• Communications of Mathematical Education
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• v.13 no.1
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• pp.305-316
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• 2002

벡터는 수학 문제해결을 위한 중요한 도구로써, 벡터를 이용한 문제해결 과정에서 학생들은 수학적 탐구 활동에 관련된 풍부한 경험을 가질 수 있다. 본 연구에서는 벡터를 이용하여 삼각형의 무게중심에 관한 정리를 증명하기 위한 수학적 탐구 능력이나 아이디어를 학생들이 준비할 수 있도록 정리 증명과 관련된 몇몇 문제들을 체계화하여 제시하였다. 이 문제들을 해결하는 과정에 관련된 탐구 능력을 추출하였으며, 체계화된 문제에 바탕을 둔 무게중심에 관한 정리 증명을 제시하였고, 증명 과정과 관련된 수학적 탐구 능력을 제시하였다.

• Communications of Mathematical Education
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• v.18 no.3 s.20
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• pp.81-94
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• 2004

수학적 창의성의 개념을 과정적 정의로서 창의적 문제해결력으로 규정하여 수학적 영재의 판별을 문제 발견의 창의성과 문제해결의 창의성으로 나누고 각각에 대한 판별검사 도구에 대하여 논의하였다.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.389-407
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• 2005

수학은 위계적이고 구조적인 특성을 가지고 있어서 학생들이 적절하게 학습하면 내적 동기유발이 가능하고 흥미 있게 학습해 나갈 수 있는 반면 단편적인 지식들로 학습하려 한다면 그 양이 방대해지고 제대로 이해하기가 어렵다. 그러므로 교사는 수학적 지식의 구조를 깨달아 지식의 본체가 내적으로 어떻게 조직되고 상호 관련되어 있는지 알아야 하고 학생들이 수학적인 아이디어와 절차를 획득하고 탐구하게 하는 적절한 문제를 제시하여 문제해결을 통해 가르쳐 가는 방법을 생각해야 할 것이다. 이 때에 학생들은 문제해결 과정에서 능동적인 역할을 하면서 자신이 학습하고 있는 것의 핵심을 인식하고 호기심을 갖고 유의미한 기능들을 이끌어내는 학습을 해야 하는데, 이는 오랜 전통의 탐구 학습과 그 맥락을 같이 하는 것이다. 수학교과 고유의 특성을 살려 지식의 구조를 가르침에 있어서 교수 방법으로의 문제해결을 통한 지도와 학습 방법으로의 탐구학습 과정은 잘 조화될 수 있다. 이러한 조화된 모습을 드러나게 하고자 초등학교 5학년 가 단계에서 '평면도형의 넓이와 둘레 사이의 관계'를 탐구하게 하는 문제해결을 통한 탐구학습 과제를 제시해 보았다. 30-40년을 거슬러 올라가는 역사를 갖는 지식의 구조나 탐구학습, 문제해결에 대한 관심은 오늘날에도 여전히 시사하는 바가 크다고 하겠다. 수학교육에 관한 연구들은 완전히 새로운 것이기보다는 이전의 것들이 주는 의미를 되새기고 오늘의 상황에 비추어 해석할 때 수학교육은 한 단계 올라서게 된다.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2009.05a
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• pp.101-106
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• 2009

수학적 사고의 입장에서 중등학생들이 수학적 문제해결에 논리적 사고와 직관적 사고가 어떻게 작용하는지를 연구하는 것은 수학교육에서 중요하고도 흥미로운 과제의 하나이다. 본 연구의 주된 목적은 중등학교 영재학생을 대상으로 이러한 문제를 조사하는 것이다. 특히 이들 중등영재학생들의 논리적 사고와 직관적 사고에 대한 선호도와 논리적 문제의 문제해결능력 사이의 관계를 조사한다.

• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.295-311
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• 2011

The importance of problem solving in mathematics education has been emphasized and many studies related to this issue have been conducted. But, studies of problem solving in the aspect of affect domain are lacked. This study found the changing pattern of emotions that occur in process of a problem solving. The results are listed below. First, students experienced a lot of change of emotions and had a positive emotion as well as negative emotion during solving problems. Second, students who solved same problems through same methods experienced different change patterns of emotions. The reason is that students have different mathematical beliefs and think differently about a difficulty level of problem. Third, whether students solved problems with positive emotion or negative emotion depends on their attitude of mathematics. Fourth, students who thought that a difficulty level of problem was relatively high experienced more negative affect than students who think a difficulty level of problem is low experienced.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.277-293
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• 2021

The purpose of this study was to find out how problem solving learning with open-ended mathematics problems for elementary school students affects their mathematical creativity and mathematical attitudes. To this end, 9 problem solving lessons with open-ended mathematics problems were conducted for 6th grade elementary school students in Seoul, The results were analyzed by using I-STATistics program to pre-and post- t-test. As a result of the study, problem solving learning with open-ended problems was effective in increasing mathematical creativity, especially in increasing flexibility and originality, which are sub-elements of creativity. In addition, problem solving learning with open-ended problems has helped improve mathematical attitudes and has been particularly effective in improving recognition needs and motivation among subfactors. In problem solving learning with open-ended problems, students were able to share various responses and expand their thoughts. Based on the results of the study, the researchers proposed that it is necessary to continue the development of quality materials and teacher training to utilize mathematical problem solving with open-ended problems at school sites.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.2
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• pp.311-331
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• 2016

The purpose of this study was to analyze mathematical errors and the effects of reflective problem posing activities on students' mathematical problem solving abilities and attitudes toward mathematics. We chose two 5th grade groups (experimental and control groups) to conduct this research. From the results of this study, we obtained the following conclusions. First, reflective problem posing activities are effective in improving students' problem solving abilities. Students could use extended capability of selecting a condition to address the problem to others in the activities. Second, reflective problem posing activities can improve students' mathematical willpower and promotes reflective thinking. Reflective problem posing activities were conducted before and after the six areas of mathematics. Also, we examined students' mathematical attitudes of both the experimental group and the control group about self-confidence, flexibility, willpower, curiosity, mathematical reflection, and mathematical value. In the reflective problem posing group, students showed self check on their problems solving activities and participated in mathematical discussions to communicate with others while participating mathematical problem posing activities. We suggested that reflective problem posing activities should be included in the development of mathematics curriculum and textbooks.

• Journal of the Korean School Mathematics Society
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• v.22 no.3
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• pp.329-350
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• 2019

Productive struggle is a student's persevering effort to understand mathematical concepts and solve challenging problems that are not easily solved, but the problem can lead to curiosity. Productive struggle is a key component of students' learning mathematics with a conceptual understanding, and supporting it in learning mathematics is one of the most effective mathematics teaching practices. In comparison to research on students' productive struggles, there is little research on preservice mathematics teachers' productive struggles. Thus, this study focused on the productive struggles that preservice mathematics teachers face in solving a non-routine mathematics problem. Polya's four-step problem-solving process was used to analyze the collected data. Examples of preservice teachers' productive struggles were analyzed in terms of each stage of the problem-solving process. The analysis showed that limited prior knowledge of the preservice teachers caused productive struggle in the stages of understanding, planning, and carrying out, and it had a significant influence on the problem-solving process overall. Moreover, preservice teachers' experiences of the pleasure of learning by going through productive struggle in solving problems encouraged them to support the use of productive struggle for effective mathematics learning for students, in the future. Therefore, the study's results are expected to help preservice teachers develop their professional expertise by taking the opportunity to engage in learning mathematics through productive struggle.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.583-605
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• 2016

Problem solving has been consistently emphasized in national mathematics curricula, whereas the foci of such an emphasis have been changed. Given this background, this study traced down major changes in emphasizing problem solving from the first national mathematics curriculum to the most recent 2015 curriculum. In particular, both the 2009 and the 2015 revised curricula were analyzed in detail to figure out the latest emphasis and trends. This paper then investigated whether a series of mathematics textbooks were aligned to the emphases of recent curricula. It finally discussed some issues that we need to reconsider with regards to problems, problem solving strategies, and the process of problem solving. As such, this study is expected to provide textbook developers with detailed implications on how to employ problem solving in new series of textbooks.

• Communications of Mathematical Education
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• v.11
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• pp.201-233
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• 2001

보통 문장제(일량, 거리, 속도 문제, 시계 문제, 농도 문제, 개수 세기, 측도 영역)는 초등학교부터 반복하며 나오며 대학 수학 능력 시험에서는 외적 문제 해결능력으로 측정되기도 한다. 문장제를 해결하는데는 사고가 여러 단계로 이루어져야 한다. 따라서 일반적으로 문장제는 난해하므로, 조직적이고 전문적인 학습지도가 이루어져야 한다. 하지만 입시위주의 교육 등 여러 여건상 잘 이루어지지 않고 있는 것이 현실이다. 본 연구에서는 문장제의 문제 해결에 필요한 해결요소를 발견하고 저해 요인을 없앨 수 있는 지도 방안으로서 소집단 토의학습에 문제해결 전략을 이용하여, 효율적인 문장제 지도 방안을 연구하고 상이한 문제에 접근하는 방법, 문제를 이용하는 방법 등을 토의학습을 통하여 다양한 풀이방법을 해결하면서 이를 통하여 사고력을 신장할 수 있도록 연구한다.