• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.3
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• pp.180-193
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• 2005

This paper deals with a multiobjective process planning problem of flexible assembly systems(FASs). The FAS planning problem addressed in this paper is an integrated one of the assignment of assembly tasks to stations and the determination of assembly routing, while satisfying precedence relations among the tasks and flexibility capacity for each station. In this research, we consider two objectives: minimizing transfer time of the products among stations and absolute deviation of workstation workload(ADWW). We place emphasis on finding a set of diverse near Pareto or true Pareto optimal solutions. To achieve this, we present a new multiobjective coevolutionary algorithm for the integrated problem here, named a multiobjective symbiotic evolutionary algorithm(MOSEA). The structure of the algorithm and the strategies of evolution are devised in this paper to enhance the search ability. Extensive computational experiments are carried out to demonstrate the performance of the proposed algorithm. The experimental results show that the proposed algorithm is a promising method for the integrated and multiobjective problem.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.137-155
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• 2009

The purpose of the present study was to analyse the effectiveness of a gifted education program. To analyse the effectiveness of an education program for the gifted affiliated with a university, the study carried out a quasi-experimental design to compare the 153 gifted students who enrolled in an education center for the gifted and the 131 potentially gifted students who were nominated by teachers for their high achievements and interests in science but without any education services for the gifted. These two groups of students were compared in the aspects of problem finding ability in science, motivation, self regulation, science-related attitudes, and science anxiety through the pre- and post-treatment settings. The results indicated that the gifted group showed a significant improvement in originality and elaboration of problem-finding ability, but the potentially gifted group showed significant decrease in most variables of problem finding. Related to motivation and self-regulated learning, gifted students showed an increase in cognitive strategy use and decrease in intrinsic value, but the potentially gifted students showed significant decreases in most variables related to motivation and self-regulation, except intrinsic value. Related to the scientific attitudes and science anxiety, there were no significant changes between pre- and post-tests in the gifted group, but significant decreases in most variables were found in the potentially gifted group. The results of paired t-test and Ancova indicate that significant differences between the gifted and the potentially gifted groups are mainly due to the significantly lowered performance in post tests in the potentially gifted group, rather than a significant increase in gifted group.

• School Mathematics
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• v.16 no.1
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• pp.19-37
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• 2014

This study investigated the degree of understanding pre-service teachers' random variable concept, based on the attention and the importance for developing pre-service teachers' ability on statistical reasoning in statistics education. To accomplish this, the subject of this study was 70 pre-service teachers belonged to three universities respectively. The teachers were given to 7 tasks on random variable and requested to solve them in 40 minutes. The tasks consisted of three contents in large; 1) one was on the definition of random variables, 2) the other was on the understanding of random variables in different/diverse conditions, and 3) another was on problem solving relevant to random variable concept. The findings are as follows. First, while 20% of pre-service teachers understood the definition of random variable correctly, most teachers could not distinguish between random variable and variable or probability. Second, there was a significant difference in understanding random variables in different/diverse conditions. Namely, the degree of understanding on the continuous random variable was superior to that of discrete random variable and also the degree of understanding on the equal distribution was superior to that of unequality distribution. Third, three types of problems relevant to random variable concept dealt with in this study were finding a sample space and an elementary event, and finding a probability value. In result, the teachers responded to the problem on finding a probability value most correctly and on the contrary to this, they had the mot difficulty in solving the problem on finding a sample space.

• Journal of the Korean earth science society
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• v.24 no.7
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• pp.604-613
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• 2003

The purpose of this study was to investigate the effect of a metastrategic activity on the development of student variable controlling abilities. Three groups of seventh graders at a middle-school in the City of Daegu participated in this study: a metastrategy activity group (ME), a problem-solving activity group (PR), and a control group (CO). The ME group was given metastrategy activity worksheets, which required students to monitor, control, and evaluate variable control strategies in a specified situation. The PR group was given problem-solving activity worksheets, which were needed to solve problems in various situations. The results were seen as follows. First, the metastrategy activity group showed better achievement (p<.05) and a longer standing effect (p<.01) than the other groups in the development of variable control ability. The problem-solving activity group was more effective than the control group (p<.05) in the development of variable controlled ability, but there was no lasting effect of the acquired ability. Second, the metastrategic activity group was more effective than the problem-solving activity group in finding fixed variables (p<.01), but not as effective in uncovering independent variables. What is not transferred to the development of the ability to find dependent variables.

• Journal of The Korean Association For Science Education
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• v.27 no.3
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• pp.263-271
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• 2007

The purpose of this study was to investigate the relationships between the ability of students' raising creative problems and academic achievement, science inquiry skills and creative personality of high school students. In order to evaluate the originality of problems, the present study used three methods: evaluation by frequency, teacher, and student. The results in this study turned out to be as follows: First, there was not much difference in the three methods. But familiar problems had the possibility of receiving higher marks. Second, the ability of students' raising creative problems was significantly correlated with academic achievement and creative personality, but there was no correlation with science inquiry skills. The subjects were divided into 2 groups by students' originality score. In the higher score group, the ability of students' raising creative problems was significantly correlated with creative personality, but in the lower score group, it was significantly correlated with academic achievement. Third, as for science inquiry skills and creative personality between two groups, there was no significant difference, whereas as for academic achievement(physics I, chemistry I), there was significant difference.

• 대한공업교육학회지
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• v.32 no.2
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• pp.23-46
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• 2007

The purpose of this study was to present improvement directions of college scholastic ability test on industry department. Industry department test were classify and abstracted sampling test on contents and movement domain, analyzed example items of college scholastic ability test on industry department. Research methods used in this study were review of related literature, the item analysis and item pattern analysis between college scholastic ability test on introduction to industry and curriculum, contents of textbook. After finding a problem of developing items, trying to find a solution to the problem and developing an up-to-date method of items was to present improvement. Based on the result of the study, some recommendations for future researches were made as follows: First, a phenomenon of making same contents items over again and no making items not on made the items ever have to cut. Second, Time to read and make sense of items have to reduce because depend on the degree of difficulty related on time to understand of items. Third, the depth of textbook contents has to develop on curriculum this year. Fourth, the succeeding study on linkage between college scholastic ability test and simulation of college scholastic ability test. Fifth, verification validity on contents of new movement domain is developed new and striking test items.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.113-139
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• 2013

The purpose of this study is to provide informations about cause of failures when students solve word problems by analyzing what errors students made in solving word problems and types of error and features of error according to problem solving strategy. The results of this study can be summarized as follows: First, $5^{th}$ grade students preferred the expressions, estimate and verify, finding rules in order when solving word problems. But the majority of students couldn't use simplifying. Second, the types of error encountered according to the problem solving strategy on problem based learning are as follows; In the case of 'expression', the most common error when using expression was the error of question understanding. The second most common was the error of concept principle, followed by the error of solving procedure. In 'estimate and verify' strategy, there was a low proportion of errors and students understood estimate and verify well. When students use 'drawing diagram', they made errors because they misunderstood the problems, made mistakes in calculations and in transforming key-words of data into expressions. In 'making table' strategy, there were a lot of errors in question understanding because students misunderstood the relationship between information. Finally, we suggest that problem solving ability can be developed through an analysis of error types according to the problem strategy and a correct teaching about these error types.

• School Mathematics
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• v.14 no.1
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• pp.85-107
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• 2012

Problem solving is important in school mathematics as the means and end of mathematics education. In elementary school, inductive reasoning is closely linked to problem solving. The purpose of this study was to examine ways of improving problem solving ability through analysis of inductive reasoning process. After the process of inductive reasoning in problem solving was analyzed, five different stages of inductive reasoning were selected. It's assumed that the flow of inductive reasoning would begin with stage 0 and then go on to the higher stages step by step, and diverse sorts of additional inductive reasoning flow were selected depending on what students would do in case of finding counter examples to a regulation found by them or to their inference. And then a case study was implemented after four elementary school students who were in their sixth grade were selected in order to check the appropriateness of the stages and flows of inductive reasoning selected in this study, and how to teach inductive reasoning and what to teach to improve problem solving ability in terms of questioning and advising, the creation of student-centered class culture and representation were discussed to map out lesson plans. The conclusion of the study and the implications of the conclusion were as follows: First, a change of teacher roles is required in problem-solving education. Teachers should provide students with a wide variety of problem-solving strategies, serve as facilitators of their thinking and give many chances for them ide splore the given problems on their own. And they should be careful entegieto take considerations on the level of each student's understanding, the changes of their thinking during problem-solving process and their response. Second, elementary schools also should provide more intensive education on justification, and one of the best teaching methods will be by taking generic examples. Third, a student-centered classroom should be created to further the class participation of students and encourage them to explore without any restrictions. Fourth, inductive reasoning should be viewed as a crucial means to boost mathematical creativity.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.