최여선 Yeoseon Choi , 김예진 Yejin Kim , 김민지 Minji Kim , 오세준 Sejun Oh

DOI:10.63311/mathedu.25.6421 JANT Vol.64(No.2) 65-87, 2025

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This study investigates how two Korean middle-school mathematics teachers noticed and reasoned while collaboratively designing an inquiry task that applies quadratic equations through block coding. Drawing on the three-phase model of professional noticing proposed by Jacobs et al. (2010) and the FOCUS Framework of Choy (2016), we analysed successive task drafts, two rounds of revisions, online-meeting transcripts, chat logs and rubric documents. The analysis traced what the teachers attended to, how they interpreted it pedagogically and what instructional decisions ensued. The results show that the teachers deliberately linked mathematical concepts, blockcoding representations and desired values/attitudes to construct a task. While their early noticing was dominated by the technical affordances of the digital tool, iterative discussions and expert feedback gradually redirected their attention toward students’ cognitive difficulties and conceptual understanding―an evolution toward “productive noticing.” The collaborative design process thus deepened the teachers’ noticing and offers a potential model for planning technology-enhanced mathematics lessons.

지민경 Minkyeong Ji , 황지현 Jihyun Hwang

DOI:10.63311/mathedu.25.6422 JANT Vol.64(No.2) 89-109, 2025

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This study is about the process of developing a validated instrument by reconceptualizing knowledge and knowing to measure secondary mathematics teachers' epistemological beliefs. The factors of epistemological beliefs were categorized into certainty of knowledge, sources of knowledge, sources of knowing, and justification of knowing. The initial items of the instrument were developed based on literature review and prior research on epistemological beliefs. Content and substance validity of the items were verified through first and second pilot tests, and expert review. The structural validity of the instrument was verified through confirmatory factor analysis. The results of this study with 141 secondary mathematics teachers confirmed the reliability and validity of the final 17-item instrument as a measure of epistemological beliefs. This study can provide a basis for observing changes in teachers' instructional design and teaching and learning methods.

여승현 Sheunghyun Yeo , 박주경 Jukyung Park , 남지현 Jihyun Nam , 임미인 Miin Lim

DOI:10.63311/mathedu.25.6423 JANT Vol.64(No.2) 111-132, 2025

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This study explores the development and application of an AI-based instructional models that emphasize teacher agency in elementary mathematics education. While recent advances in AI have led to the proliferation of personalized learning environments, many current instructional models lack practical flexibility and fail to account for the pivotal role of teachers in dynamically orchestrating classroom learning. To address this gap, the study proposes < TocToc Adaptive Block Model >, a modular instructional framework designed to support planning, implementation, and evaluation of mathematics lessons using the AI-based system < TocToc-Math >. Drawing on the theoretical framework of teacher agency―including its reiterative, projective, and practical-evaluative dimensions―the model allows teachers to flexibly arrange instructional blocks such as Engage, Explore, Execute, Evaluate, and Personalize. This study employed a development research methodology centered on literature analysis, expert consultation, and feasibility review. Field experts validated the model’s educational feasibility and contextual adaptability, and three implementation types―immersive, selective, and flexible arrangement―were derived to support varied classroom contexts. This study highlights the importance of empowering teachers as learning designers and underscores the need for long-term research on teacher agency in AI-based environments. The findings offer practical and theoretical insights into designing AI-enabled instruction that preserves pedagogical intentionality and responsiveness.

Hangil Kim , Hee-jeong Kim

DOI:10.63311/mathedu.25.6424 JANT Vol.64(No.2) 133-153, 2025

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In mathematics, generalization is undoubtedly important and critical to learning and doing mathematical reasoning and is considered as not only a means contributing to the construction of new knowledge but also the essence of mathematical reasoning. Recent reforms in mathematics education emphasize the importance of fostering functional thinking early from the elementary level, with pattern generalization (PG) recognized as a key pathway toward this goal. However, prior research has highlighted the limited variety and depth of PG opportunities presented in elementary mathematics textbooks, particularly in their support for developing foundational algebraic concepts such as variable and function. In this study, we analyzed PG tasks (PGTs) as represented in Korean elementary textbooks and U.S. elementary textbooks to examine the nature of PG tasks using the Relating- Forming-Extending framework (Ellis et al., 2022) for PG activities and another analytic framework for an analysis of the nature of PGT. Results indicate that the nature of PGT is limited in the sense that student’s recursive thinking may not sufficiently be challenged and thus be progressed to functional thinking. These findings highlight the need to reconsider how PGTs are structured in elementary mathematics textbooks in order to better support students’ progression from recursive reasoning to functional thinking.

Sang Hee Lee , Hyewon Chang

DOI:10.63311/mathedu.25.6425 JANT Vol.64(No.2) 155-180, 2025

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This study investigates the effects of a history-based mathematics lesson utilizing proportional problems from Jiuzhang Suanshu (九章算術) on the mathematical understanding and value recognition of 27 sixth-grade elementary school students. The five-session lesson was designed based on Jankvist’s (2009) framework, which distinguishes between using history as a cognitive tool and as a goal. As a cognitive tool, integrating historical problems supported the development of students’ proportional reasoning, deepened their understanding of the flexible and socially embedded nature of traditional measurement units, and fostered the refinement of mathematical thinking through peer discussion and error analysis. Students also demonstrated growth in mathematical literacy as they worked to interpret historically situated problems. To examine the use of history as a goal, pre- and postsurveys were conducted to assess students’ recognition of mathematical values, revealing statistically significant improvements across historical, cultural, practical, social, and East Asian mathematical domains. Qualitative data further indicated increased appreciation for the practicality, creativity, and cultural significance of mathematics, along with a heightened sense of pride in East Asian mathematical heritage. These findings suggest that historybased mathematics instruction can not only support conceptual development but also promote meaningful reflection on the broader value and role of mathematics in society.

Mweni Tsofa Nickson , Marguerite M. O’connor , Maundu John Nyamai

DOI:10.63311/mathedu.25.6426 JANT Vol.64(No.2) 181-195, 2025

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The article shares findings from the study’s objective to establish the influence of socio-culturally based mathematical learner identity on student achievement in mathematics. The sociocultural theory of learning formed the theoretical framework. The study applied a correlational research design on a sample size of 100 students, using a Researcher Introspection Tool and Student Mathematics Achievement Test to obtain quantitative and qualitative data. Content analysis quantified socio-culturally based mathematical learner identity data before correlated to the student achievement in mathematics. The study indicated that socio-culturally based mathematical learner identity influences student achievement in mathematics. The analyzed data were then presented in narrative and tabular forms. The study recommends designing constructive artefacts to develop problem-solving activities and the meanings of mathematical concepts.