• 과학교육연구지
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• 제45권2호
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• pp.247-256
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• 2021

수학 문제해결에서 시각적 표현은 문제 이해와 해결에 유용한 수학적 표현으로 인식되고 있다. 그렇지만 그 효과는 문제 내용이나 유형, 또는 이용되는 시각적 표현 유형에 따라 다를 수 있다. 본 연구에서는 정형화된 문제와 비정형화된 문제해결에 이용된 시각적 표현의 양상을 살펴보기 위해 초등학교 5학년 학생들을 대상으로 조사연구를 실시하였다. 분석 결과, 정답률에서는 정형화된 문제가 비정형화된 문제보다 높게 나타났다. 정형화된 문제에서는 시각적 표현을 이용하여 문제를 해결하도록 하였음도 불구하고 수식을 이용하여 해결한 비율이 높게 나타났다. 반면에 비정형화된 문제에서는 시각적 표현을 이용하여 해결한 비율이 높게 나타났다. 그렇지만 비정형화된 문제에서 시각적 표현을 이용한 대상자 중에 오답자의 비율도 높게 나타났는데, 이것은 문제 상황을 묘사하는 수준의 시각적 표현에 그친 경우였다. 따라서 다양한 유형의 시각적 표현을 문제해결에 이용할 수 있는 경험을 제공하도록 하고, 시각적 표현으로의 변환 과정에도 주의를 기울일 필요가 있다.

• 한국항공운항학회지
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• 제22권4호
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• pp.42-55
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• 2014

The purpose of this research was to identify expertise in ait traffic control by using cognitive skill analysis for novices and experts in routine and non-routine situations. The result of study was to understand expertise in air traffic control tasks in terms of what cognitive processes are responsible for the expert's high performance levels. The problem solving task was difficult for novices, but performed relatively automatically by experts in a routine situation. The difficulty could indicate the presence of controlled processing. Rather than rules and strategies, novices focused more on environmental factors, which merely increase cognitive load. In a non-routine situation, novices showed that they did not categorize the information consistently and alternative resources were not available for them. Experts, however, performed automatically a task by arranging and organizing information related to problem solving components in contexts without regard to a routine and non-routine situation. Especially experts developed a stable representation and directed alternative resources for air traffic flow and efficiency. Based on the results, cognitive processes of experts could be useful to understand expert performance and analyze the learning process, which imply the necessity of developing expertise systematically.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권1호
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권4호
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• pp.361-380
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• 2010

Some 400 Secondary One (i.e. seventh-grade) students from 10 schools were provided with non-routine mathematical problems in their normal mathematics classes as exercises for one academic year. Their attitudes toward mathematics, their conceptions of mathematics and their problem-solving performance were measured both in the beginning and at the end of the year. Hierarchical regression analyses revealed that the introduction of an appropriate dose of non-routine problems would generate some effects on the students' conceptions of mathematics. A medium dose of non-routine problems (as reported by the teachers) would result in a change of the students' conception of mathematics to perceiving mathematics as less of "a subject of calculables." On the other hand, a high dose would lead students to perceive mathematics as more useful and more as a discipline involving thinking. However, with a low dose of non-routine problems, students found mathematics more "friendly" (free from fear). It is therefore proposed that the use of non-routine mathematical problems to an appropriate extent can induce changes in students' "lived space" of mathematics learning and broaden their conceptions of mathematics and mathematics learning.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권1호
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• pp.39-51
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• 2010

The purpose of this article is to study students' responses to non-routine problems which are presented by using solely numerals or symbolic figures. Such figures have no mathematical meaning but just symbolical meaning. Most students understand geometric figures more concrete objects than numerals because geometric figures such as circles and squares can be visualized by the manipulatives in real life. And since students need not consider (unvisible) any operational structure of numerals when they deal with (visible) figures, problems proposed using figures are considered relatively easier to them than those proposed using numerals. Under this assumption, we analyze students' problem solving processes of numeral problems and figural problems, and then find out when students' difficulties arise in the problem solving process and how they response when they feel difficulties. From this experiment, we will suggest several comments which would be considered in the development and application of both numerical and figural problems.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권3호
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• pp.179-191
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• 2008

Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권3호
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• pp.793-806
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• 2010

본 연구는 2007개정 교육과정에서 강조하는 창의적인 탐구, 문제해결에 관련된 문헌연구로, 본 연구에서는 문제의 이해 단계에서 수행하는 분석의 본질 및 유형을 문헌연구를 통해 고찰하였으며, 구체적인 방정식 문제들에 대한 분석을 제시하였고, 분석을 통해 얻어진 정보들을 활용한 다양하고 비정형적인 문제해결의 방법들을 제시하였다. 이를 통해, 고등학교의 수학교실에서 방정식 단원의 다양한 해법찾기 활동에 관련된 기초자료를 제공할 수 있을 것으로 기대된다.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권2호
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• pp.111-136
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• 2018

This study suggests a framework for analyzing items based on the characteristics, and shows the relationship among the characteristics, difficulty, percentage of correct answers, academic achievement and the actual mathematical problem solving competency. Three mathematics educators' classification of 30 items of Mathematics 'Ga' type, on 2017 College Scholastic Ability Test, and the responses given by 148 high school students on the survey examining mathematical problem solving competency were statistically analyzed. The results show that there are only few items satisfying the characteristics for mathematical problem solving competency, and students feel ill-defined and non-routine items difficult, but in actual percentage of correct answers, routineness alone has an effect. For the items satisfying the characteristics, low-achieving group has difficulty in understanding problem, and low and intermediate-achieving group have difficulty in mathematical modelling. The findings can suggest criteria for mathematics teachers to use when developing mathematics questions evaluating problem solving competency.

• Journal of Nutrition and Health
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• 제26권1호
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• pp.67-75
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• 1993

Folate and iron nutrition was studied in a total of 122 pregnant, lactaging, and non-pregant, non-lactating Korean women, Serum folate levels were determined microbiologically using Lactobacillus casei(ATCC 7469), and serum iron levels was analyzed colormetrically. The average folate values of pregnant and lactating women were 5.42ng/ml and 4.14ng/ml, which were significantly lower than that of the non-pregnant, non-lactating women(7.06ng/ml). More than 1/3 of the total subjects were found to have serum folate levels lower than 3ng/ml, at which folate nutrition status can be considered inadequate. Serum iron values of pregnant(96.9ug/dl)and lactating women(93.9ug/dl) were not significantly different from that of the non-pregnant, non-lactating women (97.1ug/dl). There were however, more iron-deficient subjects in the pregnant gorup(17%) and the lactating group(19%) than in the non-pregnant, non-lactating group (8%). A statistically significant positive correlation was shown between the levels of serum folate and iron in lactating women(r=.9694, p<0.05). The results of our study document that folate deficiency is a nutritional problem as prevalent as iron deficiency in Korean women, especially during pregnancy and lactation. For these women a routine folate and iron supplementation might be necessary.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.