• Education of Primary School Mathematics
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• v.17 no.3
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• pp.205-230
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• 2014

New teaching and learning theory on various aspects about class is needed to implement education which reflects constructivism, ideally. For an ideal learner-centered mathematics class, tangible and intangible elements related to education(view of knowledge, view of leaner, teacher's role, evaluation, the form of class, learning, teaching material, etc.) should be integrated from a constructive perspective and especially, teaching material has to be premised on that learners have intellectual abilities to construct knowledge themselves, and reflect integrity of knowledge, diversity and others, and contain open attributes. In addition to this, teaching material should have characteristics different from those when objective epistemology applies, so there is a need to analyze whether teaching material has those characteristics. For this, this study compared and analyzed <1. Three-Digit Numbers> which belongs to the domain of numbers and operations out of the units of mathematics(3) textbook of the 2009 revised curriculum for the first and second grade that first introduced story-telling, and <3. Understanding of Place Values> for the second grade of constructive math class used in the U.S.

• School Mathematics
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• v.10 no.2
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• pp.181-197
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• 2008

Bertrand's Paradox is known as a paradox because it produces different solutions when we apply different method. This essay analyzed diverse problem solving methods which result from no clear presenting of 'random chord'. The essay also tried to discover the difference between the mathematical calculation of three problem solvings and physical experiment in the real world. In the process for this, whether geometric statistic teaching related to measurement and integral calculus which is the basic concept of integral geometry is appropriate factor in current education curriculum based on Laplace's classical perspective was prudently discussed with its status.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.1-8
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• 2005

In this paper, we describe H. Hopf's life and works from the historical point of view. We have a very brief mention of history and results prior to Hopf. He raised the question of the topological implications of the sign of curvature. We discuss his contributions in the field of Riemannian geometry.

• The Journal of Korean Association of Computer Education
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• v.10 no.4
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• pp.51-59
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• 2007

There is the meager level of applying computers to mathematics education. It is because the effective mathematics educational softwares and the various contents that make students' spontaneous participation through the interaction with computers are insufficient. As a solution to solve it, we design and implement the graphic component, graphic entities and function types that are supported in the component was identified through analyzing the mid/high school curriculum, using a simple script language to invoke the functionality of the component improves reusability and extendability. The component can be used to produce the mathematics educational softwares and contents easily that need the facility to draw various functions and geometric figures.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• School Mathematics
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• v.18 no.3
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• pp.441-455
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• 2016

The position as saying that the math learning needs to begin from what diversely presents concrete object or familiar situation is well known as a name dubbed CSA(Concrete-Semiconcrete-Abstract). Compared to this, a recent research by Kaminski, et al. asserts that learning an abstract concept first may be more effective in the aspect of knowledge transfer than learning a mathematical concept with concrete object of having various contexts. The purpose of this study was to analyze a class, which differently applied a guidance sequence of concrete object, semi-concrete object, and abstract concept in consideration of this conflicting perspective, and to confirm its educational implication. As a result of research, a class with the application of a concept starting from the concrete object showed what made it have positive attitude toward mathematics, but wasn't continued its effect, and didn't indicate significant difference even in achievement. Even a case of showing error was observed rather owing to the excessive concreteness that the concrete object has. This error wasn't found in a class that adopted a concept as semi-concrete object. This suggests that the semi-concrete object, which was thought a non-essential element, can be efficiently used in learning an abstract concept.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.39-51
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• 2009

The purpose of this article is to study characteristics of tangram as instructional media in combinatorialgeometric point of view, and to present basic materials and direction for efficient tangram activities in gifted education upon systematical analysis of methods of finding solutions. We can apply x=a+2b+4c to find all possible combination of solutions in tangram activities not as trial-and-error method but as analytical method. Through teacher's questions and problem posing in activities using tangram, we systematically came up with most solution and case of all possible combinations be solution in classifying properties of pieces and combining selected pieces.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.709-730
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• 2010

The inverse function of a one-to-one correspondence is explained with a graph, a numerical formula or other useful expressions. The purpose of this paper is to know how low achieving students understand the learning contents needed reversible thinking about irrational functions. Low achieving students in this study took paper-pencil test and their written answers were collected. They made various mistakes in solving problems. Their error types were grouped into several classes and identified in this analysis. Most students did not connected concepts that they learned in the lower achieving students to think in reverse order in case of and to visualize concepts of functions. This paper implies that it is very important to take into account students' accommodation and reversible thinking activity.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.395-423
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• 2019

The purpose of the study is to analyze the levels of cognitive demands and components of the reasoning process presented in the mathematical sequence section of three high school mathematics textbooks in order to provide implications for the development of reasoning tasks in the future mathematics textbooks. The results of the study have revealed that most of the reasoning tasks presented in the mathematical sequence section of the three high school mathematics textbooks seemed to require low-level cognitive demands and that low-level cognitive demands reasoning tasks required only a component of one reasoning process. On the other hand, only a portion of the reasoning tasks appeared to require high-level of cognitive demands, and high-level cognitive demands reasoning tasks required various components of reasoning process. Considering the results of the study, it seems to suggest that we need more high-level cognitive demands reasoning tasks to develop high-level cognitive reasoning that would provide students with learning opportunities for various processes of reasoning, and that would provide a deeper understanding of the nature of reasoning.