• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.291-305
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• 2009

The purpose of this article is to formulate the base that mathematical thinking power can be improved through activating the metacognitive ability of students in the math problem solving process. The guidance material for activating the metacognitive ability was devised based on a body of literature and various studies. Two high school students used it in their math problem solving process. They reported that their own mathematical thinking power was improved in this process. And they showed that the necessary strategies and procedures for math problem solving can be monitored and controled by analyzing their own metacognition in the mathematical thinking process. This result suggests that students' metacognition does play an important role in the mathematical thinking process.

• 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.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.21-45
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• 2011

It is the aim of this paper to find the requisites for the target problem solving process in reference to the base problem and to search the roles of those. Focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process, we tried to find the roles of them. We observed closely how four students solve the target problem in reference to the base problem. And so we got the following conclusions. The insight of structural similarity prepare the ground appling the solving method of base problem in the process solving the target problem. And we knew that the analytic activity can become the instrument which find out the truth about the guess. Finally the comparative activity can set up the direction of solution of the target problem. Thus we knew that the insight of structural similarity, the analytic activity and the comparative activity are necessary for similar mathematical problem to solve. We think that it requires the efforts to develop the various programs about teaching-learning method focusing on the structural similarity, analytic activity and comparative activity in stage of similar mathematical problem solving process. And we also think that it needs the study to research the roles of other elements for similar mathematical problem solving but to find the roles of the structural similarity, analytic activity and comparative activity.

• 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.

• Education of Primary School Mathematics
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• v.12 no.1
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• pp.1-20
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• 2009

The purposes of this study are to analyze elementary school student's intuitive thinking in the process of mathematical problem solving and to analyze elementary school student's errors of intuitive thinking in the process of mathematical problem solving. According to these purposes, the research questions can be set up as followings. (1) How is the state of illumination of the elementary school student's intuitive thinking in the process of mathematical problem solving? (2) What are origins of errors by elementary school student's intuitive thinking in the process of mathematical problem solving? In this study, Bogdan & Biklen's qualitative research method were used. The subjects in this study were 4 students who were attending the elementary school. The data in this study were 'Intuitine Thinking Test', records of observation and interview. In the interview, the discourses were recorded by sound and video recording. These were later transcribed and analyzed in detail. The findings of this study were as follows: First, If Elementary school student Knows the algorithm of problem, they rely on solving by algorithm rather than solving by intuitive thinking. Second, their problem solving ability by intuitive model are low. What is more they solve the problem by Intuitive model, their Self- Evidence is low. Third, in the process of solving the problem, intuitive thinking can complement logical thinking. Last, in the concept of probability and problem of probability, they are led into cognitive conflict cause of subjective interpretation.

• 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.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.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.285-301
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• 2013

The purpose of the study is to analyze the 4th graders' visual representation in mathematics problem solving process and to find out how to teach the visual representation in mathematics problem solving process. on the basis of the results, this study gives several pedagogical implication related to the mathematics problem solving. The following were the conclusions drawn from the results obtained in this study. First, The achievement level of students and using visual representation in the mathematics problem solving are closely connected. High achieving students used visual representation in the mathematics problem solving process more frequently. Second, high achieving students realize the usefulness of visual representation in the mathematics problem solving process and use visual representation to solve mathematical problem. But low achieving students have no conception that visual representation is one of the method to solve mathematical problem. Third, students tend to especially focus on 'setting up an equation' when they solve a mathematical problem. Because they mostly experienced mathematical problems presented by the type of 'word problem-equation-answer'. Fourth even through students tried visual representation to solve a mathematical problem, they could not solve the problem successfully in numerous instances. Because students who face a difficulty in solving a problem try to construct perfect drawing immediately. But generating visual representation 2)to represent mathematical problem cannot be constructed at one swoop.

• East Asian mathematical journal
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• v.26 no.4
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• pp.553-579
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• 2010

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

• School Mathematics
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• v.11 no.4
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• pp.665-683
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• 2009

The purpose of this study is to improve forward mathematics study by analyzing the effects of the teaching and learning process applied situation-based mathematical problem posing activity on problem solving ability and mathematical attitudes. For this purpose, the research questions were established as follows: 1. How the situation-based mathematical problem posing activity(WQA activity) changes the problem solving ability of students? 2. How the situation-based mathematical problem posing activity(WQA activity) changes the mathematical attitudes of students? The results of the study were as follows: (1) There was significant difference between experimental group and comparative group in problem solving ability. This means that situation-based mathematical problem posing activity was generally more effective in improving problem solving ability than general classroom-based instruction. (2) There was not significant difference between experimental group and comparative group in mathematical attitudes. But the experimental group's average scores of mathematical attitudes except mathematical confidence was higher than comparative group's ones. And there was significant difference in the mathematical adaptability. The results obtained in this study suggest that the situation-based mathematical problem posing activity can be used to improve the students' problem solving ability and mathematical attitudes