• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.103-121
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• 2008

The primary purpose of this study was to gather knowledge about $5^{th},\;6^{th},\;and\;7^{th}$ graders' proportional reasoning ability by investigating their reactions and use of strategies when encounting proportional or nonproportional problems, and then to raise issues concerning instructional methods related to proportion. A descriptive study through pencil-and-paper tests was conducted. The tests consisted of 12 questions, which included 8 proportional questions and 4 nonproportional questions. The following conclusions were drawn from the results obtained in this study. First, for a deeper understanding of the ratio, textbooks should treat numerical comparison problems and qualitative prediction and comparison problems together with missing-value problems. Second, when solving missing-value problems, students correctly answered direct-proportion questions but failed to correctly answer inverse-proportion questions. This result highlights the need for a more intensive curriculum to handle inverse-proportion. In particular, students need to experience inverse-relationships more often. Third, qualitative reasoning tends to be a more general norm than quantitative reasoning. Moreover, the former could be the cornerstone of proportional reasoning, and for this reason, qualitative reasoning should be emphasized before proportional reasoning. Forth, when dealing with nonproportional problems about 34% of students made proportional errors because they focused on numerical structure instead of comprehending the overall relationship. In order to overcome such errors, qualitative reasoning should be emphasized. Before solving proportional problems, students must be enriched by experiences that include dealing with direct and inverse proportion problems as well as nonproportional situational problems. This will result in the ability to accurately recognize a proportional situation.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.61-78
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• 2008

In this paper, we discuss about De Morgan's view on the development of algebra according to following distinctions: arithmetic, universal arithmetic, symbolic algebra, significant algebra. De Morgan thought that the differences between arithmetic and universal arithmetic lie in the usage of letters and the immediate performance of computation. In his viewpoint, universal arithmetic is a transitional phase, in which absurd phenomena occur, from arithmetic to algebra and these absurd phenomena call for algebra. The feature of De Morgan's view on the development of algebra is that symbolic calculus which consist of symbol system without symbol's meaning is acquired, then as extended meanings are furnished to symbols, symbolic calculus become logical so significant calculus is developed. For example, Single algebra is developed, as an extended meaning is furnished to a symbol -1, and double algebra is developed, as an extended meaning is furnished to a symbol $\sqrt{-1}$. According to De Morgan, a symbol system is derived from the incompleteness of a prior symbol system.

• Journal of Korean Elementary Science Education
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• v.25 no.2
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• pp.118-125
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• 2006

The purpose of the study was to research science gifted students' learning styles and perceptions on subject matter content. The data was collected from primary science and mathematics classes of a University Center for Science Gifted Education, science classes of a Metrocity Primary Gifted Education Institute, and classes of a normal school. The results of the study were that gifted students perceived the school curriculum much easier than non-gifted students did, ($X^2(4)=33.180$, p<.001), and that levels of interest in the content did not differ between the groups, but 34.6 percent of the total students responded that they found the content uninteresting. Gifted students did not see the content as being important compared to the non-gifted students, ($X^2(4)=12.443$, p<.05), and gifted students valued the methods used higher than the actual content of the textbook. The most helpful activities for their teaming that gifted students chose were projects, listening to teachers, and conducting experiments, amongst others. They also preformed 'teaming at their own speed in a mixed group'" for the study of social studies, science, and mathematics, whereas non-gifted students preformed teaming at the same speed. The two groups of science gifted students varied especially in their perceptions of most helpful activities. It is suggested that special programs for fulfilling gifted students' needs and abilities need to be developed and implemented.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.1-20
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• 2013

The aim of this study was to develop a gifted educational program in math-gifted class in elementary school using recently developed 4D-frame. This study identified how this program impacted on spatial sense and mathematical creativity for mathematically gifted students. The investigation attempted to contribute to the developments for the gifted educational program. To achieve the aim, the study analysed the 5 and 6th graders' figure learning contents from a revised version of the 2007 national curriculum. According to this analysis, twelve learning sections were developed on the basis of 4D-frame in the math-gifted educational program. The results of the study is as follows. First, a learning program using 4D-frame for spatial sense from mathematically gifted elementary school students was statistically significant. A sub-factor of spatial visualization called mental rotation and sub-factors of spatial orientations such as sense of distance and sense of spatial perception were statistically significant. Second, the learning program that uses 4D-frame for mathematical creativity was statistically significant. The sub-factors of mathematical creativity such as fluency, flexibility and originality were all statistically significant. Third, the manipulation properties of 4D-frame helped to understand the characteristics of various solid figures. Through the math discussions in the class, participants' error correction was promoted. The advantage of 4D-frame including easier manipulation helped participants' originality for their own sculpture. In summary, this found that the learning program using 4D-frame attributed to improve the spatial sense and mathematical creativity for mathematically gifted students in elementary school. These results indicated that the writers' learning program will help to develop the programs for the gifted education program in the future.

• Journal of The Korean Association For Science Education
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• v.38 no.6
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• pp.781-792
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• 2018

In modern society, as technology develops and industry diversifies, students can choose from a variety of career paths. Since science, technology, engineering, and mathematics require a longer education and experience than other fields, it is important to design science education policies based on the competencies required for science, technology, engineering, and mathematics (STEM) occupations. This study explores the definition of science and technology manpower and STEM occupations and identifies core competencies of STEM occupations using standard job information operated and maintained by the US Department of Labor ($O^*NET$). We specially analyzed ratings of the importance of skills (35 ratings), knowledge (33 ratings), and work activities (41 ratings) conducting descriptive analysis and principal component analysis (PCA). As a result, core competencies of STEM occupations consist of STEM problem-solving competency, Management competency, Technical competency, Social service competency, Teaching competency, Design competency, Bio-chemistry competency, and Public service competency, which accounts for 70% of the total variance. This study can be a reference for setting the curriculum and educational goals in secondary and college education by showing the diversity of science and technology occupations and the competencies required for STEM occupations.

• The Mathematical Education
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• v.58 no.2
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• pp.283-298
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• 2019

Among the measurement attributes included in the elementary school mathematics curriculum, perimeter, area, volume and surface area are intensively covered in fifth and sixth graders. However, not much is known about the level of student performance and difficulties in this area. The purpose of this study is to examine the understanding and performance of sixth-grade elementary school students on some ideas of measurement and ultimately to give some suggestions for teaching measurement and the development of mathematics textbooks. For this, diagnosis questions were developed in relation to the following parts: measurement of perimeter and area of plane figure, measurement of surface area and volume of solid figure, and the relationships between perimeter and area, and the relationships between surface area and volume. The performances of 95 sixth graders were analyzed for this study. The results showed children's low performance in the measurement area, especially measurement of perimeter and surface area, and relationship of the measurement concepts. Finally, we proposed the introduction order of the measurement concepts and what should be put more emphasis on teaching measurement. Specifically, it suggested that we consider placing a less demanding concept first, such as the area and volume, and dealing more heavily with burdensome tasks such as the perimeter and surface area.

• The Mathematical Education
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• v.62 no.3
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• pp.363-380
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• 2023

This study analyzed the difficulties and mathematical modeling knowledge improvement that an elementary school teacher experienced in modifying a mathematics textbook task to a mathematical modeling task. To this end, an elementary school teacher with 10 years of experience participated in teacher-researcher community's repeated discussions and modified the average task in the data and pattern domain of the 5th grade. The results are as followings. First, in the process of task modification, the teacher had difficulties in reflecting reality, setting the appropriate cognitive level of mathematical modeling tasks, and presenting detailed tasks according to the mathematical modeling process. Second, through repeated task modifications, the teacher was able to develop realistic tasks considering the mathematical content knowledge and students' cognitive level, set the cognitive level of the task by adjusting the complexity and openness of the task, and present detailed tasks through thought experiments on students' task-solving process, which shows that teachers' mathematical modeling knowledge, including the concept of mathematical modeling and the characteristics of the mathematical modeling task, has improved. The findings of this study suggest that, in terms of the mathematical modeling teacher education, it is necessary to provide teachers with opportunities to improve their mathematical modeling task development competency through textbook task modification rather than direct provision of mathematical modeling tasks, experience mathematical modeling theory and practice together, and participate in teacher-researcher communities.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.107-138
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• 2022

This study is a study that developed class materials that can apply Process-Focused Assessment to classes by paying attention to feedback using teacher learning community programs centered on teachers belonging to the same school in the field. In particular, this study was conducted with the aim of developing class materials applicable to actual classes. At this time, We thought about how to provide appropriate feedback when applying course-based evaluation in school field classes. It was conducted according to the procedure of data development research by Lee & Ahn(2021). As for the procedure of data development itself, an evaluation plan was established by establishing a strategy to reconstruct achievement standards and confirm understanding based on curriculum analysis. Next, an evaluation task, a scoring standard table, and a preliminary feedback preparation table were developed. In addition, based on these development materials, a learning guidance plan that can predict scenes when applying actual classes was developed as a result. This study has value as a practical study that can contribute to providing a link between theory and field schools. It is also meaningful in that it considered how the teacher would grasp when to provide feedback in performing rocess-Focused Assessment. Likewise, in providing feedback by teachers, it is meaningful in that it reflects in the data development how to prepare in advance and take classes according to the characteristics of the subject. Finally, it seems that the possibility of field application can be improved in that the results of the 4th class developed in this study are presented in a form applicable to the class directly in the field.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.39-55
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• 2024

Recently, the 2022 revised mathematics curriculum has established achievement standards for equal sign and equality, and efforts have been made to examine teaching methods and student understanding of relational understanding of equal sign. In this context, this study conducted a lesson that emphasized relational understanding in an introduction to equal sign, and compared and analyzed the understanding of equal sign between the experimental group, which participated in the lesson emphasizing relational understanding and the control group, which participated in the standard lesson. For this purpose, two classes of students participated in this study, and the results were analyzed by administering pre- and post-tests on the understanding of equal sign. The results showed that students in the experimental group had significantly higher average scores than students in the control group in all areas of equation-structure, equal sign-definition, and equation-solving. In addition, when comparing the means of students by item, we found that there was a significant difference between the means of the control group and the experimental group in the items dealing with equal sign in the structure of 'a=b' and 'a+b=c+d', and that most of the students in the experimental group correctly answered 'sameness' as the meaning of equal sign, but there were still many responses that interpreted the equal sign as 'answer'. Based on these results, we discussed the implications for instruction that emphasizes relational understanding in equal sign introduction lessons.

• The Mathematical Education
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• v.63 no.1
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• pp.63-83
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• 2024

The purpose of this study is to analyze the mathematical connection components of the tasks included in the trigonometric ratio unit of 3rd grade middle school textbook based on the 2015 revised mathematics curriculum and investigate teachers' perceptions and practical measures regarding these components. To this end, we analyzed the characteristics of mathematical connection tasks included in the trigonometric ratio units in nine types of 3rd grade middle school mathematics textbooks, and we conducted a questionnaire survey and interviews with one in-service math teachers in pre interview and with two in-service math teachers in this interview to investigate their perceptions and practical measures. As a result of the study, the number of tasks with external connection in the trigonometric ratio unit were less than those of internal connection. In addition, in terms of teachers' perceptions and practical measures, the perspective of analyzing tasks with mathematical connections varied depending on the teacher's perspective, and the practical measures varied accordingly. These findings are significant in that they reveal the relationship between mathematical tasks, teacher perceptions and measures to foster effectively students' mathematical connections.