• Education of Primary School Mathematics
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• v.14 no.2
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• pp.135-145
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• 2011

When mathematicians solve the new problems, they present the solutions to their colleagues for getting the approval. If the solution is accepted, it will be theorems. This phenomenon also happens to classrooms in elementary and secondary school. That is main reason to emphasize mathematical communication activities in mathematics education. This study is aimed to develop teaching and learning model for the improvement of mathematical communication ability, applicate the teaching and learning model to two groups and analyze for mathematical thoughts. This study is a case study of 3rd grader's activities. Eight students, four are group applied the teaching and learning model and four are traditional group. The results have been drawn as follows: First, students in the teaching and learning model group induced richer interactions for student's understanding and investigation when we compare to those of traditional group. Second, students in the teaching and learning model group have the chance to explain their thoughts. And we can observe students to clear on their thought through speaking and discussing. This model makes students to enhance organizing, forming and clearing in their mathematical thoughts and is effective to estimate of students thought for teacher.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.443-465
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• 2014

Mathematics subject has been recognized as a subject in which we resolve some problematic situations through the logical and mathematical thinking according to mathematical concepts, principles, and rules. So we has focused on cultivating logical and mathematical thinking abilities when teaching and learning mathematics. However according to Bruner, we can use the narrative mode of thought which supplements the logical and scientific mode of thought when we think about logical and scientific matters, and we could make meanings by doing so. On the other hand, the Ministry of Education has announced recently that it would develope the textbooks of storytelling type of mathematics, and then many people have been interested in using stories in mathematics subject. The purposes of this article are to investigate the effects and the defects of using stories in mathematics subject, to probe the narrative characteristics of mathematics, and to inquire how using mathematics narrative can make students to make meaning about mathematics which compensates the defects of using stories in mathematics subject. And the main purpose is to inquire the implications of using mathematics narrative in teaching and learning mathematics.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.455-469
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• 2007

In this study, we want to being helpful to improvement of ability to solve mathematical problem, that is grafted on the subjects being able to occur in real life, of students in teaching materials and results studied and developed in the university. For increasing ability to solve ingenious problem and growing in the learning ability of oneself leading of students. The goal of this study is to make possible open research as a result of that students look for problem around real life by one's own efforts and take interest in them through learning mathematics of parents of students, they are the most important fact of educational environment in the mathematics education - earlier than students. In particular, the goal of this study is that students have an positive attitude of mind for mathematics and maximize ability of practical application by the analytic thinking learned through experience of their parents, they survey, analyze and solve problems taken from real life in the method transmitting one's knowledge to others. This study is divided into 2 categories: education of students and education of their parents. By these, we want to disseminate advanced knowledge and theory through students improve the powers of thought, logic and inference, develop ability to solve mathematical problem, stir up motivation of learning and learn knowledge of mathematics become familiar with real life.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.275-290
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• 2002

This Study takes Peirce' abduction which is Phenomenology' first reasoning mode, as a part of mathematical reasoning with deduction and induction. Abduction(retroduction, hypothesis, presumption, and originary argument) leads a case through a result and a rule, while deduction leads a result through a rule and a case and induction leads a rule through a case and a result. Polya(1954) involved generalization, specialization, and analogy within induction, but this paper contain analogy in abduction. And metaphors and metonymies are also contained in abduction, in which metaphors are contained in analogy. Metaphors and metonymies are applied to semiosis i.e. the signification of mathematical signs. Semiotic analysis for a student's problem solving showed the semiosis with metaphors and metonimies. Thus, abductions should be regarded as a mathematical reasoning, and we must utilize abductions in mathematical teaming since abductions are thought as a natural reasoning by students.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.699-701
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• 2003

This minipaper offers a formula which is dual to that of Viskov [5]. While Viskov's can be thought of as a rising formula for Laguerre polynomials, ours is precisely the lowering one. Besides documenting the formula, which seems to be missing, we want to provide a (rather elementary) operator theory argument instead of making crude calculations. In other words, the annihilation and creation operators are confronted with lowering and rising formulae; they are often failed to be distinguished.

• East Asian mathematical journal
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• v.25 no.3
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• pp.247-262
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• 2009

Permutation and combination are the part of mathematics which can be introduced the pliability and diversity of thought. In prior studies of permutation and combination, there treated difficulties of learning, strategy of problem solving, and errors that students might come up with. This paper provides the method so that meaningful teaching and learning might occur through the systematic approach of permutation and combination. But there were little prior studies treated counting numbers that basic of mathematics' action. Therefore this paper tries to help the understanding of permutation and combination with the process of changing from informal knowledge to formal knowledge.

• Research in Mathematical Education
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• v.12 no.2
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• pp.143-149
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• 2008

Before the 14th century, China had been thought as one of the countries with the most developed mathematics all along. But after the 16th century, Chinese mathematics increasingly walked up to the eclipse. The main reasons include the following points. First, the development of neoteric mathematics was closely associated with the social industrialization, but the lags in feudal China seriously blocked the development of the capitalistic seed, and China was still in the agricultural society then and couldn't step into the industrial society, which impeded the development of mathematics concerned with the industry and commerce. Second. the increasingly carrion feudalization was one of the essential reasons to block the development of Chinese neoteric mathematics. Finally, seeing about the developing logics of Chinese neoteric mathematics, we can find it was a scattered and experiential mathematical knowledge without strict and rational self-organizing structure system, which had the limitations existing in its interior mechanism.

• Journal of the Korean School Mathematics Society
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• v.4 no.1
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• pp.1-8
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• 2001

This paper discusses some variables of innovation arised in the Mathematical Curriculum reform, This means that we should consider the curriculum change based on those variables so that the Mathematical Curriculum could be created on our culture, need of industrial society and nation's system. Those variables could be described as follows. (1) Extension of Compulsory Education (2) Needs of industrial society (3) Change of School environment (4) Integration of School subjects The research method used in the study was the interview-analysis method which the researcher firstly send the questionnaire and then have interviews with the target people. This study also suggests informally a possible solutions of problem that current mathematical curriculum is faced. Those solutions include the change of mathematics syllabus based on the adaption toward the real problems arised in real world.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.125-141
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• 2022

The purpose of this study is to analyze how pre-service teachers perceive mathematics problems by making good mathematics problems at the elementary school level and applying them to elementary school students. In this study, 86 pre-service teachers enrolled in the second and third grades of A University of Education presented good mathematics problems they thought of. In addition, these pre-service teachers predicted the solution strategies of elementary school students for the proposed mathematics problem and described the teacher's expertise while observing the problem-solving process of elementary school students. As a result of the study, pre-service teachers preferred mathematical problems needed for using mathematical concepts or algorithms, motivation, and open-ended problems as good mathematics problems, and thought that students' in-depth observation and analysis experiences could help improve teachers' problem-solving expertise. In order to enhance teachers' expertise in solving mathematics problems, the researcher proposed for pre-service teachers to observe students' mathematics problem-solving processes, to experience in developing high-quality mathematics problems, and also to distribute high-quality mathematics problems linked to textbook problems.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.45-52
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• 2003

It is said that mathematics is neutral and free from any thought. But the history of mathematics refuses it. This paper aims to investigate modernism and postmodernism in mathematics and to scrutinize them. For this, first modernism is characterized by concentrating on Descartes' philosophy, and next postmodern view which criticizes modernism is discussed. Finally it is claimed that mathematical realism and postmodernism can be comparable in different dimensions.