• School Mathematics
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• v.3 no.2
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• pp.295-324
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• 2001

Until now, There have been few studies to investigate a degree of abilities or interesting about mathematical problem-posing of first and second grades in elementary school. This is due to the fact that this students(1st and 2nd grades) have a limited amount of study time and their minds are not fully developed, and are lacking in their representation of ability to use the national language. This being the case, it is difficult to investigate their Mathematical problem-posing in a practical manner. However, our 7th elementary school Mathematics curriculum emphasizes the teaching and learning of Mathematical problem-posing from a basic level of first and second grade with emphasis on activity in teaming Mathematics. Through this study, having analysed the problems those children posed, I have found out they improved in numbers and correctness of their posed problems. And I too could found out showing to their much interesting and confidence to mathematical problem-posing and could confirmed for the children to admit themselves its merits through analyzing some questions to ask their opinions to it. I expect that this study can help to develop the teaching and learning materials for mathematical problem-posing and also to improve its methods of elementary school mathematics. The next study task is, I think, that it is necessary to accumulate the studies to investigate and analyse the practical learning activities of children for problem-posing contents of mathematics text books.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.243-262
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• 2017

This study has its purpose on improving mathematic education by analyzing the effects of the teaching and learning process which adopted 'FOCUS Problem Solving Steps' on student's mathematical problem solving ability and their mathematical attitude. The result is as follows. First, activities through FOCUS Problem Solving Steps showed positive effect on students' problem solving ability. Second, among mathematical attitudes, mathematical curiosity, reflection and value are proved to have statistically meaningful effect and from the result that analyzed changes of subject students, we could suppose that all 6 elements of mathematical attitude had positive effect. Third, by solving questions through FOCUS steps, students felt satisfaction when they success by themselves. If projects which adopted FOCUS Problem Solving Steps take effect continuously by happiness from the process of reviewing and reflecting their own fallacy and solving that, we might expect meaningful effect on students' problem solving ability. Through this study, FOCUS Problem Solving Steps had positive effect not only on students' mathematical problem solving ability but also on formation of mathematical attitude. As a result, it implies that FOCUS Problem Solving Steps need to be applied to other grades and fields and then studied more.

• School Mathematics
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• v.7 no.3
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• pp.303-318
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• 2005

If students can use mathematics to solve their problems and learn the mathematical knowledge through it, they may think mathematics useful and valuable. This study is for the teaching through problem solving in mathematics education, which I consider in terms of the problem-based learning and mathematical modeling. 1 think mathematical modeling is applied to teaching mathematics as a problem-based learning. So I developed the teaching model, and showed the example that students learn the formal and hierarchic mathematics through mathematical modeling.

• East Asian mathematical journal
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• v.35 no.4
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• pp.407-427
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• 2019

The six core competencies included in the mathematics curriculum revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the problem solving is very important for students' enhancing much higher mathematical thinking. Based on this competency, this study selected the four elements of the problem solving such as problem solving process, cooperative problem solving, mathematical modeling, problem posing. And also this study selected the domain of function which is comprised of the content of the coordinate plane, the graph, proportionality in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the four elements of the problem solving competency were shown in each textbook.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.507-516
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• 2000

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.249-265
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• 2017

Interface problem here refers to a second order elliptic problem with a discontinuous coefficient for the second order derivatives. For the corresponding boundary value problem, the maximum principle still holds but Hopf's boundary point lemma may fail. We will give an optimal power type estimate that replaces Hopf's lemma at those boundary points, where this coefficient jumps.

• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.267-283
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• 2013

Mathematical justification is the process through which one's claim is validated to be true based on proper and trustworthy data. But it serves as a catalyst to facilitate mathematical discussions and communicative interactions among students in mathematics classrooms. This study is designed to investigate the effects of mathematical justification on students' problem-solving and communicative processes occurred in a mathematics classroom. In order to fulfill the purpose of this study, mathematical problem-solving classes were conducted. Mathematical justification processes and communicative interactions recorded in problem understanding activity, individual student inquiry, small and whole group discussions are analyzed. Based on the analysis outcomes, the students who participated in mathematical justification activities are more likely to find out various problem-solving strategies, to develop efficient communicative skills, and to use effective representations. In addition, mathematical justification can be used as an evaluation method to test a student's mathematical understanding as well as a teaching method to help develop constructive social interactions and positive classroom atmosphere among students. The results of this study would contribute to strengthening a body of research studying the importance of teaching students mathematical justification in mathematics classrooms.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.545-562
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• 2009

This study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using "Protocol Analysis Method"and "Problem Behavior Graph" which is suggested by Newell and Simon as a qualitative analysis. In this study, four middle school students with high achievement in math were selected as subjects-two students for mathematical gifted group and the other two for control group also with high scores in math. The thinking characteristics of the four subjects, shown in the course of solving problems, were elicited, analyzed and compared, through the use of the creative test questionnaires which were supposed to clearly reveal the characteristics of mathematical gifted students' thinking processes. The results showed that there were several differences between the two groups-the mathematical gifted student group and their control group in their mathematical talents. From these case studies, we could say that it is significant to find out the characteristics of mathematical thinking processes of the mathematical gifted students in a more scientific way, in the sense that this result can be very useful to provide them with the chances to get more proper education by making clear the nature of thinking processes of the mathematical gifted students.