• The Mathematical Education
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• v.50 no.1
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• pp.1-12
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• 2011

It is the aim of this paper to study the target problem solving process in reference to the base problem. We observed closely how students solve the target problem in reference to the base problem. The students couldn't solve the target problem, although they succeed to find the base problem. This comes from failing to discover the structural similarity between the target problem and the base problem. Especially it is important to cognize the proper corresponding of primary components between the base problem and target problem. And there is sometimes a part component of the target problem equivalent to the base problem and the target problem can't be solved without the insight into this fact. Consequently, finding the base problem fail to reach solving the target problem without the insight into their structural similarity. We have to make efforts to have an insight into the structural similarity between the target problem and the base problem to solve the target problem.

• Knowledge Management Research
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• v.7 no.1
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• pp.1-12
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• 2006

The previous empirical research suggests that problem finding is more important than problem solving in the creative process. Problem finding is increasingly recognized in theories of creativity. In spite of the importance of problem finding, there is little research to explain problem finding in Korea. This article reviews the research about problem finding and examines the nature of problem finding, the type of problems, the relation of problem finding and problem solving, the relation of problem finding and creativity, and the serendipity. Finally, theoretical and educational implications are discussed.

• Journal of Engineering Education Research
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• v.16 no.6
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• pp.38-44
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• 2013

This study has the purpose to identify the correlation of engineering education major college students' technological problem solving tendency between technological problem solving capability. To that end, the technological problem solving tendencies of 79 students enrolled in engineering education related department in college of education, 'C' University located in Daejeon metropolitan city were examined, and the correlation of technological problem solving tendency between technological problem solving capability was analyzed through measurement of technological problem solving capability. As for the correlation among problem solving confidence a sub-element of technological problem solving tendency and technological problem solving capability, positive correlation was found in result 3, result 4 and result average. As for the correlation among approach-avoidance tendency a sub-element of technological problem solving tendency and technological problem solving capability, positive correlation was found in result 5 and result average. As for the correlation among self-control recognition degree the sub-element of technological problem solving tendency and technological problem solving capability, positive correlation was found in result 1, result 3 and result average. As for the correlation among problem solving tendency and technological problem solving capability, positive correlation was found in result 3, result 4, result 5 and result average.

• Education of Primary School Mathematics
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• v.2 no.2
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• pp.133-144
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• 1998

We examined two kinds of problem posing, 'problem making' and 'problem modifying' to find which one is more effective for improving mathematical problem solving ability according to the student's learning-levels and sexes. The results showed that 'problem making' is more effective for high and middle-level groups than 'problem modifying'. There was no big difference according to the sexes. These facts implies that making a problem when a situation was presented is more effective to develop problem solving ability than modifying a problem ： modifying some conditions and contents of given problem.

• Journal of Korean Elementary Science Education
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• v.17 no.1
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• pp.75-87
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• 1998

The problem solving processes of elementary school children who are talented in science have been seldom studied. Researchers often resort to thinking aloud method to collect data of problem solving processes. The major purpose of the study is investigating high ability elementary school students' problem solving processes through the analysis of written responses to science problems in everyday context. 67 elementary students were participated Chungcheongbuk-do Elementary Science Contest held on October, 1997. The written responses of the contest participants to science problems in everyday context were analyzed in terms of problem solving processes. The findings of the research are as follows. (1) High ability elementary students use various concepts about air and water in the process of problem solving. (2) High ability elementary students use content specific problem solving strategies. (3) The problem solving processes of the high ability elementary students consist of problem representation, problem solution, and answer stages. Problem representation stage is further divided into translation and integration phases. Problem solving stage is composed of deciding relevant knowledge, strategy, and info..ins phases. (4) High ability elementary students' problem solving processes could be categorized into 11 qualitatively different groups. (5) Students failures in problem solving are explained by many phases of problem solving processes. Deciding relevant knowledge and inferring phases play major roles in problem solving. (6) The analysis of students' written responses, although has some limitations, could provide plenty of information about high ability elementary students' problem solving precesses.

• Journal of The Korean Association For Science Education
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• v.25 no.1
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• pp.1-15
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• 2005

This study examined two students' problem solving approaches: the similarities and the differences in their problem solving approaches, and the general problem solving strategies (heuristics) the students employed were discussed. The two students represent differences not only in terms of grades earned, but also in terms of participation, motivation, attention to detail, and approaches to answering questions and problem solving. Three separate problems were selected for this study: A stoichiometry problem; a fruit salad problem; and a limiting reactant problem. Each student was asked individually on three separate occasions to contribute to this study. There are more similarities in the students' problem solving strategies than there are differences. Both students were able to correctly solve the stoichiometry and the fruit salad problems, and were unable to correctly solve the limiting reactant problem. They recognized that an algorithm could be used for both chemistry problems(a stoichiometry problem & a limiting reactant problem). Both students were unable to correctly solve the limiting reactant problem and to demonstrate a clear understanding of the Law of Conservation of Mass. Nor did they show an ability to apply it in solving the problem. However, there was a difference in each one's ability to extend what had been learned/practiced/quizzed in class, to a related but different problem situation.

• Educational Technology International
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• v.13 no.2
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• pp.283-312
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• 2012

Problem-solving ability is one of the most important learning outcomes for students to compete and accomplish in a knowledge-based society. It has been empirically proven that visualization plays a central role in problem-solving. The best performing problem-solver might have a strong visualization tendency. However, there is little research as to what factors of visualization tendency primarily related to problem-solving ability according to phases of problem-solving. The purpose of this study is to identify the relationship between visualization tendency and problem-solving ability, to determine which factors of visualization tendency influence problem-solving ability in each phase of problem-solving, and to examine different problem-solving ability from the perspective of the levels of visualization tendency. This study has found out that visualization tendency has a significant correlation with problem-solving ability. Especially, Generative Visualization and Spatial-Motor Visualization as sub-visualization tendency were more strongly related to each phase of problem-solving. It indicates that visualization tendency to generate and operate mental processing can be considered a major cognitive skill to improve problem-solving ability. Furthermore, students who have high visualization tendency also have significantly higher problem-solving ability than students with low visualization tendency. It shows that the levels of visualization tendency can predict variables related to students' problem-solving ability.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.533-551
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• 2015

Problem posing in school mathematics is generally regarded to make a new problem from contexts, information, and experiences relevant to realistic or mathematical situations. Also, it is to reconstruct a similar or more complicated new problem based on an original problem. The former is called as problem generation and the latter is as problem reformulation. The purpose of this study was to explore the co-relation between problem generation and problem reformulation, and the educational effectiveness of each problem posing. For this purpose, on the subject of 33 pre-service secondary school teachers, this study developed two types of problem posing activities. The one was executed as the procedures of [problem generation${\rightarrow}$solving a self-generated problem${\rightarrow}$reformulation of the problem], and the other was done as the procedures of [problem generation${\rightarrow}$solving the most often generated problem${\rightarrow}$reformulation of the problem]. The intent of the former activity was to lead students' maintaining the ability to deal with the problem generation and reformulation for themselves. Furthermore, through the latter one, they were led to have peers' thinking patterns and typical tendency on problem generation and reformulation according to the instructor(the researcher)'s guidance. After these activities, the subject(33 pre-service teachers) was responded in the survey. The information on the survey is consisted of mathematical difficulties and interests, cognitive and affective domains, merits and demerits, and application to the instruction and assessment situations in math class. According to the results of this study, problem generation would be geared to understand mathematical concepts and also problem reformulation would enhance problem solving ability. And it is shown that accomplishing the second activity of problem posing be more efficient than doing the first activity in math class.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.131-143
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• 2003

In this paper, we present a survey about the various graph partition problems including the clustering problem, the k-cut problem, the multiterminal cut problem, the multicut problem, the sparsest cut problem, the network attack problem, the network disconnection problem. We compare those problems focusing on the problem characteristics such as the objective function and the conditions that the partitioned clusters should satisfy. We also introduce the mathematical programming formulations, and the solution approaches developed for the problems.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.361-374
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• 2005

I analyzed the effect of problem posing teaching and teacher-centered teaching on mathematical problem-solving ability and creativity in order to know the efffct of problem posing teaching on mathematics study. After we gave problem posing lessons to the 3rd grade middle school students far 28 weeks, the evaluation result of problem solving ability test and creativity test is as fellows. First, problem posing teaching proved to be more effective in developing problem-solving ability than existing teacher-centered teaching. Second, problem posing teaching proved to be more effective than teacher-centered teaching in developing mathematical creativity, especially fluency and flexibility among the subordinate factors of mathematical creativity. Thus, 1 suggest the introduction of problem posing teaching activity for the development of problem-solving ability and mathematical creativity.