• 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.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.451-472
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• 2011

In this paper we studied problem solving related with geometric interpretation of algebraic expressions. We analyzed algebraic expressions, related these expressions with geometric interpretation. By using geometric interpretation we could find new approaches to solving mathematical problems. We suggested new problem solving methods related with geometric interpretation of algebraic expressions.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.197-215
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• 2010

Intuition plays an important role in the mathematical education as well as the process of invention in mathematics. And many mathematics educators became interested in intuition in mathematics education. So we need to analyze the effect of the characters of intuition of elementary students. In this study, the questionnaire and the interview were used. The subjects were 6 grade-103 students in the questionnaire. They were asked to solve the problems in the questionnaire which was designed by the researcher and to describe the reasons why they answered like that. Students are effected directly by the characters of intuition, ie self-evidence, intrinsic certainty, implicitness, etc. And the effect come from intuitive and ordinary experiences and the results of previous learning. In conclusion, we have to be interested in teaching via intuition and to control the effect of the characters of intuition.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.113-139
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• 2013

The purpose of this study is to provide informations about cause of failures when students solve word problems by analyzing what errors students made in solving word problems and types of error and features of error according to problem solving strategy. The results of this study can be summarized as follows: First, $5^{th}$ grade students preferred the expressions, estimate and verify, finding rules in order when solving word problems. But the majority of students couldn't use simplifying. Second, the types of error encountered according to the problem solving strategy on problem based learning are as follows; In the case of 'expression', the most common error when using expression was the error of question understanding. The second most common was the error of concept principle, followed by the error of solving procedure. In 'estimate and verify' strategy, there was a low proportion of errors and students understood estimate and verify well. When students use 'drawing diagram', they made errors because they misunderstood the problems, made mistakes in calculations and in transforming key-words of data into expressions. In 'making table' strategy, there were a lot of errors in question understanding because students misunderstood the relationship between information. Finally, we suggest that problem solving ability can be developed through an analysis of error types according to the problem strategy and a correct teaching about these error types.

• 한국정보교육학회:학술대회논문집
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• 2005.08a
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• pp.401-408
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• 2005

본 연구는 학습자 중심의 구성주의 학습 모형인 문제중심학습( Problem-Based Learning: PBL) 모형 개발을 통한 효과적인 HTML 학습 방안의 탐색을 위해 수행되었다. 초등학생이 HTML( Hyper Text Markup Language )학습을 통해 프로그래밍을 학습할 때 단순문법을 익히는 것을 넘어 프로그래밍 언어를 자율적이고 창의적으로 활용하기 위해서는 고차원적인 자기 주도적 학습 능력과 문제 해결 능력이 요구된다. 이를 위해 본 논문은 문제중심학습의 기존모형들이 갖고 있는 특징을 기반으로 하여 개발되었다. 본 연구의 문제중심학습의 절차는 문제와의 만남- 문제의 해결 전략 세우기- 문제 해결을 위한 정보수집- 문제의 해결 -평가 단계와 같다. 학습과정 에세이 기록을 통해 학습절차를 설계하고 과정을 돌이킬 수 있으며 피드백 과정을 통하여 학습의 결손을 방지하도록 하였다. 구성주의 학습 모형인 문제중심학습(PBL)을 HTML 언어교육에 적용 할 경우 학습자의 자기 주도적 학습 능력과 의사소통능력, 창의력 논리력을 키울 수 있을 것으로 기대된다.

• 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.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.265-274
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• 2002

이 프로젝트는 수학 수업 중 ‘추론’과 ‘증명’에 관련된 "문제해결과정"에 관심을 가지고, 처음 증명문제를 접하는 독일 7학년 학생들을 대상으로 문제해결능력에 필요한 요인들, 즉, 문제 해결을 위한 수학적 기본지식, 해결된 문제에 대한 인지정도, 논리적 사고 등을 관찰 분석하고 수학교사의 수학에 대한 신념(Beliefs)과 수업 방식이 학생들의 문제해결에 미치는 영향을 조사하는 것에 그 목적을 둔다. 이 프로젝트의 일부의 결과로써, 본 논문에서는 학생들 개개인의 문제해결과정과 그 능력, 그리고 수학에 대한 신념을 서술하고, 수학교사와 학생들의 서로 다른 수학에 대한 신념을 비교 분석한다.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.143-161
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• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.201-220
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• 2007

This research is designed to analyze the metacognitive thinking that mathematically gifted elementary students use to solve problems, study the effects of the metacognitive function on the problem-solving process, and finally, present how to activate their metacognitive thinking. Research conclusions can be summarized as follows: First, the students went through three main pathways such as ARE, RE, and AERE, in the metacognitive thinking process. Second, different metacognitive pathways were applied, depending on the degree of problem difficulty. Third, even though students who solved the problems through the same pathway applied the same metacognitive thinking, they produced different results, depending on their capability in metacognition. Fourth, students who were well aware of metacognitive knowledge and competent in metacognitive regulation and evaluation, more effectively controlled problem-solving processes. And we gave 3 suggestions to activate their metacognitive thinking.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.193-202
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• 2009

The purpose of this study was to investigate undergraduates' characteristics of problem-solving process through analysis of the response patterns on problem-solving laboratory. For this purpose, 18 freshmen taking a problem-solving-type general chemistry laboratory had been interviewed for the analysis of the characteristics of problem-solving process. According to the results, the students' responses have been classified into five types; trying to solve problems using new factors, trying to solve problems by finding missing factors in manual, recognizing problem-situations but just repeating the given process, not recognizing problem-situations but trying to solve doubts generated during execution, satisfying about results, and taking no further action. These results can be used as materials to suggest the role model of the students' laboratory execution and to look back on each students' execution.