• 한국수학사학회지
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• 제32권6호
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• pp.281-299
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• 2019

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제7권1호
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• pp.1-14
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• 2003

The purpose of this research is to explore teachers' role actions in teaching mathematical problem solving and to analyze the influences of the teachers'role actions on their students' activities and beliefs about problem solving. The results obtained in this study suggested that the teachers' role actions brought qualitative differences to students' activities, and students' beliefs about mathematical problem solving were consistent with the perspective held by their teachers. Therefore, teachers should help students build up desirable beliefs about problem solving. They should understand teaching mathematical problem solving and play proper roles in various situations of teaching mathematical problem solving.

• 아동학회지
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• 제28권4호
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• pp.319-331
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• 2007

This review of literature establishes a contemporary meaning of mathematical problem solving including young children's mathematical problem solving processes/assessments and teaching strategies. The contemporary meaning of mathematical problem solving involves complicated higher thinking processes. Explanations of the mathematical problem solving processes of young children include the four steps suggested by $P{\acute{o}}lya$(1957) : understand the problem, devise a plan, carry out the plan, and review/extend the plan. Assessments of children's mathematical problem solving include both the process and the product of problem solving. Teaching strategies to support children's mathematical problem solving include mathematical problems built upon children's daily activities, interests, and questions and helping children to generate new approaches to solve problems.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권2호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제26권2호
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• pp.9-13
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• 1988

Mathematics education is generally to cultivate mathematical thought. Most meaningful thought is to solve a certain given situation, that is, a problem. The aim of mathematies education could be identified with the cultivation of mathematical problem-solving ability. To cultivate mathematical problem-solving ability, it is necessary to study the nature of mathematical ability and its aspects pertaining to problem-solving ability. The purpose of this study is to investigate the relation between problem-solving ability and classficational viewpoint of mathematical verbal problems, and bet ween the detailed abilities of problem-solving procedure and classificational viewpoint of mathematical verbal problems. With the intention of doing this work, two tests were given to the third-year students of middle school, one is problem-solving test and the other classificational viewpoint test. The results of these two tests are follow ing. 1. The detailed abilities of problem-solving procedure are correlated with each other: such as ability of understanding, execution and looking-back. 2. From the viewpoint of structure and context, students classified mathematical verbal problems. 3. The students who are proficient at problem-solving, understanding, execution, and looking-back have a tendency to classify mathematical verbal problems from a structural viewpoint, while the students who are not proficient at the above four abilities have a tendency to classify mathematical verbal problems from a contextual viewpoint. As the above results, following conclusions can be made. 1. The students have recognized at least two fundamental dimensions of structure and context when they classified mathematical verbal problems. 2. The abilities of understanding, execution, and looking- back effect problem-solving ability correlating with each other. 3. The instruction emphasizing the importance of the structure of mathematical problems could be one of the methods cultivating student's problem-solving ability.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권2호
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• pp.169-180
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• 2008

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

• East Asian mathematical journal
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• 제33권4호
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• pp.381-411
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• 2017

The purpose of this study is to investigate how students' mathematical creativity changes through problem-solving instruction using problem-posing for elementary school students and to explore instructional methods to improve students' mathematical creativity in school curriculum. In this study, nonequivalent control group design was adopted, and the followings are main results. First, problem-solving lessons with problem-posing had a significant effect on students' mathematical creativity, and all three factors of mathematical creativity(fluency, flexibility, originality) were also significant. Second, the lessons showed meaningful results for all upper, middle, and lower groups of pupils according to the level of mathematical creativity. When analyzing the effects of sub-factors of mathematical creativity, there was no significant effect on fluency in the upper and middle groups. Based on the results, we suggest followings: First, there is a need for a systematic guidance plan that combines problem-solving and problem-posing, Second, a long-term lesson plan to help students cultivate novel mathematical problem-solving ability through insights. Third, research on teaching and learning methods that can improve mathematical creativity even for students with relatively high mathematical creativity is necessary. Lastly, various student-centered activities in math classes are important to enhance creativity.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권3호
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• pp.361-374
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• 2005

I analyzed the effect of problem posing teaching and teacher-centered teaching on mathematical problem-solving ability and creativity in order to know the efffct of problem posing teaching on mathematics study. After we gave problem posing lessons to the 3rd grade middle school students far 28 weeks, the evaluation result of problem solving ability test and creativity test is as fellows. First, problem posing teaching proved to be more effective in developing problem-solving ability than existing teacher-centered teaching. Second, problem posing teaching proved to be more effective than teacher-centered teaching in developing mathematical creativity, especially fluency and flexibility among the subordinate factors of mathematical creativity. Thus, 1 suggest the introduction of problem posing teaching activity for the development of problem-solving ability and mathematical creativity.

• 대한수학교육학회지:학교수학
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• 제11권4호
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• pp.665-683
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• 2009

본 연구는 문제해결력을 증진시키기 위한 방안으로 상황을 제시한 후 W(상황표현하기)-Q(문제 만들기)-A(답하기)에 의한 단계별 활동을 하여 그 효과성을 알아보았다. 이 방법을 2학년에게 한 학기동안 20차시를 적용한 결과 문제해결력은 향상된 것으로 나타났고, 태도에서는 융통성은 향상되었고 나머지 영역은 유의미한 차이는 없었지만 전반적으로 평균이 높아진 것을 확인할 수 있었다. 따라서 WQA 문제만들기 활동은 아동의 문제해결력을 증진시키고 태도를 개선하는 좋은 방법임을 알 수 있었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권2호
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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.