• 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.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권3호
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• pp.233-255
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• 2004

Problem solving in math education is of great importance. The interest on problem solving in math education is growing all over the world. Problem solving ability is important throughout the fourth-sixth national curriculum in Korea and this is also necessary in the seventh national curriculum. The writer has implemented a proper model for problem posing and this is also necessary in the seventh national curriculum that emphasizes self-leading for improvement in the classroom. This model has advantages to cultivate a good habit of students who tries to solve the problems with concrete strategies, to take part in the problem solving activity and to change their mathematical attitude.

• 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.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제23권2호
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• pp.73-85
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• 2020

본 연구는 학생들에게 제시되는 문장제의 보조문항이 학생들의 문제해결 전략과 수학적 사고에 미치는 영향을 분석하고 교육적 시사점을 논하기 위하여 수행되었다. 분석결과, 보조문항을 통하여 문제해결 전략을 안내하는 문제는 그렇지 않은 경우에 비해 여러 수준의 학생들에게 효율적인 문제해결 전략을 채택하도록 유도함으로써 상대적으로 균일한 수학적 사고를 발현 시킬 수 있었다. 그리고 중하위권 학생들이 포기하지 않고 문제를 해결하기 위한 실마리를 떠올리는데 도움을 주었다. 다만 보조문항을 통하여 전략을 제공하는 문제는 학생들에게 유추적 사고를 유발시켰는지에 대한 여부가 불분명하였다. 아울러 제공된 문제의 영향으로 스스로 떠올릴 수 있었던 전략을 채택하지 못하는 경우가 발생하였다. 이에 반해 보조문항을 최소화하여 기본적인 권고만을 제공하는 문장제 해결 상황에서 상위권 학생들의 경우, 다양한 전략을 구상해낼 수 있었지만 중하위권 학생들은 쉽게 포기하거나 답을 구하지 못하는 경우가 상대적으로 많았다.

• 한국수학사학회지
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• 제29권1호
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• pp.17-30
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• 2016

This study focused on the selection and application of mathematical problems to provide mathematically challenging tasks for the gifted elementary students. For the selection, a mathematical problem from <算術管見> of Joseon dynasty, '圓容三方互求', was selected, considering the participants' experiences of problem solving and the variety of approaches to the problem. For the application, teaching strategies such as individual problem solving and sharing of the solving methods were used. The problem was provided for 13 mathematically gifted elementary students. They not only solved it individually but also shared their approaches by presentations. Their solving and sharing processes were observed and their results were analyzed. Based on this, some didactical considerations were suggested.

• 공학교육연구
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• 제12권4호
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• pp.30-37
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• 2009

연구의 목적은 학생들의 자기효능감 수준에 따른 문제해결능력의 차이를 검증해 보는 것이었다. 즉, 자기효능감이 높은 학습자와 낮은 학습자의 PBL수업 후 문제해결능력의 차이를 살펴봄으로써 PBL 수업에서의 자기효능감의 중요성을 파악해 보고자 했다. 본 연구는 환경공학과 '환경기기분석'을 수강했던 3학년 72명의 학생들을 대상으로 진행되었다. PBL 활동을 시작하기 전 자기효능감 검사를 통해 나온 점수를 기준으로 상위 30%와 하위 30%의 학생들을 각각 선정하였고, 이들에게 문제해결 능력 사전검사를 실시하였다. 12주간의 PBL활동이 마무리 된 후 같은 학생들에게 사후 문제해결검사를 배포하고 완성하도록 요구하였다. 교정된 문제해결 능력 성취 수준이 자기효능감 상집단과 하집단에 따라 차이가 있는지를 확인하기 위하여 공분산분석을 실시한 결과, 두 집단은 유의 확률 .002로 유의수준 .01에서 유의미한 것으로 나타났다 (F=.11303, p<.01). 즉, 자기효능감 상집단의 평균(3.817)이 자기효능감 하집단의 평균(3.496)보다 높아 자기효능감은 문제해결 능력과 밀접한 관련이 있는 것으로 나타났다. 따라서 PBL 수업과정에서 학습자의 자기효능감 수준을 향상시켜 효과적인 문제해결을 할 수 있도록 도울 필요가 있다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제19권3호
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• pp.177-191
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• 2016

자연수의 덧셈과 뺄셈은 학교수학을 해 나가는데 기본기능이며, 학생들은 다양하고 효율적인 전략을 활용하여 덧셈과 뺄셈 문제를 해결할 수 있어야 한다. 본 연구에서는 교육 환경과 문화가 다른 한국과 미국 초등학교 3학년 학생들이 자연수 덧셈과 뺄셈 문제해결에서 어떤 차이를 나타내는가를 분석하였다. 분석 결과, 덧셈과 뺄셈 수식문제와 문장제 모두에서 한국 학생들의 정답률이 높았으며, 통계적으로도 유의미한 차이를 나타내었다. 또한 학생들이 문제해결에 이용한 방법 면에서도 차이가 나타났다. 합병과 구잔 상황의 문장제 해결 방법의 수에서도 한국학생들이 통계적으로 유의미 결과를 나타냈는데, 이것은 두 나라 학생들이 계산 학습에서 익히고 활용하는 방법의 차이와 각 나라의 계산 수업에서 강조점 및 교실 수업 문화를 반영한다고 볼 수 있다.

• 지식경영연구
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• 제15권4호
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• pp.15-34
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• 2014

Creative problem solving has become an important issue in many fields. Among problems, dilemma need creative solutions. New creative and innovative problem solving strategies are required to handle the contradiction relations of the dilemma problems because most creative and innovative cases solved contradictions inherent in the dilemmas. Among various kinds of problem solving theories, TRIZ provides the concept of physical contradiction as a common problem solving principle in inventions and patents. In TRIZ, 4 separation principles solve the physical contradictions of given problems. The 4 separation principles are separation in time, separation in space, separation within a whole and its parts, and separation upon conditions. Despite this attention, an accurate definitions of the separation principles of TRIZ is missing from the literature. Thus, there have been several different interpretations about the separation principles of TRIZ. The different interpretations make problems more ambiguous to solve when the problem solvers apply the 4 separation principles. This research aims to fill the gap in several ways. First, this paper classify the types of contradiction relations and the contradiction solving dimensions based on the Butterfly model for contradiction solving. Second, this paper compares and analyzes each contradiction relation type with the Butterfly diagram. The contributions of this paper lies in reducing the problem space by recognizing the structures and the types of contradiction problems exactly.

• 한국초등과학교육학회지:초등과학교육
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• 제32권1호
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• pp.104-112
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• 2013

We examined the strategies to stimulate the reflective thinking using science notebook for the improvement of problem solving ability which is one of the core skills for the future. The strategies we derived have four steps which are input, output, solving mission and reflection as my own mirror. We applied the strategies to the 6th grade class for autumn semester in order to examine the students learning process and the result. We could observe that students looked into their own learning and had a time to look back their activities in the class. We could also confirmed that science notebook would be effective to improve the problem solving as stimulating the reflective thinking. In addition, we could specify the strategy of using science notebook in the class. At a 'input' stage, students should be able to choose their own learning style as their preference and teacher need to give them proper feedback. Interaction with peers should be emphasized during the activities as 'question attack' and 'question defense' in 'output' stage and 'solving mission' stage. You should suggest the students various method to record their thought from looking back their classroom activities instead of mere writing. We also examine the students achievement from the students' notebook and Meta Cognitive Awareness test. As a result, students who had studied using science notebook showed statistically meaningful higher achievement than controlled students.

• 한국정보기술학회 영문논문지
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• 제9권1호
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• pp.77-87
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• 2019

The Butterfly model, which aims to solve contradiction problems, defines the type of contradiction for given problems and finds the problem-solving objectives and their strategies. Unlike the ARIZ algorithm in TRIZ, the Butterfly model is based on logical proposition, which helps to reduce trial and errors and quickly narrows the problem space for solutions. However, it is hard for problem solvers to define the right propositional relations in the previous Butterfly algorithm. In this research, we propose a contradiction solving algorithm which determines the right problem-solving strategy just with yes or no simple questions. Also, we implement the Butterfly Chatbot based on the proposed algorithm that provides visual and auditory information at the same time and help people solve the contradiction problems. The Butterfly Chatbot can solve contradictions effectively in a short period of time by eliminating arbitrary alternative choices and reducing the problem space.