptual clarity (Wu et al., 2013).

### III. Personalized content.

Another significant opportunity for Gen-AI in Geometry education lies in its capacity to offer individualized courses tailored to students' varying abilities. Gen-AI can create comprehensive, adaptive curricula that cater to different learning needs, ensuring that all students receive instruction suited to their level. For instance, a single Geometry course could
provide ten different pathways, each aligned with specific student competencies. This personalization not only boosts student confidence but also allows them to progress at their own pace, promoting a more effective learning environment that acknowledges individual strengths and challenges.

Gen-AI tools enhance accessibility to learning resources in Geometry, significantly improving reading outcomes and comprehension among diverse student populations. Research indicates that GenAI can cater to various learning styles, providing personalized content that adapts to individual needs. This adaptability is particularly crucial in Geometry, where students often struggle with abstract concepts. By offering interactive and engaging content, GenAI can bridge gaps in understanding, fostering an inclusive educational environment. Studies show that the use of AI-driven tools leads to increased motivation and engagement, ultimately contributing to better academic performance.

#### IV. Improving teaching practises

Gen-AI has the potential to transform teaching practices in Geometry by providing educators with innovative tools and insights. By leveraging AI analytics, teachers can better understand student learning patterns and adapt their instructional strategies accordingly (Alam, 2023). This data-driven approach fosters a culture of continuous improvement, allowing educators to refine their methodologies based on evidence of what works best for their students. Furthermore, AI can support collaborative learning experiences, facilitating peer interactions that enrich the educational process and encourage diverse problem-solving approaches in Geometry. Gen-AI models can improve teachers' teaching methods in geometry as they can adapt to each student's learning needs, providing immediate real-time feedback while allowing them to better understand students' learning performance in order to provide them with a more complete and efficient support.

### 5.4 Threats

#### I. Replacing teachers.

Gen-AI has the potential to replace traditional teaching methods by providing personalized learning and automated assessments. However, completely replacing teachers could undermine the human aspect of education, such as emotional support and social interaction (Ghimire et al., 2024). It's important to find a balance where technology improves but not completely replaces the role of teachers. Although some educators believe that Gen-AI has the ability to replace teachers in the geometry classroom, the findings of the study by Chan
et al. (2024) showed that human teachers possess unique skills (such as critical thinking), and
emotions which are irreplaceable. Gen-AI tools produce mostly procedural approaches to math
problems that are often inaccurate (Sapkota et al., 2024).

## II. Students work in isolation

The continuous use of Gen-AI tools in Geometry can lead to over-reliance on Gen-AI tools thus leading to student isolation. Gen-AI models in addition to the many benefits they have in the field of geometry can have implications for students' mental health (anxiety, stress) (George et al., 2023) due to excessive time in Gen-AI models which can lead students to isolation. The use of Gen-AI in geometry may encourage students to work independently and limit collaborative learning opportunities. However, overuse of Gen-AI models can reduce group interactions, which are essential for problem-solving and critical thinking development.

### III. Teachers/Students rely too much on it.

As students can create content and solve geometry problems, there is a risk of diminishing critical thinking skills. Finally, overestimating the capabilities of generative models, due to testing their abilities on datasets that contain easier problems, or that contain problems on which the models have been pre-trained (Zhang et al., 2024). Overuse of Gen-AI models can affect both students and teachers in geometry class. On the one hand, students can show reduced critical thinking, creativity, and problem-solving skills due to the fact that it eliminates the process of answers, similarly, teachers who heavily rely on Gen-AI models may demonstrate reduced abilities and quality of their teaching (Liu et al., 2023). Additionally, an important concern that prevails is the potential increased dependence on external service providers for Gen-AI systems. The long-term use of Gen-AI models in geometry could increase costs for schools and institutions due to the need for continuous service subscriptions and support from external AI providers.

## IV. Privacy issues

Gen-AI models raise concerns about privacy and data security in education (Bahroon et al., 2024) as they collect and analyze vast amounts of data putting sensitive information of students and teachers at risk especially when it involves young children (Dimitriadou et al., 2023). Specifically, the irresponsible use of AI-generated content for the geometry course, failure to address issues related to student and teacher data privacy, and algorithmic biases may lead to hesitation regarding the use of Gen-AI models by teachers and students (Rosario
Michel-Villarreal et al., 2023). Students' data could be vulnerable to breaches or misuse, particularly in educational environments. Privacy and security inherent to Gen-AI are related to five main concerns such as ethical, technological, regulatory and law, user and institutional perspective (Golda et al., 2024). It is necessary to provide educational programs to students and teachers on the ethical use of Gen-AI models that includes issues related to data privacy (Bukar et al., 2024) in order to address the risks that arise regarding the privacy issues of students and teachers.

# 6. Future Directions and Conclusions

An important area for future research in educational instruction is how to better integrate Gen-AI into Geometry curricula. Gen-AI is already being used for personalized virtual tutoring, and the potential exists for it to also be used as a platform for doing virtual math, problem by problem. A platform like this could work for not just high school Geometry, but for any kind of math at any level, from basic arithmetic to advanced calculus. By embracing the affordances of these new technologies, instructors may be able to reach students who have previously been left behind and, in doing so, be able to attain the elusive goal of rendering mathematics more engaging to a wider audience.

Gen-AI is indeed a powerful mathematical and geometric tool but there are benefits as well as threats, some major, others minor that will tag along with it once its adopted wide scale. It is necessary for educators to use Gen-AI models in an ethical way in order to protect the privacy of students as much as possible. Although these technologies can have the ability to support problem-solving, education and design use, there has been an increasing importance of also considering their limitations and ethical implications in order to plan a responsible future for them.

# Conflict of Interest

The authors have no financial or proprietary interests in any material discussed in this article.
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