• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.539-564
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• 2011

This study examined how elementary teachers perceive and use "problem-posing" as a way to improve students' problem-solving skills in their mathematics classrooms. In the study, a total of 193 teachers in metropolitan areas were surveyed and a subset of 4 teachers were selected for depth-interviews. Results of the study included that teachers did not have a clear understanding of the study included that teachers did not have a clear understanding of the intended meaning of "problem-posing" although many of them have heard about the idea itself. Therefore, "problem-posing" was not fully utilized in their mathematics instructional and assessment. It is suggested that there is a need to develop instructional materials and related professional development of teachers for better instruction of problem-posing in the mathematics classroom.

• 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.47 no.4
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• pp.421-436
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• 2008

Mathematics assessment doesn't mean examining in the traditional sense of written examination. Mathematics assessment has to give the various information of grade and development of students as well as teaching of teachers. To achieve this purpose of assessment, we have to search the methods of assessment. This paper is aimed to develop the open-ended problems that are the alternative to traditional test, apply them to classroom and analyze the result of assessment. 4-types open-ended problems are developed by criteria of development. It is open process problem, open result problem, problem posing problem, open decision problem. 6 grade elementary students who are picked in 2 schools participated in assessment using open-ended problems. Scoring depends on the fluency, flexibility, originality The result are as follows; The rate of fluency is 2.14, The rate of flexibility is 1.30, and The rate of originality is 0.11 Furthermore, the rate of originality is very low. Problem posing problem is the highest in the flexibility and open result problem is the highest in the flexibility. Between general mathematical problem solving ability and fluency, flexibility have the positive correlation. And Pearson correlational coefficient of between general mathematical problem solving ability and fluency is 0.437 and that of between general mathematical problem solving ability and flexibility is 0.573. So I conclude that open ended problems are useful and effective in mathematics assessment.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.99-110
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• 2005

This paper suggests an efficient approach for stochastic bicriteria programming problem (SBCPP) with random variables in both the objective functions and in the right-hand side of the constraints. The suggested approach uses the statistical inference through two different techniques: In one of them, the SBCPP is transformed into an equivalent deterministic bicriteria programming problem (DBCPP), then the nonnegative weighted sum approach will be used to transform the bicriteria programming problem into a single objective programming problem, and the other technique, the nonnegative weighted sum approach is used to transform the SBCPP to an equivalent stochastic single objective programming problem, then apply the same procedure to convert stochastic single objective programming problem into its equivalent deterministic single objective programming problem (DSOPP). In both techniques the resulting problem can be solved as a nonlinear programming problem to get the efficient solutions. Finally, a comparison between the two different techniques is discussed, and illustrated example is given to demonstrate the actual application of these techniques.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.151-167
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• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U. S. researchers. We examine the approach by illustrating its three aspects: 1) Open process (there is more than one way to arrive at the solution to a problem; 2) Open-ended problems (a problem can have several of many correct answers), and 3) What the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U. S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• 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 Educational Research in Mathematics
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• v.12 no.1
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• pp.71-79
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• 2002

Visualization have strong driving force that enables us to recognize abstract mathematics by direct and specific method in school mathematics. Specially, visual thinking helps in effective problem solution via intuition in mathematics education. So, this paper examines the meaning of visualization, the role of visualization in intuitive problem solving process and the methods for enhancement of intuition using visualization in mathematics education. Visualization is an useful tool for illuminating of intuition in mathematics problem solving. It means that visualization makes us understand easily mathematical concepts, principles and rules in students' cognitive structure. And it makes us experience revelation of anticipatory intuition which finds clues and strategy in problem solving. But, we must know that visualization can have side effect in mathematics learning. So, we have to search for the methods of teaching and learning which can increase students' comprehension about mathematics through visualization and minimize side aspect through visualization.

• 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.

• Research in Mathematical Education
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• v.13 no.2
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• pp.75-90
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• 2009

There are concepts in calculus which are difficult to teach and learn. One of these concepts is integration. However, problem posing has not yet received the attention it deserves from the mathematics education community. There is no systematic study that deals with teaching of calculus concepts by problem posing oriented teaching strategy. In this respect this study investigated the effect of problem posing on students' (prospective teachers') academic success when problem posing oriented approach is used to teach the integral concept in Calculus-II (Mathematics-II) course to first grade prospective teachers who are enrolled to the Primary Science Teaching Program of Education Faculty. The study used intervention-posttest experimental design. Quantitative research techniques were employed to gather, analyze and interpret the data. The sample comprised 79 elementary prospective science teachers. The results indicate that problem posing approach effects academic success in a positive way and at significant level.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.