강향임 Hyangim Kang

DOI: JANT Vol.63(No.4) 593-610, 2024

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The purpose of this study is to support creative inquiry activities that enable students to experience mathematical reasoning academically and explore artistic sensibilities holistically through the process of visualizing prime numbers in collaboration with ChatGPT. For this purpose, 41 second-year students from a gifted school were tasked with developing visualizations of prime numbers in collaboration with ChatGPT, and their visualization processes were analyzed. The analysis revealed the following results: First, the visualization activities provided students with creative and challenging opportunities to explore mathematical concepts. Students attempted various approaches to visualizing prime numbers and their distributions, producing creative works. Second, the study confirmed the potential of prime number visualization to offer students opportunities to capture mathematical beauty. Students expressed reactions such as amazement, interest, and happiness toward their creations. Third, ChatGPT proved to be an effective tool in the visualization of prime numbers, providing practical assistance such as saving time, suggesting ideas, and helping with coding and modifications. Students evaluated the role of ChatGPT positively. Fourth, the visualization activities helped students deepen their understanding of concepts related to prime numbers. Students reported a more profound comprehension of prime number concepts learned in number theory. Fifth, collaboration with ChatGPT served as a motivator for learning in various aspects. Students demonstrated a strong desire to further explore and take on new challenges. Sixth, the visualization of prime numbers through collaboration with ChatGPT served as an opportunity for creative convergence. As recommendations, the study emphasizes the need to foster critical thinking and awareness of over-reliance when collaborating with ChatGPT in educational settings. Furthermore, it highlights the continuous necessity for research on visualizations using AI and the development and activation of convergent visualization materials with enhanced artistic elements.

김구연 Gooyeon Kim , 여상희 Sanghee Yeo , 김영 Young Kim , 송은영 Eunyoung Song , 전혜림 Hyelim Chon , 조유진 Yujin Cho , 홍창준 Changjoon Hong , Seungwook Han , 강무성 Mooseong Kang

DOI: JANT Vol.63(No.4) 611-634, 2024

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This study examined the impact of integrated STEM learning on students’ perceptions of mathematics classes, ownership, agency, and interest and confidence in learning when learning. The aim was to enhance students’ integrated thinking competencies. The integrated STEM contents are designed in order to facilitate students’ learning of statistical thinking, encompassing the collection, analysis and interpretation of data encountered in students’ daily lives, as well as reasoning and problem solving. The content was designed with the intention of providing meaningful and integrative context, thereby facilitating problem solving and reasoning capabilities, and elucidating the process of students’ reasoning and justification. Six themes of integrated STEM content were designed, comprising four for middle school students and two for high school students. A questionnaire was conducted prior to and following the lessons in order to ascertain the students’ attitudes and feelings towards the classes, as well as their perceptions of mathematics and science. Also, an additional survey and interviews were conducted with students who participated in the theme dealing with carbon emissions with statistics, population with statistics, and global warming with statistics. The data analysis suggested the following findings: a) the students appeared to actively engage in the sharing of opinions and participation in tasks, demonstrating a sense of usefulness pertaining to mathematics, science, and statistical data, and exhibiting the development of interest and confidence in mathematics, b) the students also expressed satisfaction and interest regarding the integrated STEM contents facilitated the integration of knowledge from various subjects, and c) they would be willing to explore the theme further on their own initiative.

김리나 Leena Kim , 이수진 Soojin Lee , 방정숙 Jeongsuk Pang

DOI: JANT Vol.63(No.4) 635-656, 2024

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Teachers need to attend, interpret, and respond to students’ strengths as well as deficits in mathematical thinking, and this is also connected to improving teachers’ noticing abilities. The purpose of this study was to develop a video club based program to improve elementary teachers’ noticing skills by exploring strengths- and deficits-based framing. To achieve this purpose, we developed a program that went through a series of stages of preparation, development, and validation to notice students' mathematical thinking through strengths- and deficits-based framing, including a pre-activity, eight video club sessions, and a post-activity. The pre-activity was designed to gather preliminary information about the framing that the participanting teachers primarily used to notice the students’ mathematical thinking in video clips. The video club sessions were designed to inform participants about strengths- and deficits-based framing and to practice noticing students’ mathematical thinking in video clips using each framing approach. The sessions then used a variety of video clips to experience how to notice using schemes or sentence frames for strengths- and deficits-based framing. The post-activity was designed to explore the participants’ overall perceptions of the program and what they had learned. The paper concludes by discussing on the importance of the video club program developed and its implications for practice.

Jungeun Park , Douglas Rizzolo

DOI: JANT Vol.63(No.4) 657-673, 2024

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Based on the observation that there is a common signifier “derivative” in English used for both the derivative at a point and the derivative function and that there are two phonetically and semantically different signifiers for those objects in Korean, we explored potential differences in classroom teaching discourses aimed to teach canonic mathematical discourses about the mathematical objects that those terms signify and their relations in Korean and English. Our analysis of one Korean teacher’s and one American teacher’s classroom discourse about the derivative using the commognitive approach uncovered differences in their teaching discourse in terms of addressing metarules about the terms and connections to colloquial discourse that exist in English, but not in Korean. We also found differences in how the American teacher made connections between the derivative at a point and the derivative function and how the Korean teacher connected the two signifiers in Korean - the American teacher extended a realization of the first defined object to define the second object, and after that, made shifts in a way that precludes simultaneous use of the common signifier for both objects whereas, in Korean teacher’s discourse, no extensions were observed and the first defined object gained additional realizations.

박지현 Ji Hyun Park , 성지현 Ji Hyun Sung

DOI: JANT Vol.63(No.4) 675-706, 2024

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The purpose of this study is to examine the coherence between the content and timing of mathematics curriculum in social studies and science textbooks for elementary school grades 3-4 from both educational and substantive perspectives. For this study, we analyzed how mathematical concepts presented in social studies and science textbooks for grades 3-4, following the 2015 revised elementary school curriculum, are utilized across grade levels and semesters. We also examined differences in how these mathematical concepts, as they appear in social studies and science textbooks, are approached or deepened compared to their treatment in mathematics. The study revealed that concepts considered “reversal” in social studies and science textbooks often appear earlier than in mathematics curriculum. There were instances where concepts typically covered in middle school mathematics, such as ‘negative numbers’, were also utilized. Moreover, we identified concepts that are presented in a modified or advanced manner compared to their treatment in mathematics, and instances where concepts not typically covered in mathematics, such as radial graphs, were utilized. Based on these results, it was concluded that a clear definition of concepts is needed in the mathematics curriculum, and that close review and guidance on related concepts between subject curricula are needed when developing curriculum and textbooks.

정영우 Youngwoo Chung

DOI: JANT Vol.63(No.4) 707-723, 2024

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In this study, a method of analyzing development diagram of cubes with graph theory was considered. To this end, the development diagram of cubes covered in school mathematics was analyzed using a tree, and the method was applied to the development diagram of cubes in which the faces were arbitrarily cut. The development diagram in which the faces are arbitrarily cut becomes the subject of activity for mathematical creativity, and the higher the complexity of the structure, the more difficult it becomes to grasp the relationship with the cube. However, if the graph theory can be applied and converted into a typical degree of development, it becomes easier to grasp the structure. The graphical analysis method of the development diagram provides a new perspective to explore three-dimensional figures and development diagrams, and can be used to analyze creative products.

최은아 Eunah Choi

DOI: JANT Vol.63(No.4) 725-743, 2024

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This study examines the characteristics of calculation methods for pi and area of a circle and examples of changes over time in the way they are interpreted and handled in Joseon-Sanhak. For this purpose, We analyzed four Joseon- Sanhak books, including < Muksajipsanbeop >, < Juseogwangyeon >, < Guiljip >, and < Gosasibiijip >, representing the late 17th and 18th centuries. The specific analysis results are as follows. First, all Joseon-Sanhak books recognized that precision can be adjusted by appropriately selecting approximations of various pi according to the situation, and they still placed emphasis on Gobeob(古法) for convenience of calculation. Regarding the properties of pi, the ratio property that reveals the relationship between diameter and circumference and the approximation property due to infinity were relatively well revealed, but the remaining properties were recognized in a limited way. In addition, Joseon-Sanhak books were using various methods of calculating the area of a circle, and all methods of calculating the area of a circle contained a consistent logic of creating a rectangle with the diameter and circumference and then calculating the area in proportion to the area of the square. Meanwhile, from the late 17th century to the 18th century, cases of a gradual shift from calculation methods to strict mathematical logic related to circles were confirmed. Gujangmundab of < Juseogwangyeon > argue why all calculation methods for the area of circles are based on the area of squares, present numerical calculation results as the basis for comparing the precision of pi, and provide a general method for obtaining a more precise pi. The principles of Halwonsul were developed logically. These cases can be seen as a movement of change that seeks to reason and justify strictly logically. This change suggests that Joseon-Sanhak are advancing to a stage where they value mathematical precision beyond the practical purpose of simply applying calculation methods.

신민경 Min Kyung Shin , 고호경 Ho Kyoung Ko

DOI: JANT Vol.63(No.4) 745-766, 2024

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This study aimed to examine trends in research on the geometry domain of mathematics education in Korea through keyword network analysis. To achieve this, keywords from research papers related to mathematics education and geometry published in domestic journals from 2000 to May 2024 were collected, totaling 323 papers. The network analysis was conducted by dividing the data into the entire research period and specific curriculum revision periods. The results of the analysis showed that, first, the keyword with the highest frequency of occurrence, degree centrality, and closeness centrality was ‘middle school’, while ‘justification’ showed high centrality despite a lower frequency ranking. Second, sub-network analysis using modularity and ego network analysis identified characteristics of research across different school levels, studies on mathematical giftedness, and comparative analyses of textbooks following curriculum revisions. Third, the research keywords during curriculum revision periods indicated a shift from studies focusing on the logical structure and reasoning of Euclidean geometry to those emphasizing intuitive thinking, practicality, and real-life problem-solving, aligning with the revised curriculum’s focus. By categorizing and analyzing the research subjects in various ways, the study identified the core and connections of research topics in the geometry domain of mathematics education, aiding in the understanding of research trends and providing implications for future research.

이기마 Gima Lee , 김희정 Hee-jeong Kim

DOI: JANT Vol.63(No.4) 767-789, 2024

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This study conducted a scoping review of 19 studies on math chatbots conducted in South Korea. The study analyzed key research themes and types, mathematical content and its selection criteria, research methods, roles and design principles of chatbots, technologies employed in chatbots, and the roles of teachers and students in math chatbot research. Through this analysis, the current landscape and growth potential of the math chatbot research ecosystem were identified, leading to several directions for future research. First, ‘studies on AI and convergence’, ‘exploratory research’, ‘research on geometry content’, and ‘literature reviews’ should be expanded. Second, further studies should establish a consensus on the safety of personalized instructional chatbots and then develop technical solutions for their implementation. Third, additional studies are needed on teachers’ roles as ethical supervisors and students’ roles as ethical adherents regarding AI and chatbots. Fourth, future research should allocate adequate research resources to studies on teachers’ noticing and specialized content knowledge (SCK) in chatbot-based teaching and learning environments, as well as the impact of chatbots on students’ thinking processes. Finally, three research topics for a systematic literature review, which should be conducted once sufficient chatbot research has been accumulated, were suggested. The study provided specific directions to ensure the systematic and continuous growth of the math chatbot research ecosystem in South Korea through this analysis.