김정현 Kim Jeong Hyeon

DOI:10.7468/jksmee.2026.40.2.245 JANT Vol.40(No.2) 245-262, 2026

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This study examines the structural relationship of how high school students' Self-Directed Learning (SDL) and Private Education (PE) time affect mathematics academic achievement and interest, mediated by class participation. Using data from 4,083 sophomores in the 6th Daejeon Education Longitudinal Study (DELS, 2025), a path analysis was conducted. The results showed that both SDL and PE positively affected achievement and interest, but SDL had a consistently stronger influence. Second, SDL positively influenced class participation, confirming a significant indirect effect on achievement and interest. Conversely, PE did not significantly affect class participation, showing no indirect effect. These findings demonstrate that SDL serves as a significant background factor out-of-class efforts to active in-class participation. Consequently, the study suggests that public education should focus on fostering students' SDL capabilities rather than merely acting as a substitute for private education.

최희선 Choi Heesun

DOI:10.7468/jksmee.2026.40.2.263 JANT Vol.40(No.2) 263-287, 2026

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This study analyzed the characteristics of technological tool integration in lesson design artifacts developed by preservice mathematics teachers in teams. The main data consisted of ten lesson design reports written by 30 preservice mathematics teachers in teams of three, and the reports were compared and interpreted using two analytic dimensions: coherence of integrated design and quality of learning activity structure. The self-reported TPACK survey was used as background data to identify participants’ overall perception tendencies, whereas interviews were used as contextual data to understand the difficulties and adjustments experienced during the design process. The results showed that, for coherence of integrated design, five teams were classified at Level 1, four teams at Level 2, and one team at Level 3. For quality of learning activity structure, six teams were classified at Level 1 and four teams at Level 2, with no Level 3 cases. These findings suggest that although preservice mathematics teachers incorporated technological tools into their lesson designs, they had difficulty clarifying the pedagogical rationale for tool selection in mathematics education and extending students’ activities to include conjecturing, explaining, and justifying. Based on these findings, this study discusses the need to support preservice mathematics teachers’ experiences in designing lessons using technological tools.

김예나 Kim Yena , 신인섭 Shin Insub

DOI:10.7468/jksmee.2026.40.2.289 JANT Vol.40(No.2) 289-314, 2026

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As mathematics education has shifted toward fostering mathematical thinking, values, and attitudes, the importance of self-regulated learning (SRL) has grown. At the same time, with the advancement of digital technology and the expansion of online learning environments, AI Digital Textbooks (AI DTs) have recently been introduced into public education. Accordingly, this study aimed to examine the functional significance of AI DTs from the perspective of self-regulated learning. An analytical framework for AI DTs was developed based on policy documents published by the Ministry of Education and the Korea Education and Research Information Service (KERIS), as well as the AI-SRL framework proposed by Zhu and Sari (2026). Using this framework, AI DTs from four accessible publishers were analyzed, focusing on the first-year high school units on quadratic equations and quadratic functions. The results showed that all AI DTs provided personalized learning features and data-driven functionalities, while differences were observed in motivational support and AI tutoring functions. These features were found to be closely aligned with the phases of self-regulated learning and also provided appropriate instructional guidance for teachers. However, AI tutor and AI teaching assistant functions were implemented only to a limited extent, suggesting the need for further development and enhancement.

강윤지 Kang Yunji

DOI:10.7468/jksmee.2026.40.2.315 JANT Vol.40(No.2) 315-333, 2026

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This study explored the potential of meta-problems as an analytical tool for observing metacognitive thinking in sixth-grade students. Textbook items based on the 2022 revised mathematics curriculum were reconstructed into three levels: self-monitoring (L1), change-prediction (L2), and value-critique (L3), and were administered to 18 students. The results indicated that students demonstrated metacognitive responses, including verbalizing their thinking processes, predicting outcomes under modified conditions, and critically examining the validity of their strategies and definitions. Notably, lower-level self-monitoring appeared to function as a prerequisite for higher-level critical analysis, and students showed a shift toward perceiving mathematical knowledge from a mere tool for correct answers to an object for critical reflection. This study suggests that meta-problems can serve as a practical diagnostic and instructional tool for assessing and facilitating metacognitive functions in elementary mathematics education.

김주영 Kim Joo Young , 김민경 Kim Min Kyeong

DOI:10.7468/jksmee.2026.40.2.335 JANT Vol.40(No.2) 335-355, 2026

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As the scope of schooling extends beyond the classroom, the role of non-formal instructors involved in learners’ mathematical interactions has become increasingly important. However, their mathematical understanding and ways of explaining have not been sufficiently explored. This study employed a qualitative multiple-case study to analyze patterns of referent unit processing and representational connections that emerged in the process of explaining fraction division among three non-formal instructors. Although all three participants produced the same computational result, they showed clear differences in how they explained that result as the number of a particular unit. In particular, these differences varied according to whether they were able to reconstruct the unit meaning of the result value, and this was related not only to the coherence of their explanations but also to their tendency, in actual teaching situations, to prioritize procedural instruction over conceptual explanation. The findings suggest that the quality of out-of-school mathematics support depends not simply on whether help is provided, but on the level at which referent units are processed and explanations are organized. This study therefore highlights the need for concept-centered support for non-formal instructors.

김예린 Kim Yerin , 이수진 Lee Soo Jin

DOI:10.7468/jksmee.2026.40.2.357 JANT Vol.40(No.2) 357-386, 2026

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This study aims to lay the groundwork for implementing student-centered communication-based mathematics instruction by analyzing how teachers implement five practices and how students participate in high school mathematics classes where these practices are applied. The researcher applied these practices to their own classes and conducted an in-depth case analysis using lesson logs, recorded and transcribed materials, and student interviews. The results showed that the five practices enabled student-centered mathematical discussion classes even in high school. Their implementation was influenced by the teacher's conscious application, interactions between practices, the teacher's past experiences, anticipation of diverse reactions, and feedback methods based on the teacher's beliefs. Furthermore, repeated application of these practices under appropriate teacher control increased student participation in discussions. Task accessibility, peer involvement, teacher feedback, and a permissive atmosphere further facilitated discussions. Notably, a classroom atmosphere that tolerates errors enhanced student participation in discussions, aiding practice implementation and suggesting the feasibility of communication-centered lessons fostering mathematical discourse even in high school.

박소희 Park Sohee , 최인용 Choi Inyong

DOI:10.7468/jksmee.2026.40.2.387 JANT Vol.40(No.2) 387-414, 2026

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This study aims to analyze fifth-grade elementary students’ graph comprehension processes for bar and line graphs, and to explore the types of errors that emerge during task performance. To this end, graph comprehension tasks were administered to seven fifth-grade students, and eye-tracking data and cued retrospective interview data were collected and qualitatively analyzed. The results showed that students exhibited different visual exploration patterns depending on the task type―reading the data, reading between the data, and reading beyond the data―and that their accuracy rates were lower for line graphs than for bar graphs. In addition, four types of errors were identified: errors in problem comprehension, interpreting key terms, interpreting scale units, and interpreting points and intervals. In particular, the eye-tracking data enabled the identification of what information students explored, which exploration steps were omitted, and what difficulties they encountered when processing the visual information to meet the task requirements. This allowed for a more precise diagnosis of how and why errors occurred. This study contributes to the literature by analyzing elementary students’ graph comprehension and errors at the process level rather than merely focusing on task outcomes.

김화영 Kim Hwa-young , 김종률 Kim Jong Ryul

DOI:10.7468/jksmee.2026.40.2.415 JANT Vol.40(No.2) 415-445, 2026

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This study proposes a "white-box" Python teaching and learning model that implements internal computations directly to overcome the limitations of traditional "black-box" tools in university mathematics and engineering education. To minimize the programming burden, the model utilizes only basic control statements and arithmetic operations, while enhancing classroom applicability through Google Colab. The curriculum includes the development of algorithmic implementation models for numerical integration (Trapezoidal and Simpson's rules), extremum searching, and solving ordinary differential equations using the Runge-Kutta method. Classroom application and qualitative analysis revealed that students deeply internalized abstract calculus principles―such as infinity, limits, and higher-order derivatives―into discrete steps by translating mathematical challenges into procedural code. In conclusion, this study suggests that the white-box coding approach, which fosters both computational thinking (CT) and creative problem-solving skills through the translation of mathematical principles into code, serves as a practical alternative for creative convergence mathematics education in the AI era.

오창룡 Oh Changryong , 서보억 Suh Boeuk

DOI:10.7468/jksmee.2026.40.2.447 JANT Vol.40(No.2) 447-470, 2026

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The purpose of this study is to analyze the impact of mathematics classes using generative artificial intelligence (AI) on the learning experiences of middle school special class students with intellectual disabilities. To this end, an action research method was applied to develop a mathematics program utilizing generative AI centered on 'division operations' and 'linear equations,' which was then applied to two middle school special class students to analyze its effectiveness. The results of a qualitative analysis of the collected class recordings, interview data, and worksheets are as follows. First, students acquired successful experiences in solving mathematical problems by correcting their errors through the tutoring and feedback functions of generative AI. Second, interactions with the AI and game-like elements stimulated students' interest, leading to a positive change in their affective attitudes toward mathematics. Third, students experienced a transition from a teacher-dependent attitude to active subjects who proactively participate in their learning. However, difficulties were also identified, such as limitations in prompt input and literacy due to the characteristics of students with intellectual disabilities, as well as constraints regarding device and network environments. This study provides implications regarding the potential for utilizing generative AI in special education settings and the role of teachers.

김인옥 Kim In Ok , 심상길 Shim Sang Kil

DOI:10.7468/jksmee.2026.40.2.471 JANT Vol.40(No.2) 471-484, 2026

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This study aims to investigate, from the theoretical frameworks of Hiebert and Skemp, how examples presented in the function unit of 2nd-year middle school mathematics textbooks function as a multi-layered structure through three processes, which are concept formation-centered structure, real-life connection and extension structure, and representational transition-centered structure, in order to provide educational implications for student understanding, teacher instruction, textbook authorship, and curriculum design. With regard to student understanding, it is desirable to help students comprehend the concept of function as a coherent structure rather than a fragmented set of computational procedures, to provide opportunities for learning mathematical concepts in connection with real-world phenomena, and to offer experiences of transforming and connecting the same concept across multiple representations. Concerning teacher instruction, teachers need to guide students in extending their thinking beyond definitions toward structures and properties by emphasizing the connections among concepts, and to ensure that real-life examples are not merely presented as contextual materials but that their structural connection to the concept of function is made explicit.