허진영 Jinyoung Heo , 임수현 Soo-hyun Im

DOI: JANT Vol.63(No.3) 393-409, 2024

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The number line model, which intuitively marks numerical magnitudes in space, is widely utilized to help in understanding the magnitudes that fractions and decimals represent. The study analyzed 6th graders’ understanding of fractions and decimals, their problem solving strategies, and whether individual differences in the flexibility of various strategy uses are associated with the accuracy of numerical representation, calculation fluency, and overall mathematical achievement. As a result of the study, students showed relatively lower accuracy in representing fractions and decimals on a number line compared to natural numbers, especially for fractions with odd denominators compared to even denominators, and for two-digit decimals compared to three-digit decimals. Regarding strategy use, students primarily used benchmark, segmentation, and approximation strategies for fractions, and benchmark, rounding, and transformation strategies for decimals sequentially. Lastly, as students used various representation strategies for fractions, their accuracy in representing fractions and their overall mathematical achievement scores showed significantly better outcomes. Taken together, we suggest the need for careful instruction on different interpretations of fractions, the place value of decimals, and the meaning of zero in decimal places. Moreover, we discuss instructional methods that integrate the number line model and its diverse representation strategies to enhance students’ understanding of fractions and decimals.

김소민 Somin Kim , 서보억 Boeuk Suh , 고호경 Ho Kyoung Ko , 허난 Nan Huh

DOI: JANT Vol.63(No.3) 411-436, 2024

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This study investigated how Korean elementary, middle, and high school students perceive mathematics learning situations to determine whether the mathematics classes provided in schools met the standards of a highquality educational experience. Using a comprehensive survey that considers both formal and implementation aspects of mathematics classes, responses from 15,418 students were analyzed to gain insights into their views on the classroom environment, instructional methods, and overall learning experience. The results indicate that as students advance in grade level, their perceptions of mathematics learning situations become increasingly negative, and mathematics classes are still perceived as being teacher-centered. Additionally, it was found that mathematical manipulatives and technological tools are not being effectively utilized, and that students’ learning experiences are influenced by class size and the availability of mathematics subject-exclusive classrooms. Based on these findings, several recommendations were made to improve the quality of mathematics education and enhance students’ perceptions: implementing teaching methods that increase student engagement in learnercentered classes, providing opportunities for active and diverse use of teaching aids and technological tools beyond simple calculations, maintaining appropriate class sizes, and expanding the use of mathematics subject-exclusive classrooms. These considerations are crucial for creating a more engaging and effective mathematics learning environment that aligns with evolving educational standards and meets students’ needs. The findings of this study provide actionable insights for educators and policymakers aiming to improve the quality of mathematics education in Korea.

박혜성 Hyesung Park , 김성연 Sungyeun Kim

DOI: JANT Vol.63(No.3) 437-450, 2024

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Self-directed learning in mathematics education is crucial because it enables students to think creatively and critically while continuously improving. The purpose of this study was to examine the mediating effects of class attitude and class satisfaction in mathematics on the relationship between mathematics teacher characteristics and self-directed learning. Furthermore, the study aimed to determine whether these structural relationships differ between male and female student groups. To achieve this, the theoretical model was tested using the 9th-year data (high school 3rd grade) of the Seoul Education Longitudinal Study (SELS) 2010, comprising 2,325 students (1,187 males and 1,138 females). The results revealed that the mediating effects of mathematics class attitude and class satisfaction on the relationship between teacher characteristics in mathematics and high school students’ self-directed learning were significant. At this time, the direct effect of mathematics teacher characteristics on self-directed learning was not significant, indicating that mathematics class attitude and class satisfaction had full mediating effects. Multi-group analysis results showed no significant differences in path coefficients between male and female student groups. Based on the research findings, implications for teacher education were presented to improve high school students’ self-directed learning abilities in mathematics education, focusing on the mediating effects of affective factors in the classroom.

황지남 Jinam Hwang

DOI: JANT Vol.63(No.3) 451-466, 2024

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This study investigated elementary preservice teachers’ conceptions of a generating line, an ambiguous concept in school mathematics. The preservice teachers’ conceptions of a generating line can be classified into four types: (a) only cones have generating lines, (b) only cones and cylinders have generating lines, (c) solids of revolution have generating lines, (d) straight lines on the lateral surface are generating lines. 22.1% of all preservice teachers believed that only cones have generating lines, and most of them followed the definition of a generating line presented in elementary mathematics textbooks. The conception that only cones and cylinders have generating lines was the least investigated. However, since there were instances where generating lines were defined with the use of a director curve, it became important to explore topics more thoroughly, such as generating lines of a truncated cone. 27.9% of all preservice teachers believed that solids of revolution have generating lines. This conception was marked by differing opinions on whether spheres also have generating lines. The conception that straight lines on the lateral surface are generating lines was the most frequently investigated. This conception differs from the traditional view in school mathematics because it suggests using a director curve to define generating lines. Based on these analysis results, the researcher developed specific teaching methods that considered both subject matter knowledge and pedagogical content knowledge for preservice teachers. In addition, the researcher proposed a consensus definition of a generating line in mathematics education.

권미선 Misun Kwon

DOI: JANT Vol.63(No.3) 467-484, 2024

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The rapid advancement of generative AI has ushered in an era where anyone can create and freely utilize personalized chatbots without the need for programming expertise. This study aimed to develop a customized chatbot based on OpenAI’s GPTs for the purpose of pre-service teacher education and to analyze its educational performance in mathematics as assessed by educators guiding pre-service teachers. Responses to identical questions from a general-purpose chatbot (ChatGPT), a customized GPTs-based chatbot, and an elementary mathematics education expert were compared. The expert’s responses received an average score of 4.52, while the customized GPTs-based chatbot received an average score of 3.73, indicating that the latter’s performance did not reach the expert level. However, the customized GPTs-based chatbot’s score, which was close to “adequate” on a 5-point scale, suggests its potential educational utility. On the other hand, the general-purpose chatbot, ChatGPT, received a lower average score of 2.86, with feedback indicating that its responses were not systematic and remained at a general level, making it less suitable for use in mathematics education. Despite the proven educational effectiveness of conventional customized chatbots, the time and cost associated with their development have been significant barriers. However, with the advent of GPTs services, anyone can now easily create chatbots tailored to both educators and learners, with responses that achieve a certain level of mathematics educational validity, thereby offering effective utilization across various aspects of mathematics education.

방정숙 Jeongsuk Pang , 김리나 Leena Kim , 곽기우 Giwoo Kwak

DOI: JANT Vol.63(No.3) 485-503, 2024

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The purpose of this study is to analyze elementary school teachers’ mindsets about students’ mathematical ability. For this purpose, we developed a 20-item scale to measure teachers’ mindset through a review of the literature. In order to verify the developed scale, a survey was conducted among 158 elementary school teachers, and the structure of the items was analyzed by exploratory factor analysis. As a result, three factors were identified: “growth mindset toward change in mathematical ability”, “fixed mindset toward change in mathematical ability”, and “mindset toward innate mathematical ability”. Four groups were distinguished by latent profile analysis, using the scores on these three factors as variables, to characterize the different groups of teachers based on their mindset. The groups with the most participants in the study were, in order, growth mindset teachers, neutral mindset teachers, strong growth mindset teachers, and fixed mindset teachers. Interviews were also conducted with representative participants from each group to learn more about the characteristics of teachers in each profile. Based on the results of the study, we discussed the implications of mindset in terms of the classification of teachers’ mindset about students’ mathematical ability, the popularity of growth mindset among elementary school teachers in Korea, and research on teachers’ mindset about innate mathematical ability.

지영명 Youngmyong Jee

DOI: JANT Vol.63(No.3) 505-526, 2024

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The goal of this study was to derive implications for the design of teacher training programs related to boxplots by examining the statistical reasoning patterns of mathematics teachers in group comparison tasks using boxplots. For this purpose, 48 secondary mathematics teachers who participated in a teacher statistics camp at a local office of education were selected as participants. Four sessions of teacher training were then conducted, including basic statistical concepts related to boxplots and group comparison activities using them. Afterwards, surveys with group comparison questions using boxplots and online interviews were conducted. The collected data were analyzed with a focus on the research questions. As a result, most participants relied on summary and spread elements to reason when comparing two groups using boxplots. On the other hand, participants paid little attention to shift and signal elements, and no responses using sampling elements were identified. Additionally, the overall comparative reasoning level of the participants was primarily at level 1 with the highest frequency (44%), and no responses reached level 3. Based on these research results, this paper derives implications for the design of teacher training programs related to boxplots and provides suggestions for follow-up research.

정혜윤 Hye-yun Jung , 이지현 Jihyun Lee

DOI: JANT Vol.63(No.3) 527-547, 2024

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It is difficult for mathematics teachers to develop mathematical modeling tasks and implement mathematical modeling lessons for their students. These difficulties serve as a reason why mathematical modeling lessons are not implemented well in school mathematics. In this study, we aimed to examine how preservice mathematics teachers (PMTs) modify mathematical modeling tasks in mathematics textbooks as a way to develop mathematical modeling tasks and how they implement the mathematical modeling lesson. In particular, we focused on how the openness and reality reflected in the task and the mathematical modeling process change as PMTs modify the tasks. We collected data through PMTs’ evaluation reports on analyzing textbook tasks, task modification, lesson plans and implementations, peer evaluation, and self-evaluation. Then, we analyzed these data according to the case analysis process. The findings revealed that when PMTs modified the textbook task, they focused on and improved the openness and the defining variables and the model stages of mathematical modeling process. However, when PMTs implemented lesson, the openness and the defining variables and the model stages of mathematical modeling process were restricted again. PMTs did not focus on other stages. Based on these results, the theoretical and practical implications of the study was discussed.

오세준 Sejun Oh , 윤정은 Jungeun Yoon , 정유진 Yoojin Chung , 조윤주 Yoonjoo Cho , 심효섭 Hyosup Shim , 권오남 Oh Nam Kwon

DOI: JANT Vol.63(No.3) 549-571, 2024

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As digital·AI-based teaching and learning is emphasized, discussions on the educational use of generative AI are becoming more active. This study analyzed the mathematical performance of ChatGPT 4, Claude 3 Opus, and Gemini Advanced on solving examples and problems from five first-year high school math textbooks. As a result of examining the overall correct answer rate and characteristics of each skill for a total of 1,317 questions, ChatGPT 4 had the highest overall correct answer rate of 0.85, followed by Claude 3 Opus at 0.67, and Gemini Advanced at 0.42. By skills, all three models showed high correct answer rates in ‘Find functions’ and ‘Prove’, while relatively low correct answer rates in ‘Explain’ and ‘Draw graphs’. In particular, in ‘Count’, ChatGPT 4 and Claude 3 Opus had a correct answer rate of 1.00, while Gemini Advanced was low at 0.56. Additionally, all models had difficulty in explaining using Venn diagrams and creating images. Based on the research results, teachers should identify the strengths and limitations of each AI model and use them appropriately in class. This study is significant in that it suggested the possibility of use in actual classes by analyzing the mathematical performance of generative AI. It also provided important implications for redefining the role of teachers in mathematics education in the era of artificial intelligence. Further research is needed to develop a cooperative educational model between generative AI and teachers and to study individualized learning plans using AI.

윤정은 Jungeun Yoon , 권오남 Oh Nam Kwon

DOI: JANT Vol.63(No.3) 573-591, 2024

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The purpose of this study is to explore research trends on AI-based mathematics teaching and learning. For this purpose, a systematic literature review was conducted on 57 literatures in terms of research subject, research method, research purpose, learning content, type of AI, role of AI, and role of teachers. The results indicate that student accounted for the largest proportion at 51% among the research subjects, and quantitative research was the highest at 49% among the research methods. The purpose of study was distributed as follows: effect analysis 44%, theoretical discussion 35%, case study 21%. ‘Numbers and Operations’ and ‘Variables and Expressions’ covered learning contents most, and Intelligent Tutoring System (ITS) was used the most among the types of AI. ‘Student teaching’ was the largest parts of role of AI at 40.4%, followed by ‘teacher support’ at 22.8%, ‘student support’ at 21%, and ‘system support’ at 15.8%. The role of teachers as ‘AI recipients’ was highlighted in earlier studies, and the role of teachers as ‘constructive partner with AI’ was highlighted in more recent studies. Also, role of teachers was explored in pedagogical, AI-technological, content aspects. Through this, follow-up research was suggested and the roles that teachers should have in AI-based mathematics teaching and learning were discussed.