• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.

• The Mathematical Education
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• v.51 no.1
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• pp.47-61
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• 2012

Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.

• East Asian mathematical journal
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• v.38 no.2
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• pp.257-275
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• 2022

Recently, there are studies the argument that arithmetic rules established by the four fundamental arithmetic operations, in other words, commutative laws, associative laws, distributive laws, should be explicitly described in mathematics textbooks and the curriculum. These rules are currently implicitly presented or omitted from textbooks, but they contain important principles that foster mathematical thinking. This study aims to evaluate the current level of understanding of these computation rules and provide implications for the curriculum and textbook writing. To this end, the correct answer ratio of the five arithmetic rules for 1-4 grades 398 in five elementary schools was investigated and the type of error was analyzed and presented, and the subject to learn these rules and the points to be noted in teaching and learning were also presented. These results will help to clarify the achievement criteria and learning contents of the calculation rules, which were implicitly presented in existing national textbooks, in a new 2022 revised curriculum.

• Korean Institute of Interior Design Journal
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• no.31
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• pp.12-18
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• 2002

This study was performed to construct the spatial systems and shape grammars in architecture based on Froebel's educational idea and building gifts. Especially, it studies on the geometrical principles of Froebel's building gifts and it's types, and then illustrates applied examples about design vocabularies, spatial relations and shape rules of the spatial systems and shape grammars in architecture. The conclusions of this study that starts these purpose are as follows. First, Froebel's educational theory is based on principles and rules which are perceived through the observation of nature, and Froebel's kindergarten method consists of geometrical building gifts and categories of geometrical forms. Second, the characteristics of Froebel's building gifts are mathematical size, proportion, symmetry and the rules of spatial relation. Third, the development to the construction of spatial systems and shape grammars in architecture focus on the vocabularies of architectural elements, and Froebel's building gifts are used for illustration of examples in these formula.

• The Mathematical Education
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• v.42 no.5
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• pp.637-646
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• 2003

Visual representation is very important topic in Mathematics Education since it fosters understanding of Mathematical concepts, principles and rules and helps to solve the problem. So, the purpose of this paper is to analyze and clarify the various meaning and roles about the visual representation. For this purpose, I examine the status of the visual representation. Since the visual representation has the roles of creatively mathematical activity, we emphasize the using of the visual representation in teaching and learning. Next, I examine the errors in relation to the visual representation which come from limitation of the visual representation. It suggests that students have to know conceptual meaning of the visual representation when they use the visual representation. Finally, I suggest some examples of problem solving via the visual representation. This examples clarify that the visual representation gives the clues and solution of problem solving. Students can apprehend intuitively and easily the mathematical concepts, principles and rules using the visual representation because of its properties of finiteness and concreteness. So, mathematics teachers create the various visual representations and show students them. Moreover, mathematics teachers ask students to design the visual representation and teach students to understand the conceptual meaning of the visual representation.

• Korean Institute of Interior Design Journal
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• no.26
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• pp.95-103
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• 2001

This study was performed to search for the geometrical principles in modern architecture and design based on Frobel's educational idea and Kindergarten system. Especially, it studies on the geometrical principles of Froebel's building gifts and it's types, and then illustrates applied examples in modern architecture and design. As the architectural scope, the architecture and design theory of Frank Lloyd Wright and Bauhaus in early 20th century is analyzed. The conclusions of this study that starts these purpose are as follows. First, Froebel's educational theory is based on principles and rules which are perceived through the observation of nature, and Froebel's Kindergarten system consists of geometrical building gifts and categories of geometrical forms. Second, the characteristics of Froebel's building gifts are mathematical size, proportion, symmetry and the rules of spatial relation. Third, the influence of Froebel's kindergarten system on Bauhaus is that it based on the rational rules of $\bigtriangleup\square\bigcirc$ organized by geometrical basic forms as like Froebel's educational idea. And the influence of Froebel's Kindergarten system on Frank Lloyd Wright is that he used unit system, unity of space and structure and modular system as like the Froebel's building gifts.

• Journal of architectural history
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• v.15 no.4
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• pp.23-36
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• 2006

Since he was a leading figure in nineteenth century architecture, Viollet-le-Duc's architectural theory is crucial to the foundation of modern architecture. He has been called a Gothic Revivalist, a Structural Rationalist and a Positivist. The first title was perhaps due to his vigorous restoration of Gothic works such as $N\hat{o}tre$ Dame, but he did not adore the Gothic style just for itself. Rather, he hoped to deduce some principles from the style. So how did he manage this? In his book "Entretiens sur l'Architecture (Lectures on Architecture), published between 1864 and 1872, he mentions using Descartes' four rules for reaching architectural certainty in contrast with the chaotic situation during that modernising period. Furthermore Viollet-le-Duc's theory can be seen as a serious attempt to translates Descartes' philosophical rules into systems of architectural speculation. Descartes' four rules of doubt are anchored in mathematical propositions, and without mathematical distinctions, none of these rules are valid. In other word, mathematics for Viollet is the yardstick of judgement between distinctness and indistinctness. Many architectural problems arise from this view. In this paper, the validities of applying Descartes' method of doubt to architectural discourse will be discussed in order to address the question:-Did Viollet-le-Duc clearly grasp Cartesian method by which memory was erased from the world?

• School Mathematics
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• v.19 no.4
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• pp.713-729
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• 2017

It is the 6th curriculum that first officially mentioned the use of calculators in elementary mathematics education in Korea. Since then, the curriculum has been more widely used than in the beginning. However, in actual textbooks, it is still not enough to see the utilization situation, and guidance in this textbook is very scarce. In particular, there is no relevant study that meets the standards of achievement of the curriculum. The purpose of this study is to investigate the contents of the research on the use of the calculator in the course of the curriculum change after the 6th curriculum, and to present the complex calculation, mathematical concept, mathematical principles and rules, mathematical problem solving. In addition, the course is presented in the textbooks that are appropriate for the achievement criteria and the application process for each topic.

• Research in Mathematical Education
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• v.5 no.2
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• pp.107-118
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• 2001

Mathematics subject of the seventh national curriculum in Korea, which has been effective since 2000, strongly encourages the use of calculators and computers to help children gain a better understanding of basic mathematical concepts and develop creative thinking and problem-solving skills without spending too much time and effort on making mechanical computations. Despite the recommendation by the national curriculum, however, only a small segment of elementary school teachers have been using calculators because of the fear that children\\`s dependence on calculators might bring about negative consequences. As a result, little research has been conducted in this area as well. This study has been conducted on the assumption that calculators have the potential for being a useful instructional tool in certain areas of elementary school mathematics education. To investigate the usefulness of calculators, a review was made of the scanty literature in the area. The literature review indicated that calculators are effective when they are used for the following purposes: understanding concepts and properties in numbers and operations, deducing mathematical rules, and solving problems. In view of the available research finding, we will give some concrete learning and teaching models of such uses of calculators. The teaching-learning models are organized around three categories: concept formation, discovery of principles and rules, and problem solving. Such organization is intended to help teachers use the models with ease.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.167-179
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• 1999

The aim of this study is to improve the basic learning ability of those who make poor progress in mathematics and to keep positive and active learning attitudes in class afterward by using problems whith both make them advance their basic learning ability and supplement lack of previous learning in class or after school. supplementary problems were developed by focusing the ability of basic calculation, the comprehension of concepts, principles, and rules by analyzing necessary contents precisely each domain after itemizing learning contents each unit. the results of the study are this: 1) The students who solved the problems, that were developed to improve the basic learning ability and to supplement the earlier learning during their classes or giving homework, made significant progress in their scholastic achievement; more than those who were not involved. 2) Meaningful changes were demonstrated in the motivation for achievement among the domains of learning attitudes before and after the experiment but, not in their interest, the consciousness of purpose, attention, voluntary and efficient learning as shown in their learning habits. In this study, therefore, the problems which were developed to improve the basic learning ability and to supplement the earlier learning by focusing on the competence for basic calculation, and the comprehension of concepts, principles and rules were effective positively only in the area of motivation for achievement. there were no meaningful differences in the other domains.