박준현 Park Joon-hyun

DOI:10.7468/jksmee.2025.39.4.517 JANT Vol.39(No.4) 517-544, 2025

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The isoperimetric problem, a long-studied and fundamental topic in mathematics, has evolved through the proofs and inquiries of many distinguished mathematicians before reaching its classical solution―the circle. Inspired by Newton’s Principia, which demonstrated that celestial bodies move in elliptical orbits under an inverse-square central force, this study defines generalized conic sections, beginning with the circle and extending through the ellipse. The properties of these multi-lobed generalized conic curves are analyzed, and isoperimetric perturbed curves are introduced by applying perturbations on the circle under the condition of equal perimeter. The areas of various isoperimetric perturbed curves are computed and compared graphically with that of the circle. The Euler-Lagrange equations are presented in detail for both unconstrained and constrained cases, and a differential-equation-based approach to the isoperimetric problem is provided. This study is expected to provide an engaging resource for learners who have studied calculus and differential equations at the undergraduate level, and to serve as a useful instructional reference for educators teaching these subjects.

오서영 Oh Seo-young , 양성현 Yang Seong Hyun

DOI:10.7468/jksmee.2025.39.4.545 JANT Vol.39(No.4) 545-566, 2025

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The reality is that most content related to the history of mathematics, both domestically and internationally, is somewhat difficult to access for middle and high school students, as well as in-service teachers. Therefore, reinterpreting various historical materials in a contemporary context, tailored to the students' perspective, can hold significant educational value. This study developed teaching and learning materials based on a curriculum-based reinterpretation of "Arbelos" and "Archimedes' twin circles," and applied them to a pilot class for pre-service teachers. Given that the unit focused on quadratic curves, the developed materials were designed to enhance visual representations using GeoGebra, a mathematics learning software. The dynamic visualizations of quadratic curves help solidify the connection between algebra and geometry, promote multifaceted understanding, and enhance both the aesthetic and practical appreciation of mathematics. Based on survey results from participating pre-service teachers, the developed materials were found to be applicable to the teaching and learning of quadratic curves.

황선영 Hwang Seonyoung , 한선영 Han Sunyoung

DOI:10.7468/jksmee.2025.39.4.567 JANT Vol.39(No.4) 567-590, 2025

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Recently, mathematical modeling has been increasingly emphasized in the mathematics curriculum. However, teachers face challenges in selecting and developing appropriate tasks. This study explores the processes of task development and revision by 26 in-service mathematics teachers during a professional development program, employing a collective case study method. The teachers first selected tasks suitable for mathematical modeling and then revised them twice. The patterns of revision were analyzed based on literature reviews. The findings revealed that while in-service mathematics teachers initially prioritized realism in task selection, it was only partially reflected in the tasks. However, in the first revision, the teachers aimed to enhance the reality of the tasks. Also, although the teachers did not initially consider the complexity of the tasks, they recognized its importance during the first revision and attempted to reflect it on the task. In addition, the second revision involved simultaneously reinforcing low complexity and reducing high complexity. This study highlights the need for a systematic examination of the characteristics of mathematical modeling tasks and classroom-based research. Also, this study underscores the importance of providing education and support to strengthen teachers’ task development competencies.

민숙 Min Sook

DOI:10.7468/jksmee.2025.39.4.591 JANT Vol.39(No.4) 591-609, 2025

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This study aims to systematically examine the types of tasks designed by students, the calculus concepts applied and extended, the types of conceptual applications, and the methods of task exploration by analyzing 86 project-based learning reports conducted in undergraduate calculus courses at Korean universities. After anonymizing personal information, the data were categorized according to the use of calculus concepts, types of conceptual applications, and task exploration methods. The main findings are summarized as follows. First, most of the reports were classified as cases of external application, and more than half of them represented secondary external applications in which advanced concepts were applied to complex real-world contexts. Second, the most frequently utilized foundational concepts included integration, limits and derivatives, and space geometry, and approximately 85% of the reports integrated two or more concepts in a convergent manner. Third, task exploration methods were classified into calculation-focused and inquiry-focused types depending on the nature of the tasks, and digital tools were commonly used across all projects. These findings highlight the applicability of project-based learning in undergraduate calculus education and provide meaningful educational implications.

박만구 Park Mangoo , 김나리 Kim Nari , 김지영 Kim Jiyoung , 박수현 Park Suhyeon , 박예은 Park Yeeun , 서보억 Seo Bo-eok , 이동흔 Lee Dongheun , 이성현 Lee Seonghyeon , 정유진 Jung Yujin , 박경은 Park Kyoungeun

DOI:10.7468/jksmee.2025.39.4.611 JANT Vol.39(No.4) 611-633, 2025

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This study aims to propose a modular training system designed to enhance mathematics teachers’ core competencies and to analyze teachers’ perceptions of its necessity, field applicability, and feasibility. As part of a larger research project by Park et al. (2025) on the development of a structured competency framework and a modular professional development standard for mathematics teachers, this study first reviewed prior research and policy documents related to modular training. Based on this review, a three-stage modular training system―self-diagnosis, training recommendation, and modular training support―was proposed. To ensure content validity, two rounds of Delphi surveys were conducted with 13 experts in mathematics education, resulting in a validated questionnaire. An online survey was then administered to 59 in-service elementary, middle, and high school mathematics teachers nationwide. The results indicate that teachers perceive autonomous choice based on self-diagnosis and personalized training design as the most essential features of the modular training system. In addition, blended learning formats and short, micro-level modules were evaluated positively. The findings suggest that a modular training system has the potential to enhance mathematics teachers’ core competencies while addressing limitations of existing professional development structures. This study provides foundational data for the future development and empirical evaluation of modular professional development programs for mathematics teachers.

유진영 Yoo Jinyoung , 허난 Huh Nan

DOI:10.7468/jksmee.2025.39.4.635 JANT Vol.39(No.4) 635-659, 2025

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The purpose of this study is to propose a middle school mathematics program utilizing EduTech tools through a design-based research approach, with the aim of ensuring the learning rights of students with migrant backgrounds and fostering multicultural sensitivity among all students. This study sought to reflect contemporary educational demands and the direction of recent curriculum reforms that emphasize recognizing the interconnectedness between mathematics and diverse cultural domains, cultivating integrative thinking, and valuing educational practices that embrace cultural diversity. To this end, a six-session inquiry-based instructional program was designed, focusing on the concepts of irrational numbers and radicals and incorporating cultural contexts, literature and films, and historical materials related to mathematics. The program was integratively structured through instructional strategies such as discussion and project-based activities, oral presentations, self-assessment, and peer assessment. Although the entire program was not implemented in actual classes, this study is meaningful in that it developed a practical instructional prototype grounded in the principles of multicultural mathematics education through a design-based research framework. Furthermore, it is expected that the proposed program can be utilized to support all students, including those with migrant backgrounds, in developing mathematical thinking skills and integrative problem-solving competencies from diverse perspectives based on multicultural sensitivity.

김진호 Kim Jinho , 권미선 Kwon Misun , 김은경 Kim Eunkyung

DOI:10.7468/jksmee.2025.39.4.661 JANT Vol.39(No.4) 661-684, 2025

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Effective mathematics learning is grounded in literacy for learning, with vocabulary constituting a core component of such literacy. Accordingly, this study analyzed the difficulty levels and frequency of vocabulary presented in the 2022 revised mathematics textbooks for grades 1-2 in elementary school, with the aim of deriving implications for mathematics education. The results of the vocabulary difficulty analysis indicated that approximately 4-15% of the total vocabulary used in each semester consisted of words at Level 3 or higher, which may pose difficulties for students. Among these, certain terms such as bundle and pattern were found to be used with meanings that are narrower than their everyday usage or in polysemous ways within the mathematics textbooks, highlighting the need for explicit vocabulary instruction that takes semantic differences into account. In addition, vocabulary related to units was frequently used across all grades and semesters, regardless of grade level. A number of vocabulary items that could be taught in connection with integrated subjects, including yugwa, yakgwa, and gangjeong, were also identified. The vocabulary frequency analysis further revealed that certain words, including number, to tell, and expression, were commonly used across both grades 1 and 2. Based on these findings, this study proposes systematic approaches to vocabulary instruction to support students’ understanding of mathematical concepts and offers practical implications for the future development of mathematics textbooks.

방정숙 Pang Jeongsuk , 전지원 Jeun Jiwon

DOI:10.7468/jksmee.2025.39.4.685 JANT Vol.39(No.4) 685-706, 2025

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This study aimed to design and implement mathematics lessons that emphasize the relational understanding of the equal sign for first-grade elementary students and to derive instructional implications for teaching. Based on prior research on students’ understanding of the equal sign and teaching strategies that highlight relational meaning, an instructional approach appropriate for first graders was developed. The five lessons from the “Addition and Subtraction” unit in the second semester were reconstructed and implemented in the classroom. In the redesigned lessons, relational models and linking cubes were used to express relationships as equations and to highlight the relational meaning of the equal sign through representing various equation structures. Subtraction equations and three-number expressions were treated as objects of reasoning, and deliberately larger numbers were introduced to provide opportunities for students to reason about equivalence. Structurally meaningful equations were also presented to help students recognize the underlying structure of equations. The findings revealed that even first-grade students were able to reason about equations in various ways and solve equations with unknowns when guided through relational understanding of the equal sign. This study suggests that lessons emphasizing relational understanding can effectively support young learners’ conceptual development and encourage further research on early-grade approaches to teaching mathematical equivalence.

황수빈 Hwang Su Bhin , 이경화 Lee Kyeong-hwa , 신동조 Shin Dongjo , 유연주 Yoo Yun Joo , 박진형 Park Jin Hyeong

DOI:10.7468/jksmee.2025.39.4.707 JANT Vol.39(No.4) 707-727, 2025

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This study investigates how middle school students utilize generative AI feedback in a web-based statistical inquiry environment and examines changes in their inquiry strategies and affective domains using log data-based learning analytics. Using a GPT-4o API-enhanced tool, the inquiry processes of 13 students were collected. K-means clustering identified three inquiry patterns: ‘Visualization-oriented’, ‘Analysis-oriented’, and ‘Balanced’. The Analysis-oriented group improved consistently across stages, while the Balanced group excelled in problem definition. Notably, the Visualization-oriented group showed significant growth in interpretation through graph exploration. Post-surveys indicated increased interest and value. Specifically, the Analysis-oriented group showed increased value perception, the Balanced group improved in confidence, and the Visualization-oriented group showed increased interest. These findings suggest that the effects of AI feedback vary by inquiry style and highlight the utility of log-based diagnostics for designing adaptive support.

오세준 Oh Se Jun , 강일선 Kang Il Sun , 김현나 Kim Hyun Na , 박정숙 Park Jeong Sook , 변효중 Byeon Hyo Jung , 이재교 Lee Jaegyo , 정인옥 Jeong In-ok , 조상현 Cho Sanghyun , 채혜남 Chae Hye Nam , 최정원 Choi Jeongwon , 하은경 Ha Eun Kyung

DOI:10.7468/jksmee.2025.39.4.729 JANT Vol.39(No.4) 729-763, 2025

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This study aimed to develop a student workbook and a teacher guide to ensure minimum achievement levels in high school mathematics elective courses (< Algebra >, < Calculus I >, and < Probability and Statistics >) under Korea’s 2022 Revised National Curriculum and the credit-based high school system. We analyzed the curriculum, prior studies, and research-school reports and conducted a focus group interview with seven teachers and researchers to identify field needs. Based on these findings, we organized the program book into 10 sessions for achievement-standard learning, 1 “Mathematics Together” activity session, and 3 affective-support sessions, and designed session-level components and four differentiated instructional strategies. Draft versions of the program book and teacher guide were developed for each course and then reviewed twice by two field teachers per course to examine the appropriateness and completeness of the materials; revisions were made accordingly. By providing concrete and practical teaching and learning resources for ensuring minimum achievement levels, this study is expected to strengthen teachers’ capacity to implement minimum-achievement-level assurance instruction.