박준현 Park Joon-hyun

DOI:10.7468/jksmee.2026.40.1.1 JANT Vol.40(No.1) 1-30, 2026

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The isoperimetric problem has been studied for centuries, and the fact that its solution is a circle has been progressively established through the works of several gifted mathematicians. In this paper, we provide a mathematical modeling and analysis using matrix methods to explain why the solution to the polygonal isoperimetric problem must be an equilateral polygon. By utilizing Mathematica, we extracted information on eigenvalues, eigenvectors, and characteristic polynomials of matrices that are difficult to compute manually. Furthermore, to verify whether the theoretically predicted results correspond to the actual geometric behavior, we employed Geogebra to present multi-stage graphical illustrations. In addition, the study presents a perspective that allows the results to be interpreted in a more advanced framework, drawing on concepts from advanced linear algebra such as properties of Markov matrices and the Perron-Frobenius theorem. This study will be of particular interest to undergraduate students who have completed a course in linear algebra. It offers an opportunity for students to appreciate the usefulness of matrices as mathematical tools in explaining various real-world phenomena.

김수연 Kim Su Yeon , 윤정은 Yoon Jung Eun

DOI:10.7468/jksmee.2026.40.1.31 JANT Vol.40(No.1) 31-54, 2026

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This study aims to analyze how mathematical literacy and digital literacy are reflected in the achievement standards of the 2015 and 2022 revised mathematics curricula. Based on a review of relevant literature, key cognitive components were identified and used to construct an analytical framework, and a two-stage analysis consisting of initial coding and secondary classification was conducted. The results show that mathematical literacy maintains a structure centered on mathematical reasoning in both curricula, while elements related to mathematical modeling and decision-making in real-world contexts are slightly expanded in the 2022 revised curriculum. In addition, a hierarchical pattern was identified across school levels, with reasoning-oriented conceptual understanding emphasized in middle school and problem solving and application-oriented activities strengthened in high school. Digital literacy showed similar patterns across the two curricula, and was primarily manifested through the use of technological tools integrated into mathematical activities such as problem solving, data interpretation, and representation transformation.

최희선 Choi Heesun

DOI:10.7468/jksmee.2026.40.1.55 JANT Vol.40(No.1) 55-74, 2026

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This study aimed to explore patterns of change in preservice mathematics teachers’ TPACK self-perceptions before and after participating in a course on technological tool use. To this end, a course including lesson design and teaching demonstrations using technological tools was implemented for 25 preservice mathematics teachers, and data were collected through pre- and post-surveys of TPACK self-perception, a post-survey of perceived importance, and semi-structured interviews. The results showed that self-perceptions in TK, TPK, and TPACK increased significantly and that TCK, TPK, and TPACK appeared to be more closely related after the course than before. In addition, perceived importance was higher than self-perception in several domains, with a relatively notable gap in TCK, which was measured with a single item. Interview findings indicated that preservice mathematics teachers understood technological tools as resources for designing representations and activities that make mathematical meaning visible, although they also recognized difficulties in translating such ideas into actual classroom instruction. These findings suggest that experiences of lesson design and teaching demonstrations using technological tools may be related to an expansion of preservice mathematics teachers’ TPACK self-perceptions toward a more integrated and practical perspective.

지승훈 Ji Seunghoon , 권나영 Kwon Na Young , 김소민 Kim Somin

DOI:10.7468/jksmee.2026.40.1.75 JANT Vol.40(No.1) 75-90, 2026

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This study was designed to investigate mathematics teachers’ perceptions of the inclusion of values and attitudes as a component in the 2022 revised mathematics curriculum. The research focused on two central questions: (1) how mathematics teachers perceive the achievement standards incorporating values and attitudes introduced in the 2022 revised curriculum, and (2) how they perceive the assessment of subject competencies related to these elements. This qualitative case study was conducted with six secondary school mathematics teachers in the Incheon region, using in-depth interviews based on semi-structured interview protocols. The findings indicate that the participating teachers acknowledged the importance of students’ attitudes toward mathematics and responded positively to the inclusion of values and attitudes as content elements in the revised curriculum. However, among the three categories of content elements, they tended to assign relatively lower importance to values and attitudes. In addition, the teachers reported difficulties in practically assessing achievement standards that reflect values and attitudes in classroom settings. The discussion addresses implications for implementing curricular changes that emphasize not only mathematical knowledge and procedures but also values and attitudes, and suggests directions for future research.

도주원 Do Joowon

DOI:10.7468/jksmee.2026.40.1.91 JANT Vol.40(No.1) 91-111, 2026

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This study aimed to develop and explore the practical applicability of teaching practices based on real-life examples of the 14 factors that influence student thinking during lessons, as suggested by Liljedahl(2021/2024), to implement a thinking classroom in mathematics that promotes students' ‘thinking’ as a prerequisite for learning. For this purpose, practical teaching practices grounded in these 14 factors were designed and applied to mathematics lessons with one sixth-grade elementary school class. Concrete teaching cases were empirically analyzed, and the effectiveness of these practices was examined through surveys. The findings suggest that it is possible to formulate practical teaching practices for creating a thinking classroom in mathematics and verify their effectiveness. Furthermore, a thinking classroom in mathematics can provide meaningful learning experiences. The results of this study can serve as foundational data for improving teaching and learning methods and developing concrete teaching practices to design learner-centered lessons and foster students' ‘thinking’.

오영석 Oh Young-seok , 안후상 An Hoosang , 김원 Kim Won

DOI:10.7468/jksmee.2026.40.1.113 JANT Vol.40(No.1) 113-142, 2026

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The purpose of this study was to analyze mathematical errors appearing in translation tasks among linear function representations for two low-achieving eighth graders, and to develop ‘Looking tasks’ and questioning strategies that facilitate the process of forming those errors into mathematical meaning. To this end, an instrumental case study was conducted in which analytic tasks were developed based on the learning trajectory of Ahn and Oh (2021), each student’s errors were analyzed through iterative diagnosis, and customized ‘Looking tasks’ were designed and implemented. The results revealed that both students followed unique learning trajectories differing from the general one, and new types of errors not previously reported in the literature were identified. ‘Looking tasks’ and questioning strategies designed according to the looking-back principle, developmental node appropriateness principle, and self-correction principle facilitated the process of forming the students’ errors into mathematical meaning, with task sequencing playing a particularly important role in error resolution. These findings suggest that in-depth diagnosis is necessary for analyzing errors of low-achieving students, and that developing customized tasks based on each student’s developmental node and error characteristics is essential.

김유리 Kim Yuri , 신보미 Shin Bomi

DOI:10.7468/jksmee.2026.40.1.143 JANT Vol.40(No.1) 143-163, 2026

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The purpose of this study is to analyze the characteristics and developmental patterns of middle school students’ covariational reasoning as they explore variables through dragging in a classroom environment using AlNuSet, a dynamic algebraic engineering tool. To this end, dynamic variable-based algebra tasks were designed based on the “Change and Relationship” strand of the 2022 revised Korean mathematics curriculum and implemented in five class sessions with 26 first-year middle school students. Students’ verbal interactions and records of their manipulations in AlNuSet were collected during the lessons and qualitatively analyzed using the covariational reasoning framework proposed by Thompson and Carlson. The results show that students’ covariational reasoning appeared in diverse forms, ranging from qualitative recognition of change to coordination of individual values, reasoning based on units of change, and further to the recognition of invariant relationships that hold across the entire process of change. In particular, Level 4 covariational reasoning did not emerge as a fixed or isolated stage, but rather appeared in combination with other levels and functioned as an important cognitive stepping stone for transitions from qualitative reasoning to more advanced forms of covariational reasoning. In addition, some students, without direct teacher guidance, autonomously adjusted the scope of their exploration by using features such as domain settings and tracking functions, thereby extending their reasoning toward the accumulation of change units and invariant relationships. These findings suggest that dynamic algebra tasks using AlNuSet support students in conceptualizing variables not as fixed unknowns but as varying quantities, and facilitate the progressive development of covariational reasoning. Furthermore, this study provides concrete instructional design implications for early algebra instruction in middle school, highlighting how covariational reasoning can serve as a central means for exploring connections between algebra and functions.

이재교 Lee Jaegyo , 오세준 Oh Se Jun

DOI:10.7468/jksmee.2026.40.1.165 JANT Vol.40(No.1) 165-191, 2026

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This study examines how statistical inference is represented in the high school interdisciplinary elective textbook Practical Statistics developed under the 2022 revised national curriculum in Korea, and interprets its characteristics through a comparative analysis with six Probability and Statistics textbooks. The analysis focuses on the definition, notation, explanation, and interpretation of core inferential statistics concepts common to both subjects―random variables, normal distribution, confidence intervals, and sample proportions―as well as the types of presentation and use of technological tools in the “Data Analysis” domain of Practical Statistics. The findings indicate that Practical Statistics places greater emphasis on intuitive approaches grounded in real-life contexts and on visualization and automated computation through technological tools, whereas Probability and Statistics tends to foreground symbolic representation and formal definitions to ensure logical coherence and mathematical rigor of concepts. These differences not only reflect the distinct curricular orientations of the two subjects but also have substantive implications for the ways students construct inferential reasoning and for the instructional focus adopted in classroom practice. Based on these results, this study suggests textbook design strategies that connect conceptual rigor with interpretation-centered approaches, and highlights the need to diversify technology-based tasks in order to expand opportunities for student-driven statistical inquiry.

김주현 Kim Juhyeon , 방정숙 Pang Jeongsuk

DOI:10.7468/jksmee.2026.40.1.193 JANT Vol.40(No.1) 193-215, 2026

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In the elementary mathematics textbooks aligned with the 2022 revised curriculum, QR codes have been widely introduced as one of the means to facilitate access to a variety of digital learning resources. However, systematic analyses of the types of materials and instructional functions associated with QR codes in elementary mathematics textbooks remain limited. To address this gap, this study analyzed nine elementary mathematics textbook series for Grades Three and Four developed under the Korea’s 2022 revised national curriculum. The analysis examined the distribution of QR codes across textbooks and content domains, the types of materials provided through QR codes, and their instructional uses. The results revealed substantial differences among textbooks not only in the quantity of QR codes but also in the types of content and patterns of use. These findings suggest that guidelines for QR code implementation should move beyond formal or technical considerations to incorporate the pedagogical characteristics of the linked materials. Based on these findings, this study discusses specific implications for the design and development of QR codes in elementary mathematics textbooks.

이정민 Lee Jungmin , 조민식 Cho Minshik

DOI: JANT Vol.40(No.1) 217-243, 2026

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This study investigate the quantitative processes involved in constructing relationships between two covarying quantities by examining functional thinking through the dual constructs of change and accumulation. Grounded in a covariational perspective on functions, the study aims to articulate the flow of functional reasoning that integrates these two elements and to model a corresponding learning trajectory. A design experiment was conducted with three ninth-grade students, who engaged in a task involving the filling of a rectangular bathtub at a constant rate. As students constructed a continuous relationship between time and water height, they reasoned about change using ratios and rates of change, while accumulation served as the basis for quantifying the relationship between the two quantities. The findings show that recognizing covariation is essential for quantifying continuous relationships through accumulation. Through analysis of students’ reasoning, the study identifies characteristic patterns of thinking related to change and accumulation and elaborates a learning trajectory for functional thinking that incorporates these components.