김민아 Mina Kim , 김병우 Byoungwoo Kim , 허완규 Wangyu Heo , 이봉주 Bongju Lee

DOI:10.63311/mathedu.25.6511 JANT Vol.65(No.1) 1-21, 2026

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This study aims to develop instructional design principles for AI-integrated mathematics education that are teacher-centered and grounded in authentic school contexts, as well as to propose actionable guidelines for implementing these principles in classroom practice. To identify practical needs in the field, a needs analysis was first conducted with in-service teachers. Based on those results, a modified Delphi survey was employed to refine and validate the design principles. A total of 11 experts consistently participated across four Delphi rounds, during which iterative feedback and individualized communication supported the systematic improvement and consensus-building of the principles. The final outcomes of the study include five key instructional design principles: individualized learning, AI literacy, goal-oriented instructional planning, reality-based mathematics education, and a balanced integration of collaborative learning. Additionally, 18 implementation guidelines were derived to provide concrete pathways for operationalizing these principles in school settings. As a field-based approach that connects theoretical insights with classroom realities, this study contributes to strengthening teachers’ roles as instructional designers in AI-enhanced mathematics education. The findings, representing expert consensus, offer foundational evidence for future research, resource development, and policy support related to AI-based teaching and learning in mathematics. Ultimately, this work is expected to inform the advancement of mathematics education that responds proactively to evolving technological and societal demands.

Sun Hee Kim , Jihyun Hwang

DOI:10.63311/mathedu.26.6512 JANT Vol.65(No.1) 23-42, 2026

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This study investigated the concept of meta-affect in the context of mathematics learning, addressing the need for assessment tools and providing insights into the application of feedback based on these measurements. Meta-affect, which involves the awareness, evaluation, regulation, and utilization of emotions in learning, is a crucial but under-researched area in mathematics education. We developed and validated scenario-based assessment items using the Delphi survey approach and implemented a nominal response model. Our findings reveal that the tool demonstrates content, substantive, and structural validity and supports convergent validity when compared with a traditional Likert-scale assessment. Our analysis offers a more nuanced assessment by placing students in hypothetical yet realistic learning contexts, eliciting more authentic responses. Furthermore, we examine the critical role of feedback in enhancing students’ learning experiences. Effective feedback tailored to students’ levels of meta-affect informs them about their current status and guides them toward higher levels of meta-affect. This study significantly contributes to the discourse on meta-effects in mathematics education. It also opens avenues for future research to improve educational practices through students’ meta-effects on mathematics learning.

오세준 Sejun Oh

DOI:10.63311/mathedu.26.6513 JANT Vol.65(No.1) 43-59, 2026

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This study explored how preservice mathematics teachers interpreted evidence of students’ participation and understanding when using “vibe-coding”-based web tools during microteaching, and how they articulated improvement directions for tool-mediated lessons. Twenty-two second-year preservice mathematics teachers in Seoul participated in a 15-week course involving a vibe-coding lecture, web-based instructional tool development, a workshop with one-to-one feedback, revision, and microteaching. Final reflection journals were thematically analyzed, while lesson plans and artifact reports were used for contextual triangulation. The findings showed that preservice teachers tended to describe students’ “high participation” mainly in terms of behavioral evidence such as submission rates, whereas evidence of discourse participation, such as spontaneous questions or student-led discussion, was limited. Judgments about understanding were mixed across quantitative formative assessment results, qualitative impressions, and descriptions in which no data were presented. Meanwhile, developing web-based instructional tools through vibe coding was perceived to offer advantages in visualization and rapid prototyping, but also constraints related to technical stability, usability, and the possible weakening of procedural performance. This study proposes design principles for teacher education that reconceptualize generative AI-based tool development not merely as “making tools,” but as fostering evidence-based reflection and instructional orchestration.

조은영 Eun Young Cho , 김래영 Rae Young Kim

DOI:10.63311/mathedu.26.6514 JANT Vol.65(No.1) 61-88, 2026

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Amid accelerating digital transformation and increasing social complexity, adults are expected to engage with quantitative information beyond basic computation, including reasoning, modeling, communication, and information processing in diverse real-life contexts. However, adult mathematics education in Korea remains institutionally underdeveloped and tends to frame the mathematical competencies required of adults within a limited, arithmetic-centered 3Rs perspective. In response, this study aimed to develop mathematical literacy standards for adults from a lifelong learning perspective. Mathematical literacy is defined as an integration of knowledge, skills, and attitudes required to meet social demands across adulthood. The research employed a three-stage developmental design involving a literature review, an analysis of the adult literacy mathematics curriculum, an adult perception survey, and expert reviews. The results from this study produced the final standards structured into three domains: (a) mathematical practices―communication, modeling, reasoning, and information processing―organized along the PISA mathematical processes (formulating, employing, interpreting/evaluating); (b) mathematical content―quantity and number, space and shape, change and relationships, uncertainty and prediction, mathematics and science and technology, mathematics in society and culture, and history of mathematics; and (c) affective domain―overcoming math anxiety, valuing mathematics, active use of mathematics, and collaborative engagement. These standards developed in this study are expected to serve as a foundational framework for discussing adult mathematics education from a lifelong learning perspective, examining continuity between school mathematics and adult learning, and guiding curriculum design, program development, and evaluation across adult learning contexts.

김원영 Wonyeong Kim , 김연수 Yeansu Kim

DOI:10.63311/mathedu.26.6515 JANT Vol.65(No.1) 89-115, 2026

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The purpose of this study is to re-examine the formula for solving cubic equations, commonly known as Cardano’s method, within the context of school mathematics, and to analyze the mathematical discourse and the role of disturbances that emerge during the processes of proving and exploring the cubic formula. Building on the work of Koichu and Zazkis (2021), which emphasized that disturbances arising in the process of proving and exploring the cubic formula can serve as opportunities for learning among undergraduate and graduate students, the present study extends this line of research to a different population. Guided by Lee (2004)’s suggestion that exploring the cubic formula can be a challenging and engaging learning topic for mathematically advanced students, this study selected students from J Science High School as participants and analyzed their discourse and levels of algebraic justification during the tasks. The role of mathematical disturbances that emerged in these processes was also examined. Students experienced disturbances and revealed several misconceptions in new contexts. However, they not only used these difficulties as learning opportunities but also demonstrated a high level of justification. These findings suggest that, with appropriate pedagogical support and careful selection of learners, the cubic formula can be meaningfully incorporated into school mathematics as a topic that promotes connected mathematical exploration. Furthermore, this study provides a concrete case illustrating how algebraic justification is manifested and developed through learners’ mathematical discourse.

황윤선 Yun Sun Hwang

DOI:10.63311/mathedu.26.6516 JANT Vol.65(No.1) 117-133, 2026

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The purpose of this study is to apply a Mathematical Logic-Based Instructional Model (MLIM) consisting of ‘Questioning, Mathematical Modeling, and Proof’ to a discrete mathematics course to alleviate the cognitive barriers experienced by engineering students and to analyze the changes in learners’ perception of logical thinking and their learning experiences. To this end, the model was applied to an actual university lecture for computer engineering majors, and surveys were conducted three times throughout the semester (beginning, middle, and end). The collected data were analyzed using a mixed-methods approach, performing both quantitative analysis of 5-point Likert scale items and qualitative analysis of descriptive responses. The quantitative results showed that learners reported positive changes in their perceptions of logical thinking through the class, and expressed high agreement on the necessity of understanding key units and recalling prerequisite concepts. In particular, positive perceptions of logical thinking significantly increased at the end of the semester compared to the beginning. The qualitative analysis revealed that Thought Elicitation through the instructor’s questioning, Logical Structuring through visualization, and Formal Justification through stepwise reasoning, along with support for understanding through recalling prerequisite concepts, played important roles in the learning experience. Many learners responded that they came to perceive proofs and logical formulas not as objects of rote memorization but as a ‘process of thinking’. Furthermore, they reported a sense of intellectual achievement, specifically citing a clearer conceptual understanding of major topics such as matrices and functions. These findings suggest that the MLIM is perceived by learners as effective in structuring the logical thinking process while alleviating the cognitive load of engineering students. This study demonstrates that discrete mathematics instruction can be transformed from calculation-or procedure-centered learning to education that reflects on and justifies thinking processes. It is significant in presenting a logic-centered instructional model applicable to actual university lecture settings, and further research is suggested to verify its validity and effectiveness by extending its application to various majors and liberal arts courses.

이규희 Gyuhee Yi

DOI:10.63311/mathedu.26.6517 JANT Vol.65(No.1) 135-149, 2026

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The purpose of this study is to analyze how high school students’ mathematics-related career course choice relates to the integrated structure of cognitive-affective characteristics manifested in their mathematical writing. To this end, a two-dimensional integrated framework capable of simultaneously coding cognitive and affective aspects was developed and applied to analyze students’ inquiry reports. The participants included 111 eleventh-grade students in Seoul (42 in the choice group and 69 in the non-choice group). The analysis framework integrated three cognitive elements (structure, meaning construction, and expression elements) and five affective elements (career utility, everyday utility, intrinsic interest, mathematical identity, and outcome expectation). The results indicated statistically significant differences between the two groups across all sub-variables, with distinct patterns of integration among these variables observed for each group. The choice group maintained consistently high scores across both cognitive and affective elements, exhibiting an integrated pattern. In contrast, the non-choice group showed relatively lower scores in meaning construction within the cognitive domain, as well as in mathematical identity and outcome expectation within the affective domain. This study is significant in that it utilizes mathematical writing as a methodological tool to capture learners’ internal structures and presents a two-dimensional integrated framework for analyzing cognitive-affective characteristics. Furthermore, by identifying the differential structures based on course choice, this research provides practical foundational data for establishing directions in career-linked mathematics education.

장현석 Hyun Suk Chang

DOI:10.63311/mathedu.26.6518 JANT Vol.65(No.1) 151-173, 2026

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In this study, middle and high school students were analyzed for understanding and functional thinking about the translation of quadratic functions according to grade and gender. To this end, first, the test tool was reconstructed based on previous studies. The results of analyzing this by using the data applied to a total of 106 students consisting of 34 middle school students and 72 high school students are as follows. First, for middle and high school students, there was no significant difference between grades and sex in the understanding of translation in the x-axis or y-axis direction of the quadratic function. Second, the understanding of translation in the x-axis direction of the quadratic function tended to be lower than the understanding of translation in the y-axis direction of the quadratic function. However, as the grade went up, the difference in understanding of translation in the x-axis and y-axis directions of the quadratic function tended to decrease. Third, the understanding of translation in the x-axis right directions of the quadratic function tended to be lower than that of the quadratic function in the x-axis left directions, and the understanding of translation in the y-axis downward directions of the quadratic function tended to be lower than that of the quadratic function in the y-axis upward direction. Fourth, as a result of error analysis, the collision phenomenon between geometric and algebraic thinking appeared more in the translation of the quadratic function in the x-axis direction than in the y-axis direction of the quadratic function. Based on these results, this study discussed functional thinking and teaching and learning implications related to translation of quadratic functions of middle and high school students.

한혜숙 Hyesook Han , 옥보명 Bo-myung Ok , 최희선 Heesun Choi

DOI:10.63311/mathedu.26.6519 JANT Vol.65(No.1) 175-199, 2026

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This study aims to analyze how cross-curricular themes are reflected in the nine first-grade middle school mathematics textbooks based on the 2022 revised mathematics curriculum and to derive implications for the integrated teaching of these themes within mathematics education. The analysis revealed that among the ten major cross-curricular themes, ‘environment and sustainable development’, ‘multicultural‘, ‘safety and health’, ‘character’, and ‘career’ education were most frequently addressed, while other themes appeared infrequently. These themes were mainly found in the domains of ‘data and probability’ and ‘change and relationship’, which are closely related to real-life contexts. Regarding representation types, examples in the form of ‘problems’ were most common. In terms of presentation, cross-curricular themes were most frequently shown merely as ‘illustrations’ without explanations or explicit references, and ‘question-based prompts’ appeared very rarely. These themes were primarily present within the ‘main lesson’, mostly in the form of ‘problems’. Based on these results, two key implications can be drawn. First, the use of ‘question-based prompts’ should be expanded to enable cross-curricular themes to be addressed more meaningfully within the mathematics curriculum. ‘Prompts’ provide students with opportunities to think deeply about the themes and to connect mathematical concepts with real-life contexts. Second, rather than presenting cross-curricular themes only as fragmented elements within individual problems, structuring units around specific themes at the subunit level can provide students with more continuous and meaningful learning experiences.

이상희 Sang Hee Lee , 장혜원 Hyewon Chang

DOI:10.63311/mathedu.26.65110 JANT Vol.65(No.1) 201-222, 2026

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This study examined the effects of a history of mathematics-based Creative Problem Solving (CPS) lesson on fifth-grade students’ mathematical creative thinking and creative attitude. The CPS lesson incorporating the history of mathematics was designed to immerse students in historical problem situations, allowing them to use mathematicians’ ideas as clues to extend their inquiries through divergent thinking and to reconverge them into mathematical concepts. To this end, Clairaut’s Elements de geometrie (1741/2023) was utilized as a historical source, and a seven-session lesson was implemented in the unit ‘Perimeter and Area of Polygons’. The results of the pre- and post-tests with two creative thinking items and the CAS-K (Creative Attitude Scale for Korean elementary students) showed significant improvement in creativity (p=0.010, p<0.001) and in creative attitude (p=0.025). In particular, lower- and middle-achieving students showed significant improvement on Item 1, whereas all groups improved significantly on Item 2, with especially pronounced gains among middle- and higher-achieving students. These results indicate that a history-based CPS lesson can foster creative development across diverse proficiency levels. Affectively, students reported not only enhanced creative attitudes but also the joy of doing mathematics and a sense of discovery. These findings suggest that the history of mathematics serves not merely as a motivational tool but as a means of engaging students in creative mathematical inquiry enriched by affective experiences such as the joy of discovery and the feeling of achievement.