허남구 Nam Gu Heo

DOI:10.63311/mathedu.25.6441 JANT Vol.64(No.4) 437-458, 2025

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Artificial intelligence demonstrates human-like thought processes and is also capable of analogical reasoning. Although analogical reasoning is an important strategy for mathematical problem solving, analogy problems with low procedural similarity may not be solvable by directly applying the solution method of the base problem. This study aims to analyze the problem solving of generative AI on analogy problems with low procedural similarity. For this purpose, GPT-4o and Gemini 2.5 Pro were tasked with solving the problem of finding the Fermat point of a concave quadrilateral and constructing conic sections given an eccentricity. The findings are as follow. First, generative AI attempted to utilize the solution method of the base problem when solving the Fermat point problem of a concave quadrilateral. Second, appropriate feedback must be provided for incorrect answers in order for generative AI to solve problems correctly. Third, generative AI was able to propose generalized propositions. Fourth, generative AI improved propositions through the lemma-in-corporation method. Fifth, in construction problems with low procedural similarity, generative AI sometimes solved the target problem by employing different methods of the base problem.

조윤주 Yoonjoo Cho , 권오남 Oh Nam Kwon

DOI:10.63311/mathedu.25.6442 JANT Vol.64(No.4) 459-474, 2025

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This study aims to apply mathematics extended-response assessments developed based on IB to Korean middle and high school students, analyze students’ thinking and expression patterns, and empirically examine the potential for securing scoring reliability in extended-response assessments. Student responses were analyzed based on the SOLO taxonomy, and item-specific expression patterns at each thinking level were examined. After systematic rater training, each rater independently scored the responses, and inter-rater reliability was examined by calculating ICC. The analysis revealed a wide range of thinking levels, from pre-structural to extended abstract levels. A clear correlation was observed between students’ overall performance and their cognitive complexity; higher-achieving students tended to reach higher SOLO levels. This suggests that IB-based extended-response assessments can precisely capture individual cognitive structures, such as the flow of thinking, connections between concepts, and potential for transfer, rather than simply judging correctness of answers. The ICC analysis showed that most items achieved values above 0.90, indicating a high level of scoring consistency among raters. These results may contribute to enhancing the perception of fairness in assessment in subjects like mathematics, which are centered on logical structures. This study may serve as a practical foundational resource for the domestic applicability of IBbased mathematics extended-response assessments and the improvement of assessment systems.

오세준 Sejun Oh

DOI:10.63311/mathedu.25.6443 JANT Vol.64(No.4) 475-493, 2025

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This study explored pre-service mathematics teachers’ experiences of collaborative lesson design using AI Digital Textbooks (AIDTs), focusing on changes in their perceptions and the characteristics of their design practices. Eighteen pre-service teachers participated in a pre-post survey and a collaborative lesson design project. The survey measured lesson design competencies and perceptions of AIDT, while qualitative data were collected from lesson plans, peer discussions, and expert reviews. The results showed significant improvements in certain areas, particularly content knowledge & resource application and perceptions of AIDT’s effectiveness, interaction, and interest & motivation. Expert evaluation of nine lesson designs further revealed how pre-service teachers attempted to integrate AIDT functions (e.g., diagnostic tests, auto-grading, dashboards) with mathematical content and pedagogical strategies, showing initial manifestations of AI-TPACK. The findings suggest that AIDT-based collaborative lesson design can enhance digital teaching competencies and highlight the value of case-based learning and collaborative design activities in teacher education programs.

이윤경 Yunkyung Lee , 장혜원 Hyewon Chang , 이상희 Sanghee Lee

DOI:10.63311/mathedu.25.6444 JANT Vol.64(No.4) 495-521, 2025

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This study aimed to analyze the characteristics of noticing demonstrated by pre-service elementary teachers during the design and reflection stages of mathematics lessons they independently planned and implemented during their teaching practicum. Based on the components of noticing suggested by Goodwin (1994), Sherin and van Es (2009), and Jacobs et al. (2010), an analytical framework focusing on mathematical, pedagogical (instruction/learning), and contextual aspects was developed. A case study was conducted with two pre-service teachers, and data were collected through pre- and post-reflection journals and in-depth interviews. The analysis revealed that the participants most frequently exhibited a pedagogical focus during the design and reflection stages, which led to reflective practices aimed at reconstructing teaching strategies in response to students’ reactions. In contrast, the mathematical focus was limited in terms of extending to hierarchical or advanced conceptual connections, and the contextual focus was also confined to certain background factors, showing insufficient attempts to structurally incorporate students’ diverse backgrounds. These findings suggest that noticing should not be approached as a single, isolated activity but rather be developed through repeated, case-based training within the cyclical process of designing and reflecting on lessons.

최인선 Inseon Choi , 박수민 Soomin Park , 김래영 Rae Yeong Kim

DOI:10.63311/mathedu.25.6445 JANT Vol.64(No.4) 523-542, 2025

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This study investigates the possibility of assessing the newly introduced topics of matrices and population proportion on the College Scholastic Ability Test (CSAT) as the 2022 revised mathematics curriculum is implemented in high schools. The analysis focuses on curricular changes and achievement standards related to these topics, and considers their assessability through the development of items aligned with the structure and requirements of the CSAT mathematics section. The results show that matrices may be assessed both as an independent component of ‘Common Mathematics1’ and through items that integrate matrix-related ideas within broader mathematical contexts. Population proportion can likewise be assessed in Probability and Statistics through tasks that require students to engage in reasoning and interpretation. The study also identifies several limitations in fully reflecting the educational intentions of these topics within the constraints of the CSAT assessment framework. Accordingly, this study suggests that, in order for the aims and intentions of the 2022 revised mathematics curriculum to be faithfully reflected in assessment, consistent national-level guidelines are needed that expand the interpretation of achievement standards, diversify assessment methods, and broaden the range of item contexts, so that instruction and assessment within the CSAT can be more organically aligned.

Jukyung Park , Hoyun Cho , Jung Youn Colen , Na Young Kwon , Seunghyun Yeo , Jinho Kim , Byungeun Pak

DOI:10.63311/mathedu.25.6446 JANT Vol.64(No.4) 543-557, 2025

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This study examines the role of digital and AI-empowered mathematics textbooks in modern education, focusing on how teachers’ backgrounds―including grade level taught, teaching experience, and prior exposure to digital resources―shape their perceptions of these tools. As digital transformation and artificial intelligence (AI) continue to redefine educational methodologies, it is essential to understand how these factors influence teachers’ views and their adoption of digital and AI-empowered mathematics textbooks. This study surveys in-service teachers across grades 1-12 and carries out a comprehensive analysis to identify key factors that shape the adoption and effectiveness of AI-empowered mathematics education. The results indicate that teachers’ familiarity with and confidence in digital tools play a significant role in their willingness to integrate AI-empowered resources into their teaching practices. The findings provide insights for optimizing AI-empowered learning environments and offer practical implications for curriculum development and teacher training programs.

오민영 Minyoung Oh , 방정숙 Jeongsuk Pang

DOI:10.63311/mathedu.25.6447 JANT Vol.64(No.4) 559-578, 2025

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The purpose of this study was to propose and elaborate the definition and process of the mathematics teachers’ teaching practice called “responsive explaining,” and to clarify the necessity and significance of this practice in the context of teaching elementary students struggling with basic academic ability in mathematics. This study qualitatively analyzed a case in which a mathematics teacher decided and continuously adjusted what, how, and when to explain to an elementary student struggling with basic academic ability in mathematics while implementing responsive explaining. The findings define responsive explaining as a teaching practice in which the teacher determines and continously adjusts the content, method, and timing of explanations based on the students’ understanding of mathematics and of doing mathematics. Responsive explaining was characterized by eliciting students’ prior understanding related to the teacher’s explanation, using student-generated representations, and strategically delaying explanations. Finally, this study discussd that responsive explaining is a necessary teaching practice for supporting students with basic academic ability in mathematics and proposed follow-up research on the development of an evaluation framework for responsive explaining and its relationship to mathematical agency. This study is significant in that it approaches research on basic academic ability in mathematics from the perspective of teachers’ teaching practices.

정은영 Eun Young Jung , 고호경 Ho Kyoung Ko

DOI:10.63311/mathedu.25.6448 JANT Vol.64(No.4) 579-593, 2025

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An abstract of the manuscript, 200-300 words. The rapid acceleration of digital transformation has heightened interest in integrating artificial intelligence (AI) into mathematics education to provide personalized feedback, foster self-directed learning, and support affective engagement. This study presents the design and implementation of SuriBot, a scenario-based AI chatbot developed to enhance concept learning in middle school mathematics. Grounded in concept-based learning, cognitive flexibility, and social-emotional learningtheories, SuriBot was built using NAVER Cloud’s Clova Chatbot Builder and deployed via the Naver TalkTalk platform to ensure accessibility. Our five-phase research procedure involved: (1) theoretical and prior research analysis to extract core design principles; (2) content structuring to align chatbot dialogue with the revised 2022 mathematics curriculum; (3) scenario design to map concept hierarchies and embed affective feedback; (4) chatbot implementation, creating 1,379 dialogue sets, 50 supporting images, and 88 dialogue tags organized into 372 scenario blocks; and (5) iterative testing and refinement through internal and pilot evaluations. SuriBot delivers multimodal responses―including text definitions, visual aids, interactive quizzes, and external learning links―and offers scaffolded feedback and retries tailored to learners’ performance and emotional state. Preliminary analysis indicates that the scenario-based approach effectively guides students through progressive concept exploration while maintaining engagement and reducing math anxiety through positive reinforcement. The integration of structured feedback loops and varied response types supports both cognitive understanding and emotional resilience. This research contributes a practical model for AI-enhanced mathematics instruction, demonstrating how carefully crafted dialogue scenarios can bridge curriculum goals with learner needs.

김주희 Juhee Kim , 이정환 Jeong Hwan Lee , 이수진 Soo Jin Lee

DOI:10.63311/mathedu.25.6449 JANT Vol.64(No.4) 595-619, 2025

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This study aims to analyze the aspects of procedural performance and conceptual understanding in middle school students’ prime factorization problem-solving and to derive educational implications by comparing differences based on the learning timeframe. A task-based test was administered to 1,750 first and second-year middle school students to analyze their error types and problem-solving strategies. The results revealed a clear “procedureconcept disconnect,” with many students performing procedures correctly yet making errors in exponential notation (14.1%) or failing to recognize the task’s objective (12%). Furthermore, a “knowledge disconnection” was observed, as only 6.9% of students utilized their prime factorization results in subsequent tasks, reverting to elementarylevel methods. Notably, the second-year group, one year post-learning, showed improved procedural fluency but a significantly decreased ability to connect and apply the concept. Based on these results, this study proposes the educational implication that the utility of the concept should be emphasized from the initial introduction to prime factorization and that tasks must be provided to link it to subsequent concepts.

이예진 Ye-jin Lee , 장혜원 Hyewon Chang

DOI:10.63311/mathedu.25.64410 JANT Vol.64(No.4) 621-644, 2025

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The purpose of this study is to establish types of connections among mathematical concepts in mathematics education, explore their theoretical foundations. It further aims to structure and visualize these relationships as knowledge structures. Based on the 2022 revised elementary mathematics curriculum, 88 concepts were selected, and connection types were identified through deductive criteria supported by literature review, further corroborated by additional analyses. Expert validation was conducted, followed by network analysis of concept nodes to derive structural features of knowledge. The findings reveal two major connection types. Simplification- complexification (SC) connections arise from sequential relationships in teaching and learning, where cognitive adjustment and restructuring are essential. Transversal (TR) connections are grounded in essential similarities that transcend curriculum domain boundaries, enabling both direct and indirect connections. From the SC connections, 52 nodes were extracted and categorized into three groups, while 28 nodes were extracted from the TR connections, forming knowledge structures centered on the big idea of equal partitioning. The network analysis revealed 57 links in the SC connection network and 30 links in the TR connection network, with fractions and division serving as central hubs within the knowledge structure.