• The Mathematical Education
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• v.46 no.4
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• pp.503-519
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• 2007

In this study, the instrument of mathematical problem posing ability and mathematical creativity ability tests were considered, and the differences between gifted and regular students in the ability were investigated by the test. The instrument consists of each 10 items and 5 items, and verified its quality due to reliability, validity and discrimination. Participants were 218 regular and 100 gifted students from seventh grade. As a result, not only problem solving but also mathematical creativity and problem posing could be the characteristics of the giftedness.

• The Mathematical Education
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• v.42 no.1
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• pp.57-67
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• 2003

In this paper we analyze educational aspects of a mathematical problem. As a result of the analysis, we extract five meaningful mathematical knowledge and ideas. Corresponding with these we suggest some chains of mathematical problems that are expected to activate student's self-oriented mathematical investigation.

• The Mathematical Education
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• v.42 no.2
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• pp.137-157
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• 2003

Mathematical Problem solving has had the largest focus in the spread of mathematical topics since 1980. In Korea, most of the articles on problem solving appeared 1980s and 1990s, during which there were special concerns on this issue. And there is general acceptance of the idea that the famous statement "Problem solving must be the focus of school mathematics"(NCTM, 1980, p.1) in Agenda for Action, reflected in the curriculum of Korea. In a historical review focusing on the problem solving in the National Curriculum of Mathematics, we can infer that the primary goal of mathematics instruction should be to have students become competence problem solver. However, the practices of mathematics classroom and the trends of research in mathematical problem solving have oriented to ′teaching about problem solving′ and ′teaching for problem solving′. The issue of teaching via problem solving′ remain unsolved in the community of mathematics education and we need much more attention to this issue.

• The Mathematical Education
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• v.57 no.2
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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.

• Research in Mathematical Education
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• v.13 no.3
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• pp.181-195
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• 2009

Students' approaches to mathematical problem solving vary greatly with each other. The main objective of the current study was to compare students' performance with different thinking styles (divergent vs. convergent) and working memory capacity upon mathematical problem solving. A sample of 150 high school girls, ages 15 to 16, was studied based on Hudson's test and Digit Span Backwards test as well as a math exam. The results indicated that the effect of thinking styles and working memory on students' performance in problem solving was significant. Moreover, students with divergent thinking style and high working memory capacity showed higher performance than ones with convergent thinking style. The implications of these results on math teaching and problem solving emphasizes that cognitive predictor variable (Convergent/Divergent) and working memory, in particular could be challenging and a rather distinctive factor for students.

• The Mathematical Education
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• v.57 no.3
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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.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.311-331
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• 2016

The purpose of this study was to analyze mathematical errors and the effects of reflective problem posing activities on students' mathematical problem solving abilities and attitudes toward mathematics. We chose two 5th grade groups (experimental and control groups) to conduct this research. From the results of this study, we obtained the following conclusions. First, reflective problem posing activities are effective in improving students' problem solving abilities. Students could use extended capability of selecting a condition to address the problem to others in the activities. Second, reflective problem posing activities can improve students' mathematical willpower and promotes reflective thinking. Reflective problem posing activities were conducted before and after the six areas of mathematics. Also, we examined students' mathematical attitudes of both the experimental group and the control group about self-confidence, flexibility, willpower, curiosity, mathematical reflection, and mathematical value. In the reflective problem posing group, students showed self check on their problems solving activities and participated in mathematical discussions to communicate with others while participating mathematical problem posing activities. We suggested that reflective problem posing activities should be included in the development of mathematics curriculum and textbooks.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.307-312
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• 1994

The authors have been devoted to researches on fuzzy theories and their applications, especially control theory and application problems, for recent years. In this paper, the authors present results on a comparison of optimal solutions between ones of an ordinary-typed mathematical linear programming problem(O.M.I.P. problem) and ones of a Zimmerman-typed fuzzy mathematical linear programming problem (F.M.L.P. problem), and comment about the sensitivity (differences and fuzziness on between O.M.L.P. problem and F.M.L.P. problem) on optimal solutions of these mathematical linear programming problems.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.2
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• pp.101-124
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• 2008

The purpose of this study is to test if problem posing based on structural approach cooperative learning has a positive effect on mathematical achievement and mathematical disposition. For this purpose, this study carried out tasks as follows: First, we design a problem posing teaching learning program based on structural approach cooperative learning. Second, we analyze how problem posing based on structural approach cooperative learning affects students' mathematical achievement. Third, we analyze how problem posing based on structural approach cooperative learning affects students' mathematical disposition. The results of this study are as follows: First, in the aspect of mathematical achievement, the experimental group who participated in the problem posing program based on structural approach cooperative teaming showed significantly higher improvement in mathematical achievement than the control group. Second, in the aspect of mathematical disposition, the experimental group who participated in the problem posing program based on structural approach cooperative teaming showed positive changes in their mathematical disposition. Summing up the results, through problem posing based on structural approach cooperative learning, students made active efforts to solve problems rather than fearing mathematics and, as a result, their mathematical achievement was improved. Furthermore, through mathematics classes enjoyable with classmates, their mathematical disposition was also changed in a positive way.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.565-586
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• 2005

The purpose of this paper is to analyze the selection difference of mathematical problem solving strategy by mathematical learning style, that is, the intellectual, emotional, and physiological factors of students, to allow teachers to instruct the mathematical problem solving strategy most pertinent to the student personality, and ultimately to contribute to enhance mathematical problem solving ability of the students. The conclusion of the study is the followings: (1) Students who studies with autonomous, steady, or understanding-centered effort was able to solve problems with more strategies respectively than the students who did not; (2) Student who studies autonomously or reconfirms one's learning was able to select more proper strategy and to explain the strategy respectively than the students who did not; and (3) The differences of the preference to the strategy are variable, and more than half of the students were likely to select frequently the strategy 'to use a formula or a principle' regardless of the learning style.