• 한국수학교육학회지시리즈A:수학교육
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• 제48권2호
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• pp.149-167
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• 2009

This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

• 대한공업교육학회지
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• 제30권1호
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• pp.37-45
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• 2005

The purpose of this study is to find out the relationship between the Multiple Intelligence and the technological problem solving and the differences between the two. There were a group of 200 third grade middle school students that were comprised of 100 boys and 100 girls and what the difference is exited between the boys and the girls. To measure the students' Multiple Intelligence, MI(Multiple Intelligent)Test designed by Youngrin, Moon was used. As the testing instrument of the Technological problem Solving, we use the test developed by National Center for Research on Evaluation, Standards, and Students Testing(CRESST). The results were; First, In comparison with the boys and girls' multiple intelligence part, there were individual differences in musical intelligence, bodily-kinesthetic intelligence, logical-mathematical intelligence, and naturalistic intelligence of multiple intelligence. Second, In comparison to the technological problem solving part, there were individual differences in self-regulation and there was a mild difference in understanding of the contents. Third, The multiple intelligence related with the self-regulation is continuous with logical-mathematical intelligence, intra-personal intelligence and linguistic intelligence. Fourth, The multiple intelligence related with the technological problem solving strategy is continuous with logical-mathematical intelligence and musical intelligence. Fifth, The multiple intelligence related with the understanding of the contents is continuous with the logical-mathematical intelligence and naturalistic intelligence. To improve the students' technological problem solving ability, it is required the development of the curriculum which focus on the improvement of logical-mathematical intelligence, musical intelligence, intra-personal intelligence, linguistic intelligence and naturalistic intelligence of the students.

• 한국수학교육학회지시리즈A:수학교육
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• 제48권2호
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• pp.141-148
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• 2009

The article discusses roles of analysis in problem solving, especially the problem posing. The author shows the procedure of analysis like the presentation of the hypothesis, the reasoning for the necessary conditions and the sufficient condition. Finally the author suggests that the analysis should be reviewed in the school mathematics.

• East Asian mathematical journal
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• 제34권4호
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• pp.429-449
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• 2018

The purpose of this study is to investigate how the mathematical creativity of middle school mathematical gifted students is represented through the process of problem posing activities. For this goal, they were asked to pose real-world problems similar to the tasks which had been solved together in advance. This study demonstrated that just 2 of 15 pupils showed mathematical giftedness as well as mathematical creativity. And selecting mathematically creative and gifted pupils through creative problem-solving test consisting of problem solving tasks should be conducted very carefully to prevent missing excellent candidates. A couple of pupils who have been exerting their efforts in getting private tutoring seemed not overcoming algorithmic fixation and showed negative attitude in finding new problems and divergent approaches or solutions, though they showed excellence in solving typical mathematics problems. Thus, we conclude that it is necessary to incorporate problem posing tasks as well as multiple solution tasks into both screening process of gifted pupils and mathematics gifted classes for effective assessing and fostering mathematical creativity.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권4호
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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.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제25권2호
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• pp.451-472
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• 2011

수학의 다양한 영역들 사이의 연결성은 수학 자체의 발달 과정 뿐만 아니라, 학생들의 수학 학습에서도 중요한 역할을 한다. 본 연구에서는 수학 문제에 포함된 대수식의 기하학적 해석을 통해 새로운 문제해결 방법을 탐구하였다. 특히 수학 문제해결에서 기하학적 접근에 대해 고찰하였고, 고등학교 수준의 비정형적인 문제들을 기하학적 해석을 통해 해결하며, 이에 관련된 문제해결의 특정들을 분석하였다. 본 연구에서 제시하는 자료들은 고등학교의 교수-학습 과정에서 직접 활용될 수 있을 것이다.

• East Asian mathematical journal
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• 제26권4호
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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.

• 한국수학사학회지
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• 제22권3호
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• pp.113-130
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• 2009

수학 문제해결 교육에 가장 많은 영향을 끼친 것은 폴리아(G. Polya)의 이론이다. 폴리아가 제시하는 발견술은 수학 문제해결 과정을 명시적으로 세분화여 드러내고 정리한 것이다. 이와는 달리, 수학 문제해결 과정의 암묵적 차원을 강조하고 있는 폴라니(M. Polanyi)의 이론은 폴리아의 이론과 상보적 관계에 있는 것으로 조명될 필요가 있다. 이 글에서는 폴라니의 인식론을 개관하고, 이를 바탕으로 하는 그의 문제해결 교육 이론을 고찰한다. 지식과 앎을 개인의 마음의 총체적 작용으로 보는 폴라니는 문제해결에 있어서 지적, 정서적 부분과 함께 헌신과 몰두를 강조한다. 또한 명시적 앎 이면에 있는 묵식에 있어서 교사의 역할을 중시한다. 이와 같은 폴라니의 관점은 현재 우리나라 학생들의 수학 문제 해결 양상을 이해하고 문제점을 파악하는 데에도 의미 있는 시사를 제공한다.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권4호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권1호
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• pp.123-134
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• 2007

In the article, representations useful in mathematics education are introduced and show how they are related in the context of mathematics education. They are classified in three categories: representations in mind, representations for understanding and problem solving, and mathematical representations.