• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.167-189
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• 2005

본고에서는 영재교육에서 실제 학습자료의 부족과 이산수학의 중요성이 부각되고 있는 최근의 동향을 감안하여, 초등학교 영재교육에 적용 가능한 이산수학 프로그램을 개발하고자 한다. 우선 프로그램의 개발에 선행하여 관련 이론에 대한 고찰을 하였으며 제 7차 초등학교 수학과 교육과정의 이산수학 관련 내용을 분석하석 교육과정의 내용을 심화 ${\cdot}$ 발전할 수 있는 방안에 초점을 두었다. 특히 이산수학과 관련된 기존의 수학학습 프로그램들은 대부분 순수 수학적 이론을 제시하고 그에 따른 문제를 풀어보는 형식으로 구성되어 있는데, 본고에서는 이산수학의 이론을 중심으로, 문제해결에서 알고리즘적으로 사고하는 능력을 키울 수 있도록 하는 것에 초점을 두어 프로그램을 개발하고자 한다. 즉, 프로그램 자체가 하나의 수학적 원리를 탐구해 가는 과정이 되는 것이다. 또한 이산수학이 수학적 문제해결 학습과 연관됨에 착안하여 프로그램은 Polya의 문제해결학습을 바탕으로 구성하고자 한다.

• Education of Primary School Mathematics
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• v.17 no.2
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• pp.95-111
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• 2014

The purpose of this study is to determine the relationship between metacognition and math creative problem solving ability. Specific research questions set up according to the purpose of this study are as follows. First, what relation does metacognition has with creative math problem-solving ability of mathematically gifted elementary students? Second, how does each component of metacognition (i.e. metacognitive knowledge, metacognitive regulation, metacognitive experiences) influences the math creative problem solving ability of mathematically gifted elementary students? The present study was conducted with a total of 80 fifth grade mathematically gifted elementary students. For assessment tools, the study used the Math Creative Problem Solving Ability Test and the Metacognition Test. Analyses of collected data involved descriptive statistics, computation of Pearson's product moment correlation coefficient, and multiple regression analysis by using the SPSS Statistics 20. The findings from the study were as follows. First, a great deal of variability between individuals was found in math creative problem solving ability and metacognition even within the group of mathematically gifted elementary students. Second, significant correlation was found between math creative problem solving ability and metacognition. Third, according to multiple regression analysis of math creative problem solving ability by component of metacognition, it was found that metacognitive knowledge is the metacognitive component that relatively has the greatest effect on overall math creative problem-solving ability. Fourth, results indicated that metacognitive knowledge has the greatest effect on fluency and originality among subelements of math creative problem solving ability, while metacognitive regulation has the greatest effect on flexibility. It was found that metacognitive experiences relatively has little effect on math creative problem solving ability. This findings suggests the possibility of metacognitive approach in math gifted curricula and programs for cultivating mathematically gifted students' math creative problem-solving ability.

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.193-204
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• 2017

The purpose of the study was to investigate and develop a practical approach to integrating student-driven mathematical problems posing in mathematics instruction. A problem posing activity was performed during regular mathematics instruction. A total of 540 mathematical problems generated by students were recorded and analysed using systemic procedures and criteria. Of the problems, 81% were mathematically solvable problem and 18% were classified as error type problems. The Mathematically solvable problem were analysed and categorized according to the complexity level; 13% were of a high-level, 30% mid-level and 57% low-level. The error-type problem were classified as such within three categories: non-mathematical problem, statement or mathematically unsolvable problem. The error-type problem category was distributed variously according to the leaning theme and accomplishment level. The study has important implications in that it used systemic procedures and criteria to analyse problem generated by students and provided the way for integrating mathematical instruction and problem posing activity.

• 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.

• Communications of Mathematical Education
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• v.8
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• pp.137-150
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• 1999

본 연구의 목적은 아동들의 수학 교과에 대한 정의적 특성과 수학적 문제 해결력, 추론 능력간의 상호 관계를 구명하고, 이러한 관계들은 아동의 지역적인 환경에 따라 차이가 있는지를 분석하는 것이다. 본 연구를 통하여 얻은 결론은 다음과 같다. 정의적 특성의 하위 요인 중 수학적 문제 해결력과 귀납적 추론 능력에 대한 설명력이 가장 높은 요인은 수학교과에 대한 자아개념인 것으로 나타났으며, 연역적 추론 능력에 대한 설명력은 학습 습관이 가장 높은 것으로 나타났다. _그리고 귀납적 추론 능력이 연역적 추론 능력 보다 수학적 문제 해결력에 대한 설명력이 더 높은 것으로 나타났으며, 수학적 문제 해결력과 귀납적 추론 능력은 지역별로 유의한 차가 나타났으나 연역적 추론 능력은 지역간 유의한 차이가 나타나지 않았다.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.351-374
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• 2018

The purpose of this study is to support the understandings of teachers about the instructional strategies of collaborative problem solving and mathematical modeling as presented in the 2015 revised mathematics curriculum. For this, tasks of the Cubes unit from six grader's and lesson plans were developed. The specific problem solving processes of students and the practices of teachers which appeared in the classes were analyzed. In the course of solving a series of problems, students have formed a mathematical model of their own, modifying and complementing models in the process of sharing solutions. In particular, it was more effective when teachers explicitly taught students how to share and discuss problem-solving. Based on these results this study is expected to suggest implications on how to foster students' problem solving ability as mathematical subject competency in elementary classrooms.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.131-154
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• 2014

The purpose of this study was to examine the effect of essay writing-centered mathematics instruction on problem solving and mathematical deposition in the elementary school. For the present study, two 6th grade classes with equivalent achievement in terms of problem solving and mathematical disposition based on the pretest. A total of 15 mathematics lessons focused on writing activities were administered to the experiment group for two months, while the textbook-based traditional lessons were given to the comparison group. Both quantitative and qualitative methods were adopted to analyze the data. The results of the present study showed that essay writing-centered mathematics teaching is statistically superior that the textbook-based mathematics teaching with respect to students' problem solving and mathematical disposition. In addition, it was evidenced that essay writing-centered mathematics instruction makes an influence on students' perceptions toward essay-based assessment in a positive way.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.175-196
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• 2009

In this paper we analyze Ziv's geometrical differentiated teaching and learning materials using inner structure of mathematics problems. In order to analyze inner structure of mathematics problems we in detail describe problem solving process, and extract main frame from problem solving process. We represent inner structure of mathematics problems as tree including induced relations. As a result, we characterize low-level problems and middle-level problems, and find some differences between low-level problems and middle-level problems.

• Proceedings of the Korean Society of Computer Information Conference
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• 2011.01a
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• pp.159-162
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• 2011

이 연구는 인지기제를 활용한 문제기반학습이 학습자의 학업성취도와 수학적 태도에 미치는 효과를 분석하였다. 우선 초등학교 수학과 학습에서 학습자들의 인지과정을 안내할 수 있는 문제기반학습 설계를 위해 문제기반학습 모형에 란다(N. Landa)의 인지기제 교수학습설계이론을 적용하여 인지기제 활용 문제기반학습 모형을 도출하였다. 그리고 초등학교 수학과 4학년 2학기 4개 단원의 8차시를 추출하여 문제를 개발하고 서울시 소재 'ㅈ' 초등학교 4학년 학생들 중 동질집단으로 확인된 2개 학급에 이 모형을 적용하였다. 연구 결과 인지기제 활용 문제기반학습을 적용한 실험집단과 적용하지 않은 통제집단 간 학업성취도 효과에 있어서 통계적으로 유의한 차이가 있었다. 또한 수학적 태도와 관련해서는 하위영역 중 수학에 대한 자아개념과 수학에 대한 태도 영역에서는 유의한 차이가 있었으나 수학에 대한 학습습관 영역에서는 유의한 차이를 보이지 않았다. 특히 세부영역별로 자신감, 흥미, 우월감, 주의집중, 목적의식, 자율학습에 있어서 유의한 차이를 보였으며, 학습기술 적용과 성취동기에 대해서는 유의한 차이가 없었다.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.123-139
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• 2019

This study analyzed how problem-posing tasks included in Korean middle school mathematics textbooks were distributed in terms of content area, task type, and context of task to investigate that the mathematics textbooks are giving students ample opportunities for problem-posing activities. The analysis of 10 mathematics textbooks for first grade in middle school according to the revised mathematics curriculum in 2015 found that the problem-posing tasks contained in the textbooks are insufficient in quantity and not evenly distributed in terms of content areas. There were also more problem-posing tasks with relatively moderate constraints than those with strong or weak constraints in terms of mathematical constraints. In addition, there were more problem-posing tasks that were not requiring students to make a new context, and more often camouflage contexts were used. Based on this, implications for improving mathematics problem-posing tasks in mathematics textbook were suggested.