이호수 Lee Hosoo , 최근배 Choi Keunbae

DOI: JANT Vol.38(No.4) 487-512, 2024

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This study analyzed the response types and accuracy rates of pre-service elementary teachers in solving problems involving the areas of inscribed and non-inscribed triangles within a fixed rectangle. These problems were based on equiareal transformations using the sum or difference of two rectangles' areas. The findings are as follows: First, the analysis of student responses to questions about the area transformation of inscribed triangles revealed that there was no significant difference in the use of double-area transformations, reasoning, the Cavalieri principle, or accuracy rates between two groups of different grade levels. In contrast, when comparing two groups of the same grade level, significant differences in response types and accuracy rates were observed depending on the type of examples provided to assist problem-solving. Second, student responses to questions about the area transformation of non-inscribed triangles exhibited patterns similar to those for the transformation of inscribed triangles. Third, in the group provided with specific examples, it was expected that students would derive the concept of double-area transformations for right triangles and engage in manipulative activities. However, it was found that a significant number of students relied on the Cavalieri principle, which they had already internalized, rather than using double-area transformations. Fourth, the analysis of student responses to comparisons between questions revealed that groups of different grade levels but provided with the same examples showed a tendency to solve the inscribed triangle transformation questions more successfully than the non-inscribed triangle questions. A strong positive correlation was found between the two types of questions. On the other hand, in the group provided with specific examples, there was no statistically significant difference in success rates between the two question types, though a strong correlation between them was still evident. Finally, students' approaches to transformations using double-area methods and the Cavalieri principle lacked diversity. These findings suggest important educational implications, emphasizing the need for pre-service elementary teachers to gain experience in manipulative activities related to geometric education.

이형주 Lee Hyeongju

DOI: JANT Vol.38(No.4) 513-536, 2024

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Ultimately, in order to expand the base of liberal arts mathematics, this study conducted a study on the development of liberal arts mathematics subjects to provide students from all disciplines, including humanities and society, with opportunities and environments to take liberal arts courses in various fields. To this end, literature studies such as pure liberal arts mathematics operations at domestic universities were conducted, and cases of mathematics related to culture were explored. In addition, by analyzing internal validation, satisfaction, and feedback from students and experts, it was possible to secure the validity of the derived curriculum after revision and supplementation. As a result, CVI .96 and IRA .86 were secured in subject development and operation and class curriculum for each week. CVI .96 and IRA .80 showed high consistency between the content validity index and evaluators in the usability evaluation. In addition, positive results were obtained regarding satisfaction and feedback after class, and positive results were obtained as a useful lecture considering interest in free writing. This study is significant in that it is a study on the development of liberal arts mathematics subjects centered on the case of University A, and it aims to expand the base of liberal arts mathematics by providing students with a variety of mathematical perspectives and inspiring interest. * 2020

김지인 Kim Jiin , 김구연 Kim Gooyeon

DOI: JANT Vol.38(No.4) 537-561, 2024

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This study examined the understanding of proportional reasoning of prospective secondary mathematics teachers and the strategies they employ in solving tasks pertaining to this topic. The questionnaire developed in the previous study was revised and reviewed, and four preservice teachers enrolled in a teacher education institution in Seoul were interviewed. The transcripts of these interviews were analyzed to identify the characteristics of preservice teachers’ thinking in proportional reasoning. The results of the analysis indicated that, initially, the preservice teachers exibited confusion regarding the distinction between the terms “ratio” and “proportion.” Notably, they demonstrated a tendency to perceive the referece quantity as a whole at all times, interpreting the ratio as a function. Secondly, it appeared that they did not develop reasoning based on the meaning of the proportional situation, despited the fact that grasping the meaning of the proportional situation is the fundamental aspect of proportional reasoning. This was particularly evident in qualitative reasoning tasks that did not involve numbers, as the preservice teacher used superfical terms to recognize proportional situations, even though grasping the meaning of proportional situations is central to proportional reasoning.

손태권 Son Taekwon , 심혜진 Shim Hyejin , 여승현 Yeo Sheunghyun

DOI: JANT Vol.38(No.4) 563-585, 2024

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This study explored the change patterns of students’ mathematics academic achievement during three years of middle school in connection with their academic achievement in the first year of high school. As a research method, the change patterns of middle school mathematics achievement were analyzed using a latent growth mixed model, and four achievement groups (low, middle, high, and high-rising) were derived. In addition, the correlation between each achievement group and high school first-year achievement was confirmed through regression analysis. In particular, the moderating effects of teachers’ teaching and assessment methods perceived by students on high school achievement were analyzed. The results of the study showed that mathematics achievement during middle school had a significant effect on high school grades, and in particular, the high-rising group showed the highest results in high school achievement. In addition, it was confirmed that students’ perceptions of teachers’ teaching and assessment methods affected high school first-year academic achievement, and the interaction effect was different for each group. Based on these research results, we suggested political direction for improving mathematics academic achivement related to teachers' teaching and assesment method.

김윤민 Kim Yun Min , 허난 Huh Nan , 고호경 Ko Ho Kyoung , 김형식 Kim Hyeong Sik , 신민경 Shin Min Kyung , 안서현 Ahn Seo Hyun , 강수산 Kang Soo San , 손복은 Son Bok Eun

DOI: JANT Vol.38(No.4) 587-607, 2024

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This study aims to develop and implement a mathematics program specifically designed for senior citizens, with the goal of drawing insights for future program development and operation. To achieve this, six programs were developed to enhance mathematical thinking and problem-solving skills in real-life contexts. The programs were implemented over approximately two weeks in a local institution with 40 participants. The results emphasize the necessity of context-based mathematics programs that consider the daily lives and learning characteristics of senior citizens. Satisfaction and participation levels were notably higher in activities linked to real-life situations. Therefore, this study suggests the expansion of outreach mathematics programs for seniors, the refinement of senior-specific programs, and the establishment of sustainable operation plans in collaboration with local communities to promote lifelong learning opportunities for all.

한인기 Han Inki

DOI: JANT Vol.38(No.4) 609-630, 2024

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Problem-solving has been continuously emphasized in the mathematics curriculum. In particular, the 2022 revised mathematics curriculum recommends transforming given problems or making new problems based on the process and results of problem-solving. Although various articles on mathematics problem making have been published in journals in the field of mathematics education in Korea, studies on problem making method have not been conducted in a diverse manner. In particular, systematic research on problem making methods, which emphasize ‘transforming given problems or making new problems based on the results of problem-solving’ as highlighted in the mathematics curriculum, remains insufficient. This study utilizes deductive problem making method in triangle construction problems to make various problems that share similar problem-solving methods and examines several pedagogical characteristics related to deductive problem making method. In deductive problem making method the problem-solving process were divided into several steps (substructures) and problems were made by altering the elements of these substructures, thereby deductive problem making method is aligned with the problem-making direction emphasized in the mathematics curriculum. This study confirms the potential applicability of the deductive problem making method in the geometry, and the results are expected to serve as materials for promoting the teaching and learning intended by the mathematics curriculum.

최여선 Choi Yeoseon , 조민식 Cho Minshik

DOI: JANT Vol.38(No.4) 631-650, 2024

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This study explores whether engaging in conjecturing activities using dependency and invariant in a dynamic geometry environment can improve students' understanding of the conditions and conclusions in geometric properties. Four 9th-graders participated in a 10-session course, during which methods of using dependency and types of invariants were categorized based on students' Algeo Math screens, activity sheets, and conversations. The activities were analyzed according to the stages of the MD Conjecturing Model, and the following results were obtained. First of all, students tended to explore dependencies and invariants using dragging rather than following construction sequences, and the invariants they mentioned during the investigation process were often included in the conditional statements they proposed as conjectures. Furthermore, students engaged in analytical thinking on their own during the conjecturing process, and the activity of conjecturing with dependency and invariant in a dynamic geometry environment proved effective for understanding conditions and conclusions. The results of this study are expected to contribute to enhancing students' understanding of conditions and conclusions in the geometry domain.