이상구 Sang-gu Lee , 박도영 Doyoung Park , 이재윤 Jae Yoon Lee , 임동선 Dong Sun Lim , 이재화 Jae Hwa Lee

DOI: JANT Vol.63(No.2) 123-138, 2024

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This study described the utilization of ChatGPT in teaching and students’ learning processes for the course "Introductory Mathematics for Artificial Intelligence (Math4AI)" at ‘S’ University. We developed a customized ChatGPT and presented a learning model in which students supplement their knowledge of the topic at hand by utilizing this model. More specifically, first, students learn the concepts and questions of the course textbook by themselves. Then, for any question they are unsure of, students may submit any questions (keywords or open problem numbers from the textbook) to our own ChatGPT at https://math4ai.solgitmath.com/ to get help. Notably, we optimized ChatGPT and minimized inaccurate information by fully utilizing various types of data related to the subject, such as textbooks, labs, discussion records, and codes at http://matrix.skku.ac.kr/Math4AI-ChatGPT/. In this model, when students have questions while studying the textbook by themselves, they can ask mathematical concepts, keywords, theorems, examples, and problems in natural language through the ChatGPT interface. Our customized ChatGPT then provides the relevant terms, concepts, and sample answers based on previous students’ discussions and/or samples of Python or R code that have been used in the discussion. Furthermore, by providing students with real-time, optimized advice based on their level, we can provide personalized education not only for the Math4AI course, but also for any other courses in college math education. The present study, which incorporates our ChatGPT model into the teaching and learning process in the course, shows promising applicability of AI technology to other college math courses (for instance, calculus, linear algebra, discrete mathematics, engineering mathematics, and basic statistics) and in K-12 math education as well as the Lifespan Learning and Continuing Education.

Hyejin Park , Eric D. Manley

DOI: JANT Vol.63(No.2) 139-163, 2024

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The purpose of this study is to examine the capabilities of ChatGPT as a tool for supporting students in generating mathematical arguments that can be considered proofs. To examine this, we engaged students enrolled in a mathematics pathways course in evaluating and revising their original arguments using ChatGPT feedback. Students attempted to find and prove a method for the area of a triangle given its side lengths. Instead of directly asking students to prove a formula, we asked them to explore a method to find the area of a triangle given the lengths of its sides and justify why their methods work. Students completed these ChatGPT-embedded proving activities as class homework. To investigate the capabilities of ChatGPT as a proof tutor, we used these student homework responses as data for this study. We analyzed and compared original and revised arguments students constructed with and without ChatGPT assistance. We also analyzed student-written responses about their perspectives on mathematical proof and proving and their thoughts on using ChatGPT as a proof assistant. Our analysis shows that our participants’ approaches to constructing, evaluating, and revising their arguments aligned with their perspectives on proof and proving. They saw ChatGPT’s evaluations of their arguments as similar to how they usually evaluate arguments of themselves and others. Mostly, they agreed with ChatGPT’s suggestions to make their original arguments more proof-like. They, therefore, revised their original arguments following ChatGPT’s suggestions, focusing on improving clarity, providing additional justifications, and showing the generality of their arguments. Further investigation is needed to explore how ChatGPT can be effectively used as a tool in teaching and learning mathematical proof and proof-writing.

최인용 Inyong Choi , 김화경 Hwa Kyung Kim , 정인우 In Woo Chung , 송민호 Min Ho Song

DOI: JANT Vol.63(No.2) 165-186, 2024

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Despite the growing attention on artificial intelligence-based automated scoring technology as a support method for the introduction of descriptive items in school environments and large-scale assessments, there is a noticeable lack of foundational research in mathematics compared to other subjects. This study developed an automated scoring model for two descriptive items in first-year middle school mathematics using the Random Forest algorithm, evaluated its performance, and explored ways to enhance this performance. The accuracy of the final models for the two items was found to be between 0.95 to 1.00 and 0.73 to 0.89, respectively, which is relatively high compared to automated scoring models in other subjects. We discovered that the strategic selection of the number of evaluation categories, taking into account the amount of data, is crucial for the effective development and performance of automated scoring models. Additionally, text preprocessing by mathematics education experts proved effective in improving both the performance and interpretability of the automated scoring model. Selecting a vectorization method that matches the characteristics of the items and data was identified as one way to enhance model performance. Furthermore, we confirmed that oversampling is a useful method to supplement performance in situations where practical limitations hinder balanced data collection. To enhance educational utility, further research is needed on how to utilize feature importance derived from the Random Forest-based automated scoring model to generate useful information for teaching and learning, such as feedback. This study is significant as foundational research in the field of mathematics descriptive automatic scoring, and there is a need for various subsequent studies through close collaboration between AI experts and math education experts.

신병철 Byoungchul Shin , 이준수 Junsu Lee , 유연주 Yunjoo Yoo

DOI: JANT Vol.63(No.2) 187-207, 2024

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In this study, we explored the feasibility of automatically scoring descriptive assessment items using GPT-4 based ChatGPT by comparing and analyzing the scoring results between teachers and GPT-4 based ChatGPT. For this purpose, three descriptive items from the permutation and combination unit for first-year high school students were selected from the KICE (Korea Institute for Curriculum and Evaluation) website. Items 1 and 2 had only one problem-solving strategy, while Item 3 had more than two strategies. Two teachers, each with over eight years of educational experience, graded answers from 204 students and compared these with the results from GPT-4 based ChatGPT. Various techniques such as Few-Shot-CoT, SC, structured, and Iteratively prompts were utilized to construct prompts for scoring, which were then inputted into GPT-4 based ChatGPT for scoring. The scoring results for Items 1 and 2 showed a strong correlation between the teachers’ and GPT-4’s scoring. For Item 3, which involved multiple problem-solving strategies, the student answers were first classified according to their strategies using prompts inputted into GPT-4 based ChatGPT. Following this classification, scoring prompts tailored to each type were applied and inputted into GPT-4 based ChatGPT for scoring, and these results also showed a strong correlation with the teachers’ scoring. Through this, the potential for GPT-4 models utilizing prompt engineering to assist in teachers’ scoring was confirmed, and the limitations of this study and directions for future research were presented.

진혜성 Hyeseong Jin , 서보억 Boeuk Suh

DOI: JANT Vol.63(No.2) 209-231, 2024

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The education sector is undergoing significant changes due to the Fourth Industrial Revolution and the advancement of artificial intelligence. Particularly, the importance of education based on artificial intelligence is being emphasized. Accordingly, the purpose of this study is to develop a statistics education program using deep learning prediction in high school mathematics and to examine the impact of such statistically problem-solving-centered statistics education programs on high school students' statistical literacy and computational thinking. To achieve this goal, a statistics education program using deep learning prediction applicable to high school mathematics was developed. The analysis revealed that students' understanding of context improved through experiencing how data was generated and collected. Additionally, they enhanced their comprehension of data variability while exploring and analyzing various datasets. Moreover, they demonstrated the ability to critically analyze data during the process of validating its reliability. In order to analyze the impact of the statistics education program on high school students’ computational thinking, a paired sample t-test was conducted, confirming a statistically significant difference in computational thinking between before and after classes (t=-11.657, p<0.001).

Ipek Saralar-aras , Yasemin Cicek Schoenberg

DOI: JANT Vol.63(No.2) 233-254, 2024

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This paper delves into the symbiotic integration of coding and mathematics education, aimed at cultivating computational thinking and enriching mathematical problem-solving proficiencies. We have identified a corpus of scholarly articles (n=38) disseminated within the preceding two decades, subsequently culling a portion thereof, ultimately engendering a contemplative analysis of the extant remnants. In a swiftly evolving society driven by the Fourth Industrial Revolution and the ascendancy of Artificial Intelligence (AI), understanding the synergy between these domains has become paramount. Mathematics education stands at the crossroads of this transformation, witnessing a profound influence of AI. This paper explores the evolving landscape of mathematical cognition propelled by AI, accentuating how AI empowers advanced analytical and problem-solving capabilities, particularly in the realm of big data-driven scenarios. Given this shifting paradigm, it becomes imperative to investigate and assess AI's impact on mathematics education, a pivotal endeavor in forging an education system aligned with the future. The symbiosis of AI and human cognition doesn't merely amplify AI-centric thinking but also fosters personalized cognitive processes by facilitating interaction with AI and encouraging critical contemplation of AI's algorithmic underpinnings. This necessitates a broader conception of educational tools, encompassing AI as a catalyst for mathematical cognition, transcending conventional linguistic and symbolic instruments.

김초희 Chohee Kim , 장혜원 Hyewon Chang

DOI: JANT Vol.63(No.2) 255-272, 2024

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This study aims to design mathematics-integrated classes that cultivate artificial intelligence (AI) thinking and to analyze students’ AI thinking within these classes. To do this, four classes were designed through the integration of the AI4K12 Initiative’s AI Big Ideas with the 2015 revised elementary mathematics curriculum. Implementation of three classes took place with 5th and 6th grade elementary school students. Leveraging the computational thinking taxonomy and the AI thinking components, a comprehensive framework for analyzing of AI thinking was established. Using this framework, analysis of students’ AI thinking during these classes was conducted based on classroom discourse and supplementary worksheets. The results of the analysis were peer-reviewed by two researchers. The research findings affirm the potential of mathematics-integrated classes in nurturing students’ AI thinking and underscore the viability of AI education for elementary school students. The classes, based on AI Big Ideas, facilitated elementary students’ understanding of AI concepts and principles, enhanced their grasp of mathematical content elements, and reinforced mathematical process aspects. Furthermore, through activities that maintain structural consistency with previous problem-solving methods while applying them to new problems, the potential for the transfer of AI thinking was evidenced.

육지은 Jieun Yuk , 허난 Nan Huh , 고호경 Hokyoung Ko

DOI: JANT Vol.63(No.2) 273-294, 2024

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Recently, interest in Edu-Tech, which applies new technologies to the educational field, is growing. Edu-Tech is now being naturally used in schools, allowing both teachers and students to adapt to these changes. Particularly, there’s significant attention on using Edu-Tech to bridge the educational gap through various teaching and learning strategies. This study focuses on the importance of self-directed task management by students for supplementary learning. It developed and utilized a math learning platform that enables teachers to easily provide and manage necessary tasks for students. Initially, the study developed “Sussam-MathTeacher” a problem-based learning application for middle school students, aimed at enhancing problem-solving abilities. This platform operates as a task management system, allowing teachers to assign or recommend problems to either the entire class or individual students. It aims to improve students’ problem-solving abilities through a process that includes presenting necessary tasks, monitoring their own progress in solving problems, and self-assessing growth. Through this study, students demonstrated improved problem-solving skills by tackling tasks suited to their levels using “Sussam” highlighting the critical role of teachers in the digital educational environment.

Idowu David Awoyemi , Feliza Marie S. Mercado , Jewoong Moon

DOI: JANT Vol.63(No.2) 295-318, 2024

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This narrative review explores the transformative potential of immersive virtual reality (IVR) in enhancing high school students’ mathematics competence, viewed through the lens of the technological, pedagogical, and content knowledge (TPACK) framework. This review comprehensively illustrates how IVR technologies have not only fostered a deeper understanding and engagement with mathematical concepts but have also enhanced the practical application of these skills. Through the careful examination of seminal papers, this study carefully explores the integration of IVR in high school mathematics education. It highlights significant contributions of IVR in improving students' computational proficiency, problem-solving skills, and spatial visualization abilities. These enhancements are crucial for developing a robust mathematical understanding and aptitude, positioning students for success in an increasingly technology-driven educational landscape. This review emphasizes the pivotal role of teachers in facilitating IVR-based learning experiences. It points to the necessity for comprehensive teacher training and professional development to fully harness the educational potential of IVR technologies. Equipping educators with the right tools and knowledge is essential for maximizing the effectiveness of this innovative teaching approach. The findings also indicate that while IVR holds promising prospects for enriching mathematics education, more research is needed to elaborate on instructional integration approaches that effectively overcome existing barriers. This includes technological limitations, access issues, and the need for curriculum adjustments to accommodate new teaching methods. In conclusion, this review calls for continued exploration into the effective use of IVR in educational settings, aiming to inform future practices and contribute to the evolving landscape of educational technology. The potential of IVR to transform educational experiences offers a compelling avenue for research and application in the field of mathematics education.

오영석 Young-seok Oh , 김동중 Dong-joong Kim

DOI: JANT Vol.63(No.2) 319-334, 2024

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The purpose of this study was to reveal the discursive constructs of AI-based mathematical objects by analyzing how concrete objects used in the optimization content of AI mathematics textbooks are transformed into discursive objects through naming and discursive operation. For this purpose, we extracted concrete objects used in the optimization contents of five high school AI mathematics textbooks and developed a framework for analyzing the discursive constructs and discursive operations of AI-based mathematical objects that can analyze discursive objects. The results of the study showed that there are a total of 15 concrete objects used in the loss function and gradient descent sections of the optimization content, and one concrete object that emerges as an abstract d-object through naming and discursive operation. The findings of this study are not only significant in that they flesh out the discursive construction of AI-based mathematical objects in terms of the written curriculum and provide practical suggestions for students to develop AI-based mathematical discourse in an exploratory way, but also provide implications for the development of effective discursive construction processes and curricula for AI-based mathematical objects.