• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.183-198
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• 2018

In this paper, I theoretically considered joining and separating activities and revisited the textbooks from 7 countries and Korean mathematics textbooks from 5th revised curriculum to 2015 revised curriculum to find implication for the treatment of 0 in the joining and separating activities. The 'joining' has definition and properties similar to addition, but the 'separating'is difficult to define and is not considered to have properties similar to subtraction. In the sense of computation, joining and separating can be seen as' part-part-to-whole' situations, but are just part of the addition and subtraction situations. The analysis of textbooks from 7 counties showed that Singapore and Malaysia textbooks already studied zero and then included it in joining and separating activities, but other countries did not include it as joining and separating activities. The textbooks of South Korea have consistently suggested not to include zero, but teacher's guide has shown that there is a little consistency in the treatment of zero. As a conclusion, I suggested that it was necessary to propose a proper context of the situation in order to introduce joining and separating without including 0 in terms of student level and to propose that a more consistent presentation of zero handling in the teaching in the teacher's guide.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• Journal of Korean Elementary Science Education
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• v.43 no.3
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• pp.433-445
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• 2024

This study aims to compare and analyze the educational contents of the material area in the elementary science curriculums of North and South Korea. The research subjects are materials and motion and energy (partial) areas of the revised science curriculum of South Korea in 2022 and materials around us and science in daily life (partial) areas of the nature and education program of North Korea in 2013. This study compared the elements of the educational content of the material domain between North and South Korea according to the grade. Furthermore, the reflection of the material domain goals of North and South Korea at the international level was analyzed using the evaluation framework of the Trends in International Mathematics and Science Study (TIMSS) 2023 for the material content domains for fourth-grade elementary schools. Four teachers who majored in elementary science education and one expert in science education participated in the analysis. The results are as follows. First, in terms of the properties of matter, the content covered in the curriculum of North and South Korea differed in application period by grade and in the scope and level of content. Second, regarding material change, North Korea did not cover acids and bases but included methods for speeding up dissolution. Third, North Korea reflected the goal of the TIMSS 2023 properties of materials more highly than South Korea. Fourth, similar to the results for the analysis on the properties of materials, North Korea reflected the goal of the TIMSS 2023 for changes of materials more highly than did South Korea. In conclusion, the elements and timing of application of the material contents differed between North and South Korea, and the degree of reflection of goals at the international level was found to be higher for North Korea. In the future, this study hopes that cooperation and research on the development of integrated science and curriculum will occur along with the revitalization of educational exchange between North and South Korea from the perspective of the preparation for unification beyond the ideological conflict between them.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.511-536
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• 2017

The present study aims to investigate ways in which pre-service secondary mathematics teachers anticipate 1) students' responses to specific mathematical tasks which are chosen or devised by the participating pre-service teachers as requiring students' higher cognitive demand and, 2) their roles as math teachers to scaffold students' mathematical thinking. To achieve the goal, we had our pre-service teachers to engage in an adapted version of Spangler & Hallman-Thrasher(2014)'s Task Dialogue writing activity whose focus was to develop pre-service elementary teachers' ability to orchestrate mathematical discussion. 14 pre-service teachers who were junior at the time enrolled in the Mathematics Teaching Method Course were subjects of the current study. In-depth analysis of both Task Dialogues which pre-service secondary mathematics teachers wrote and audiotapes of the group discussions while they wrote the dialogues suggests the following results: First, the pre-service secondary teachers anticipated how students would approach a task based on their own teaching experiences. Second, they were challenged not only to anticipate more than one correct students' responses but to generate questions for the predicted correct-responses to bring forth students' divergent thinking. Finally, although they were aware that students' knowledge should be the crucial element guiding their decision-making process in teaching, they tended to lower the cognitive demands of tasks by providing students with too much guidance which brought forth the use of procedural knowledge. The study contributes to the field as it provides insights as to what to attend in designing teacher education course whose goal is to provide a foundation for developing pre-service teachers' ability to effectively orchestrate mathematical discussion.

• Journal of The Korean Association of Information Education
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• v.19 no.1
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• pp.11-20
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• 2015

The researches on the concept of justice and utilization for Computational Thinking with SW education are being actively discussed. However, a program has developed in conjunction with the actual elementary curriculum is not much. In this study, we have developed an educational program in applied mathematics based on CT. First, a separated view for a CT Application of mathematical concepts and objectives are set in three different application models. In order to achieve the CT-based math lessons, we also have developed a teaching and learning materials. We applied the developed materials in class, and to evaluate the satisfaction of learners. In addition to the validation of school application, we conducted a survey of professionals and teachers. The results of the analysis, the data showed that are helpful in the development of the student' CT ability as well as the ability to be helpful teaching and learning in school.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.43-55
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• 2011

The purpose of this study was to investigate the effects of inquiry oriented instruction on the learning of area formulas. For this purpose, current elementary mathematics textbook(2007 revised version) which deal with area formulas was reviewed and then the experimental research on inquiry oriented instruction in area formulas was conducted. The results of this study as follow; First, there was no significant effect of inquiry oriented instruction on the mathematical achievement in area formula problems. Second, there was no significant effect on the memorization of area formulas. Third, there was significant effect on the generalization of area formulas. Forth, there was significant effect on the methods of generalization of area formulas. Fifth, through inquiry activities, the students can learn mathematical ideas and develop creative mathematical ideas. Finally, implications for teaching area formulas through inquiry activity was discussed. We have to introduce new area formula through prior area formulas which had been studied, and make the students inquire the connection between each area formulas.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.327-344
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• 2006

This study examined the proof levels and understanding of constituents of proving by three mathematically gifted 6th grade korean students, who belonged to the highest 1% in elementary school, through observation and interviews on the problem-solving process in relation to constructing a rectangle of which area equals the sum of two other rectangles. We assigned the students with Clairaut's geometric problems and analyzed their proof levels and their difficulties in thinking related to the understanding of constituents of proving. Analysis of data was made based on the proof level suggested by Waring (2000) and the constituents of proving presented by Galbraith(1981), Dreyfus & Hadas(1987), Seo(1999). As a result, we found out that the students recognized the meaning and necessity of proof, and they peformed some geometric proofs if only they had teacher's proper intervention.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.107-122
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• 2015

This research aims to suggest a math-based convergence instructional model. The convergence instructional model with emphasis on problem solving ability was developed based on each subject and the STEAM model. Then, the appropriateness and limit of the classroom model were investigated, through examining the aspects of its realization in each stage of the class instruction model while enacting a four part lesson on 6th graders. As a result, each stage of the classroom instruction model influenced in helping the students discover various problem solving skills, critically examine the process of the solving, and attain positive perspectives on the classroom instruction. However, appropriate intervention of the teacher was needed to lead the students to further synthesize the explored issues in mathematics and to expand the scope of their emotional experience. This paper closes with suggestions in implementing math based convergence lessons.

• Education of Primary School Mathematics
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• v.16 no.1
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• pp.21-33
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• 2013

In this study, We analyzed the mathematical thinking of sixth grade students showed mathematics lessons through the application of Lakatos' methodology and search for the role of their teachers in this lessons. We supposed to find the solution to the way of teaching-learning regarding the Lakatos' methodology for the elementary school level. According to the stages of presenting a problem situation, suggesting an initial conjecture, examining the conjecture, and improving the conjecture, we had lessons 8 times that are applied to Lakato's methodology. We gathered and analyzed data from lessons and interviews recording videotapes, documents for this study. The participants showed a lot of mathematical thinking. They understood the problem situation with the skill of fundamental thinking and suggested the initial conjecture by the skill of developmental thinking and they found a counter-example to be able to rebut the initial conjecture by critical thinking. Correcting the conjecture not to have counter-example, they drew developmental thinking and made their thinking generalize.

• Research in Mathematical Education
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• v.8 no.2
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• pp.107-114
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• 2004

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.