• 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.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권3호
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• pp.289-309
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• 2018

There has been a gradually increasing focus on adopting mathematical modeling techniques into school curricula and classrooms as a method to promote students' mathematical problem solving abilities. However, this approach is not commonly realized in today's classrooms due to the difficulty in developing appropriate mathematical modeling problems. This research focuses on developing reformulation strategies for those problems with regard to mathematical modeling. As the result of analyzing existing textbooks across three grade levels, the majority of problems related to the real-world focused on the Operating and Interpreting stage of the mathematical modeling process, while no real-world problem dealt with the Identifying variables stage. These results imply that the textbook problems cannot provide students with any chance to decide which variables are relevant and most important to know in the problem situation. Following from these results, reformulation strategies and reformulated problem examples were developed that would include the Identifying variables stage. These reformulated problem examples were then applied to a 7th grade classroom as a case study. From this case study, it is shown that: (1) the reformulated problems that included authentic events and questions would encourage students to better engage in understanding the situation and solving the problem, (2) the reformulated problems that included the Identifying variables stage would better foster the students' understanding of the situation and their ability to solve the problem, and (3) the reformulated problems that included the mathematical modeling process could be applied to lessons where new mathematical concepts are introduced, and the cooperative learning environment is required. This research can contribute to school classroom's incorporation of the mathematical modeling process with specific reformulating strategies and examples.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제10권1호
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• pp.55-70
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• 2006

The purpose of this study was to develop math creative problem solving test in order to identify the mathematically gifted on the basis of their math creative problem solving ability and evaluate the goodness of the test in terms of its reliability and validity of measuring creativity in math problem solving on the basis of fluency in producing valid solutions. Ten open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 open math test items were administered to 2,029 Grade 5 students who were recommended by their teachers as candidates for gifted education programs. Fluency, the number of valid solutions, in each problem was scored by math teachers. Their responses were analyzed by BIGSTEPTS based on Rasch's 1-parameter item-response model. The item analyses revealed that the problems were good in reliability, validity, difficulty, and discrimination power even when creativity was scored with the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creativity of the candidates for math gifted education programs. In addition, it discriminated applicants for two different gifted educational institutions and between male and female students as well.

• 한국과학교육학회지
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• 제10권1호
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• pp.57-64
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• 1990

In this study, novices' protocols were investigated on the basis of Mayer's analysis of mathematical problem solving. These protocols were obtained by Jae-Sool Kwon and Seong-Wang Lee(1988) by means of thinking aloud while 20 sophomore students in a department of physics education were solving physics problems on Newton's low of motion. The results of investiqation are as follows; (1) We proposed an effective method in analyzing protocols on physics porblem solving (2) We could find the defective types of knowledge of individuals who got an incorrect solution, through analyzing the cause of failure individually (3) The fact that many students considered first the frictional force as muntiplying the coefficient of friction by perpendicular force rather than as resistance of motion, was found And students' misconception on the coefficient of friction was found. (4) If such analyses of test items and protocols are used in physics education, they will be very useful for finding the faults of problem-solving process, and for setting and scoring subjective problems in physics

• 한국수학교육학회지시리즈A:수학교육
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• 제41권3호
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• pp.341-360
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• 2002

The purpose of the study was to investigate the effectiveness of dynamic software in solving high school analytic geometry problems compared with traditional algebraic approach. Three high school students who have revealed high performance in mathematics were involved in this study. It was considered that they mastered the basic concepts of equations of plane figure and curves of secondary degree. The research questions for the study were the followings: 1) In what degree students understand relationship between geometric approach and algebraic approach in solving geometry problems? 2) What are the difficulties students encounter in the process of using the dynamic software? 3) In what degree the constructions of geometric figures help students to understand the mathematical concepts? 4) What are the effects of dynamic software in constructing analytic geometry concepts? 5) In what degree students have developed the images of algebraic concepts? According to the results of the study, it was revealed that mathematical connections between geometric approach and algebraic approach was complementary. And the students revealed more rely on the algebraic expression over geometric figures in the process of solving geometry problems. The conceptual images of algebraic expression were not developed fully, and they blamed it upon the current college entrance examination system.

• 한국과학교육학회지
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• 제16권3호
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• pp.295-302
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• 1996

The purpose of this study was to investigate the effects of training and use of worked-example on chemical problem-solving learning. Schema acquisition and rule automation are the basic components of skilled problem-solving, which are dependent on appropriately focused attention and sufficient cognitive resources. Training and use of worked-example facilitate schema acquisition and rule automation, so improve problem-solving learning. The subjects of this study were 60 high school students. The average age was 17 years old. Then, they were randomly assigned to each groups and the chemical reaction problems used as experimental materials. The independent variables of this study were training and use of worked-examples and dependent variables were time for solution and the number of error. The results of this study were as follows; 1. The worked-example groups spent significantly less time on solution for acquisition problems than the conventional problem groups. 2. The long-acquisition groups spent significantly less time on solution for acquisition problems than the short-acquisition groups. 3. The modified worked-example groups did not spend significantly less time on solution for acquisition problems than the worked-example groups.

• 대한화학회지
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• 제46권4호
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• pp.353-363
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• 2002

이 연구의 목적은 일반고와 과학고 학생들의 정신용량과 풀이 방법에 따른 산화 환원 반응식 완결 과정의 특성을 분석하여 산화 환원 단원의 교수학습 지도에 시사점을 얻고자 하는데 있다. 일반고 학생 79명과 과학고 학생 57명을 대상으로 하여 정신요량 검사, 산화 환원 반응식 완결 검사를 실시하였으며, 문항 유형별로 학생들의 문제 풀이 실패 유형과 성공 유형을 추출하여 분석틀을 개발하고 개발한 분석틀에 의하여 정신용량과 풀이 방법에 따라 실패 사례와 성공 사례를 분석하여 나타나는 특징을 알아보았다. 일반고 학생들과 과학고 학생들 모두 산화 환원 개념 이해 정도가 낮을수록 미정계수법을 많이 선택하였으며 미정계수법을 선택한 학생들은 정신용량이 클수록 문제 풀이의 성공률이 높았다. 또한, 산화 환원 개념 이해 정도가 높은 학생들은 산화수법이나 이온 자법을 더 많이 선택하였고 정신용량에 관계없이 문제 풀이의 성공률이 높게 나타났다. 학생들의 풀이 과정을 분석한 결과 성공 유형은 산화 환원의 개념 이해 정도가 높고 풀이 방법에 관계없이 풀이 단계 수를 줄이 학생들이었다. 실패 유형은 물이 방법에 따라 다르게 나타났다. 미정계수법을 선택한 학생들의 실패 유형은 계산 과정 중 틀린 경우, 미정방정식을 잘못 세운 경우 문제 풀이 과정중 고려해야 할 변인을 모두 고려하지 못한 경우 풀이 과정이 복잡하여 중단한 경우였다. 산화수법을 선택한 학생들의 실패 유형은 산화수를 잘못 결정한 경우 질량균형 또는 전하균형을 고려하지 않은 경우였다.

• 컴퓨터교육학회논문지
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• 제16권5호
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• pp.9-16
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• 2013

컴퓨팅적 사고(Computational Thinking)는 실세계와 다양한 학문 분야에 적용될 수 있는 보편적 문제해결 능력으로 컴퓨터 과학 분야의 핵심역량이자 미래 인재가 필수적으로 갖추어야 할 소양이다. 컴퓨팅적 사고는 문제를 분석하고 문제 해결에 적합한 컴퓨팅 원리 및 전략들을 선택, 적용하는 경험을 통해 증진될 수 있다. 본 연구에서는 학습자에게 컴퓨팅적 사고를 기반으로 한 문제 해결 경험을 제공하기 위한 퍼즐기반 학습을 설계하고 초등정보영재 교육에서의 적용 가능성을 탐색하였다. 학습에 활용된 퍼즐 문항들은 학습자 수준에 맞게 구성된 서술형 퍼즐로 제약조건, 최적화, 확률, 통계, 패턴인식, 전략의 6가지 유형으로 분류된다. 퍼즐 기반 학습을 초등학교 6학년 영재학급에 적용한 결과, 학습자의 컴퓨팅적 사고 및 문제해결성향에 긍정적인 영향을 준 것을 확인하였다. 이는 컴퓨팅적 문제 해결 원리를 포함한 퍼즐 해결 경험이 흥미와 통찰을 유도하고, 실세계와 유사한 다양한 문제 해결 경험을 제공하기 때문인 것으로 판단된다.

• Spatial Information Research
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• 제1권1호
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• pp.63-72
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• 1993

현재의 GIS가 감당할 수 있는 것은 모든 공간적 문제는 아니다. 그동안 알려진 GIS는 정보를 생산해 내는 정보위주의 GIS일뿐 정보의 다각적 이해와 의사결정과 정에 깊이 관여하지 못하였다. 단순문제(structured problems)들을 해결하기에는 정보위주의 GIS가 적합하지만 계획과 설계와 같은 비단순문제(ill-structured problems)들을 다루기에는 미흡한 단계이며, 이 단계에서 도약하기 위해 개념위주의 SDSS(Spatual Decision Suppert System)로 발전되어야 한다. 이 글에서는 개념위주의 SDSS가 비단순문제 해결을 지원하기 위한 기구로서 소개되며 정보위주 GIS의 미래상으로 비젼(vision)을 제시한다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제2권1호
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• pp.3-13
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• 1998

In mathematics education we have focused on how to improve the problem-solving ability, which makes its way to the new direction with the introduction of meta-cognition. As meta-cognition is based on cognitive activity of learners and concerned about internal properties, we may find a more effective way to generate learners problem-solving power. Its means that learners can regulate cognitive process according to their gorls of learning by themselves. Moreover, they are expected to make active participation through this process. If specific meta problems designed to develop meta-cognition are offered, learners are able to work alone by means of their own cognition and regulation while solving problems. They can transfer meta-cognition to the other subjects as well as mathematics. The studies on meta-cognition conducted so far may be divided into these three types. First in Flavell(［3］) meta-cognition is defined as the matter of being conscious of one's own cognition, that is, recognizing cognition. He conducted an experiment with presschoolers and children who just entered primary school and concluded that their cognition may be described as general stage that can not link to specific situation in line with Piaget. Second, Brown(［1］, ［2］) and others argued that meta-cognition means control and regulation of one's own cognition and tried to apply such concept to classrooms. He tried to fined out the strategies used by intelligent students and teach such types of activity to other students. Third, Merleary-Ponty (1962) claimed that meta-cognition is children's way of understanding phenomena or objects. They worked on what would come out in children's cognition responding to their surrounding world. In this paper following the model of meta-cognition produced by Lester (［7］) based on such ideas, we develop types of meta-cognition. In the process of meta-cognition, the meta-cognition working for it is to be intentionally developed and to help unskilled students conduct meta-cognition. When meta-cognition is disciplined through meta problems, their problem-solving power will provide more refined methods for the given problems through autonomous meta-cognitive activity without any further meta problems.