• School Mathematics
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• v.15 no.3
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• pp.551-568
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• 2013

The purpose of this study is to verify the research trends on 101 articles about mathematical creativity published in domestic journals. The analysis criteria are as follows: (1)What kind of terms the articles use to refer to the creativity in mathematics education, (2)Whether the researchers conceptualize such the terms or not, (3)Whether the definitions are domain-specific or not, (4)What perspectives, categories and levels of the articles have on creativity. The results of this study show the following. First, numerous articles used 'mathematical creativity' in order to point to the creativity in mathematics education. Second, among the 101 selected articles, 60 (59.4%) provided an explicit definition of the mathematical creativity and 19(18.8%) provided an implicit definition. Among the 79 articles, only 43(54.4%) provided domain-specific definitions. Second, the percentage of articles preferring one perspective over the other 3 perspectives were similar. Third, the rate of articles which focused on press(environment) of all categories (person, process, product, press) was low. Fourth, regarding the levels of creativity, most articles were done on little-c creativity level, on the other hand, the articles having an interest in mini-creativity were very rare. Based on these results, necessities of explicit and domestic-specific definition, whole approach of mathematical creativity, and articles focusing on the mini-creativity level should be reported.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.505-516
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• 2013

The purpose of this paper is to analyse the essence of proportional reasoning and to analyse the contents of the textbooks according to the mathematics curriculum revised in 2007, and to seek the direction for developing the proportional reasoning in the elementary school mathematics focused the task variables. As a result of analysis, it is found out that proportional reasoning is one form of qualitative and quantitative reasoning which is related to ratio, rate, proportion and involves a sense of covariation, multiple comparison. Mathematics textbooks according to the mathematics curriculum revised in 2007 are mainly examined by the characteristics of the proportional reasoning. It is found out that some tasks related the proportional reasoning were decreased and deleted and were numerically and algorithmically approached. It should be recognized that mechanical methods, such as the cross-product algorithm, for solving proportions do not develop proportional reasoning and should be required to provide tasks in a wide range of context including visual models.

• 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.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.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.307-319
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• 2009

Current school mathematics introduces addition/subtraction between natural numbers, fractions, decimal fractions, and square roots, step-by-step in order. It seems that, however, school mathematics focuses too much on learning the calculation method of addition/subtraction between each stages of numbers, to lead most of students to understand the coherent principle, lying in addition/subtraction algorithm between real numbers in all. This paper raises questions on this problematic approach of current school mathematics, in learning addition/subtraction. This paper intends to clarify the fact that, if we recognize addition/subtraction between numbers from the viewpoint of 'measuring' and 'common measure', as Dewey did when he argued that the psychological origin of the concept of number was measuring, then we could find some common principles of addition/subtraction operation, beyond the superficial differences among algorithms of addition/subtraction between each stages of numbers. At the end, this paper suggests the necessity of improving the methods of learning addition/subtraction in current school mathematics.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.91-110
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• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• Communications of Mathematical Education
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• v.12
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• pp.463-477
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• 2001

국가의 국가경쟁력은 학창시절 학생의 학력만큼 중요하다. 성인의 경우, 학력을 위한 노하우는 체험을 통해 터득할 수 있었다. 그러나 국가경쟁력에 관해서는 우물 안 내부관점을 벗어나기 힘들어 추진 방향과 제도 운영에 자칫 시행착오를 범하기 쉽다. 이는 사안에 대해 본질적인 접근보다 껍데기만을 쫓기 때문이었다. 이 현상을 분석하려면 관점과 보이지 않는 영역의 것들을 다룰 수 있는 수학적 사고법이 필요하며, 이 능력은 현 지식정보화 사회에서 매우 긴요하다. 그러나 현실은 여러 가지 이유로 수학적 사고법을 비롯한 기초학문을 위기로 몰아가고 있고, 안타깝지만 그 중심에 수학교육이 자리잡고 있다. 수학교육의 위기를 유발하는 요인으로 제도 운영에 관한 건이 있다. 제도 운영에서 한 변수의 변화, 예로 대입의 계열교차지원 허용 건, 교원임용고시에서 교과교육학 영역의 출제 건과 복수전공, 부전공 자격소지자에 대한 가산점 부여 건은 수학교육과 교육과정에 직, 간접적으로 영향을 미친다. 이 관계를 사범대학 수학교육과 현장의 사례를 통하여 조명하고, 그 문제점을 지적하고자 한다. 현 사범교육은 졸업이수학점 140학점 체제하에서 제 7차 교육과정에 따른 복수전공, 부전공 우대 정책을 펴고 있다. 수학교육과의 경우, 부전공 열풍이 불어 전공선택 과목이 3학년 1학기부터 폐강될 위기에 처해 있다. 교양교육의 고사 또는 전광교육이 예전보다 반으로 줄어들게 된 사범대학 실상에 비애감을 느끼게 된다. 이는 전문화된 교사 양성, 나아가 미래 국가경쟁력 향상에 심각한 저해 요소로 작용할 것이다. 복잡다단한 세상에서 최적화를 향한 개선 노력이 멈춰서는 안 된다. 현행 교원임용고시 운영상의 문제점을 공론화하고, 수학교육인의 중지를 모아야 할 긴박한 시점이다. 이를 계기로 교원임용고시의 운영개선과 수학교육과 교육과정을 한층 더 견실하게 하는 데에 이바지하고자 한다. 것이라면 후속연구로 이러한 가능성을 실험연구로 검증하고자 한다.toceros resting spores/Chaetoceroe vegetative cells도 80 cm 보다 상층에서는 높게 나타나 규조온도지수 분포와도 일치하는 경향을 보인다. 이상의 규조군집 분석 결과에 의하면, 홀로세의 후빙기동안 본 연구 지역인 동해 북동부에는 대마 난류의 유입이후 현재와 유사한 환경이 우세하게 발달했으나, 난류종 P. doliolus의 변화는 동해내에서 대마난류의 세기가 반복되었음을 지시하고 있다./3 수준으로 높다. 결론적으로 풍부한 화학물질들을 함유한 제주해류는 남해 및 동해의 생지화학적 과정들에 있어 상당히 중요함을 시사한다.다. 수조 상층수 중 Cu, Cd, As 농도는 모든 FW, SW수조에서 시간이 지남에 따라 일관성 있게 감소하였고, 제거속도는 Cu가 다른 원소에 비해 빨랐다. 제거속도는 FW 3개 수조 중 FW5&6에서 세 원소 모두 가장 느렸고, SW 3개 수조 중에서는 SW1&2에서 가장 빨랐다. SW와 FW간 제거속도 차이는 세 원소 모두 명확치 않았다 Cr은 FW에서 전반적으로 감소하는 경향을 보였지만 SW에서는 실험 초기에 감소하다 24시간 이후에는 증가 후 일정한 양상을 보였다. Pb은 FW에서 전반적으로 감소했지만 SW에서는 초기에 급격히 증가 후 다시 급격히 감소하는 양상을 보였다 Pb 또한 Cu, Cd, As와 마찬가지로 SW1&2에서 제거속도가 가장 빠르게 나타났다. FW 상층수 중 Hg는 시간에 따라 급격히 감소했고, 제거속도는 Fw5&6에서 가장 느렸다. 이러한 결과에 근거할 때 벼가 자라고 있고 이분해성 유기물이 풍부한 FW1&2, FW3&4 토양과 상층수에서는 유기물의 분해 활동이 활발하였지만, 벼가 경작되지 않는 FW5&6과 SW 에서는 유기물이 상대적으로 결핍되어 유기물의 분해활동이 적었을 것으로 판단된다

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.415-435
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• 2007

A transition from elementary to secondary school, and among grades, among learning contents is a essential problem in education. A connectivity between learning contents is important in student's growth and development. A gap between lower grades and higher grades in elementary school is no less extensive than a gap between elementary mathematics and secondary mathematics. In this paper, we start with a critical mind about a transition and connectivity between lower grades and higher grades in elementary school. In order to compare between elementary grades, we firstly focus 4th grade mathematics which finish lower grades and start higher grades at the same time. First, we make up a questionnaire to 4th grade students and teachers in charge 4th grade. A questionnaire is composed of questions about the degree of difficulty in the learning(and teaching) of 4th grade mathematics comparing with 3rd grade mathematics. Second, we compare to lower grades lessons(1st grade) and 4th grade lessons using a qualitative method. we analyze the lesson contents, activities and time through 'analysis of the learning course'. And we compare the pattern of eliciting questions, question patterns, nomination patterns and feedback patterns between 1st grade and 4th grade lessons. We hope that this paper is a fundamental sources in investigating a connectivity between lower grades and higher grades in elementary mathematics in the future.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.85-100
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• 2005

In recent papers (Pak et al., Pak and Kim), it was suggested to positively use the history of mathematics for the education of mathematics and discussed the determining problem of the order of instruction in mathematics. There are three kinds of order of instruction - historical order, theoretical organization, lecturing organization. Lecturing organization order is a combination of historical order and theoretical organization order. It basically depends on his or her own value of education of each teacher. The present paper considers a concrete problem determining the order of instruction for the concept of angle. Since the concept of angle is defined in relation to figures, we have to solve the determining problem of the order of instruction for the concept of figure. In order to do this, we first investigate a historical order of the concept of figure by reviewing it in the history of mathematics. And then we introduce a theoretical organization order of the concept of figure. From these basic data we establish a lecturing organization order of the concept of figure from the viewpoint of problem-solving. According to this order we finally develop the concept of angle and a related global property which leads to the so-called Gauss-Bonnet theorem.