• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.163-186
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• 2004

구성주의에 기반한 7차 교육과정에서 교사 중심의 수업에서 학생 중심의 수업으로 전환을 강조하고 있다. 또한 지식을 객관적인 존재라는 의식에서 벗어나 학생들 스스로에 의해 구성되어진다는 것을 강조하고 있다. 이러한 시점에서 교실 수업의 개선은 당연한 흐름이며 교사들의 의식 전환 또한 당연한 것이다. 7차 교육과정에서 문제해결력을 바탕으로 한 수학적 힘의 신장을 강조하고 있다. 이러한 시대적 요청에 부응하는 교수법의 개발에 있어서 문제해결력과 창의적 사고력 학습법에 대한 연구는 필연적이다. 따라서 본 연구의 목적은 어떤 문제설정 방법이 문제해결력과 창의력을 향상시키는데 보다 더 효과가 있는지 알아보는데 그 목적이 있다.

• School Mathematics
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• v.7 no.3
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• pp.303-318
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• 2005

If students can use mathematics to solve their problems and learn the mathematical knowledge through it, they may think mathematics useful and valuable. This study is for the teaching through problem solving in mathematics education, which I consider in terms of the problem-based learning and mathematical modeling. 1 think mathematical modeling is applied to teaching mathematics as a problem-based learning. So I developed the teaching model, and showed the example that students learn the formal and hierarchic mathematics through mathematical modeling.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.545-562
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• 2009

This study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using "Protocol Analysis Method"and "Problem Behavior Graph" which is suggested by Newell and Simon as a qualitative analysis. In this study, four middle school students with high achievement in math were selected as subjects-two students for mathematical gifted group and the other two for control group also with high scores in math. The thinking characteristics of the four subjects, shown in the course of solving problems, were elicited, analyzed and compared, through the use of the creative test questionnaires which were supposed to clearly reveal the characteristics of mathematical gifted students' thinking processes. The results showed that there were several differences between the two groups-the mathematical gifted student group and their control group in their mathematical talents. From these case studies, we could say that it is significant to find out the characteristics of mathematical thinking processes of the mathematical gifted students in a more scientific way, in the sense that this result can be very useful to provide them with the chances to get more proper education by making clear the nature of thinking processes of the mathematical gifted students.

• Journal of Elementary Mathematics Education in Korea
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• v.7 no.1
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• pp.23-44
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• 2003

The purpose of the study is to examine the phenomenon presented the process of problem solving activities of students with the mathematical context information accompanied problem based on Freudenthal's mathematizing theory and Realistic Mathematics Educations about cognitive and emotional aspects. In conclusion, taking a look at the results of study, open-ended contextual problem was had to offer in order to pull out various solutions. Teachers should help students develop their own methods, discuss their methods with others' and reinvent formal mathematics and its constructive process under the guidance of the teachers.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.327-344
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• 2005

솔리테르(solitaire) 중 간단한 게임인 자리바꾸기 문제에 대해 학습자로 하여금 다양한 해결방법을 산출 하도록 한 후, 그 과정에서 학생들의 수학적 창의성의 발현 과정을 추적해 본다. 제시한 문제 해결 과제에 대한 학습자들의 반응과 해답을 분석함으로써 수학적 창의성에서의 인지적 구성요소인 확산성, 유창성, 논리성, 유연성, 독창성과 정의적 구성요소에 해당하는 적극성, 독자성, 집중성, 정밀성 등이 어떻게 나타나고 있는가를 살펴본다. 또한 그렇게 함으로써 각 구성요소의 의미와 특성을 규명하고자 하며, 나아가 이들 구성요소를 판별할 수 있는 방안에 대한 기초 자료를 제공하고자 한다.

• 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.

• School Mathematics
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• v.18 no.3
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• pp.541-569
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• 2016

The purpose of the study is to investigate elementary school students' creativity-integrated thinking ability and problem solving ability of core ability in 2015 revision curriculum of mathematics department. In addition, the relation between students' creativity-integrated thinking ability and problem solving ability was analyzed on problem solving process. As result, students' both abilities showed moderate level. Furthermore, students' creativity-integrated thinking ability and problem solving ability showed positive correlation.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.85-99
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• 2017

In order to improve mathematical problem-solving ability, there has been a need for research on practical application of meta-affect which is found to play an important role in problem-solving procedure. In this study, we analyzed the characteristics of the sociodynamical aspects of the meta-affective factor of the successful problem-solving procedure of small groups in the context of collaboration, which is known that it overcomes difficulties in research methods for meta-affect and activates positive meta-affect, and works effectively in actual problem-solving activities. For this purpose, meta-functional type of meta-affect and transact elements of collaboration were identified as the criterion for analysis. This study grasps the characteristics about sociodynamical function of meta-affect that results in successful problem solving by observing and analyzing the case of the transact structure associated with the meta-functional type of meta-affect appearing in actual episode unit of the collaborative mathematical problem-solving activity of elementary school students. The results of this study suggest that it provides practical implications for the implementation of teaching and learning methods of successful mathematical problem solving in the aspect of affective-sociodynamics.

• The Mathematical Education
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• v.58 no.4
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• pp.519-530
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• 2019

According to previous studies, meta-affect based on the interaction between cognitive and affective elements in mathematics learning activities maintains a close mechanical relationship with the learner's mathematical ability in a similar way to meta-cognition. In this study, in order to grasp these characteristics phenomenologically, small group problem-solving cases of 5th grade elementary mathematically gifted children were analyzed from a meta-affective perspective. As a result, the two types of problem-solving cases of mathematically gifted children were relatively frequent in the types of meta-affect in which cognitive element related to the cognitive characteristics of mathematically gifted children appeared first. Meta-affects were actively acted as the meta-function of evaluation and attitude types. In the case of successful problem-solving, it was largely biased by the meta-function of evaluation type. In the case of unsuccessful problem-solving, it was largely biased by the meta-function of the monitoring type. It could be seen that the cognitive and affective characteristics of mathematically gifted children appear in problem solving activities through meta-affective activities. In particular, it was found that the affective competence of the problem solver acted on problem-solving activities by meta-affect in the form of emotion or attitude. The meta-affecive characteristics of mathematically gifted children and their working principles will provide implications in terms of emotions and attitudes related to mathematics learning.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.619-640
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• 2011

The study aims the introducing the items for the assessment of mathematical thinking including mathematical reasoning, problem solving, and communication and the analyzing on the responses of the 5th grade pupils. We categorized the area of mathematical reasoning into deductive reasoning, inductive reasoning, and analogy; problem solving into external problem solving and internal one; and communication into speaking, reading, writing, and listening. And we proposed the examples of our items for each area and the 5th grade pupils' responses. When we assess on pupil's mathematical reasoning, we need to develop very appropriate items needing the very ability of each kind of mathematical reasoning. When pupils solve items requesting communication, the impact of the form of each communication seem to be smaller than that of the mathematical situation or sturucture of the item. We suggested that we need to continue the studies on mathematical assessment and on the constitution and utilization of cognitive areas, and we also need to in-service teacher education on the development of mathematical assessments, based on this study.