• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.461-483
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• 2017

The ability to think mathematically and to reason inductively are basics of logical reasoning and the most important skill which students need to acquire through their Math curriculum in elementary school. For these reasons, we need to conduct an analysis in their procedure in inductive reasoning and find difficulties thereof. Therefore, through this study, I found parts which covered inductive reasoning in their Math curriculum and analyzed the abilities and characteristics of students in solving a problem through inductive reasoning.

• School Mathematics
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• v.14 no.1
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• pp.85-107
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• 2012

Problem solving is important in school mathematics as the means and end of mathematics education. In elementary school, inductive reasoning is closely linked to problem solving. The purpose of this study was to examine ways of improving problem solving ability through analysis of inductive reasoning process. After the process of inductive reasoning in problem solving was analyzed, five different stages of inductive reasoning were selected. It's assumed that the flow of inductive reasoning would begin with stage 0 and then go on to the higher stages step by step, and diverse sorts of additional inductive reasoning flow were selected depending on what students would do in case of finding counter examples to a regulation found by them or to their inference. And then a case study was implemented after four elementary school students who were in their sixth grade were selected in order to check the appropriateness of the stages and flows of inductive reasoning selected in this study, and how to teach inductive reasoning and what to teach to improve problem solving ability in terms of questioning and advising, the creation of student-centered class culture and representation were discussed to map out lesson plans. The conclusion of the study and the implications of the conclusion were as follows: First, a change of teacher roles is required in problem-solving education. Teachers should provide students with a wide variety of problem-solving strategies, serve as facilitators of their thinking and give many chances for them ide splore the given problems on their own. And they should be careful entegieto take considerations on the level of each student's understanding, the changes of their thinking during problem-solving process and their response. Second, elementary schools also should provide more intensive education on justification, and one of the best teaching methods will be by taking generic examples. Third, a student-centered classroom should be created to further the class participation of students and encourage them to explore without any restrictions. Fourth, inductive reasoning should be viewed as a crucial means to boost mathematical creativity.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.405-422
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• 2017

Nim games were divided into three stages : one file, two files and three files game, and inquiry activities were conducted for middle school mathematically gifted students. In the first stage, students easily found a winning strategy through deductive reasoning. In the second stage, students found a winning strategy with deductive reasoning or inductive reasoning, but found an error in inductive reasoning. In the third stage, no students found a winning strategy with deductive reasoning and errors were found in the induction reasoning process. It is found that the tendency to unconditionally generalize the pattern that is formed in the finite number of cases is the cause of the error. As a result of visually presenting the binary boxes to students, students were able to easily identify the pattern of victory and defeat, recognize the winning strategy through game activities, and some students could reach a stage of justifying the winning strategy.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.461-472
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• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.295-323
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• 2011

This study is based on the recognition that teacher educators have to focus their attention on developing pre-service teachers' statistical reasoning for statistics education of school mathematics. This paper investigated knowledge on pre-service teachers' statistical reasoning. Statistical Reasoning Assessment (SRA) is performed to find out pre-service teachers' statistical reasoning ability. The research findings are as follows. There was meaningful difference in the statistical area of statistical reasoning ability with significant level of 0.05. This proved that 4 grades pre-service teachers were more improve on statistical reasoning than 2 grades pre-service teachers. Even though most of the pre-service teachers ratiocinated properly on SRA, half of pre-service teachers appreciated that small size of sample is more likely to deviate from the population than the large size of sample. A few pre-service teachers have difficulties in understanding "Correctly interprets probabilities(be able to explain probability by using ratio" and "Understands the importance of large samples(A small sample is more likely to deviate from the population)".

• Communications of Mathematical Education
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• v.13 no.2
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• pp.425-455
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• 2002

본 연구는 수학교육에서 강조되고 있는 수학적 힘의 구성 요소 중의 하나인 수학적 추론 능력에 대한 교사들의 구체적인 이해를 돕고, 문제 해결 과정에서 학생들의 추론 능력을 분석하고 평가하는 데 도움을 주기 위해 문헌 연구 및 학생반응 분석결과에 기초하여 귀납적, 유비적, 연역적 추론능력에 대한 평가기준을 개발하였다. 또한, 개발된 평가기준을 구체적인 문제에 적용하였으며 이를 기초로 문제점을 수정 ${\cdot}$ 보완한 후, 전문가의 타당성 검증과 동일한 학생반응에 대한 채점결과의 일치도를 알아봄으로써 신뢰도 검증을 실시하였다.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.

• Journal of Korean Elementary Science Education
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• v.23 no.1
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• pp.61-73
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• 2004

The purpose of this study was to suggest a grounded theory on the process of undergraduate students' generating pattern-knowledge about scientific episodes. The pattern-discovery tasks were administered to seven college students majoring in elementary education. The present study found that college students show five types of procedural knowledge represented in the process of pattern-discovery, such as element, elementary variation, relative prior knowledge, predictive-pattern, and final pattern-knowledge. Furthermore, subjects used seven types of thinking ways, such as recognizing objects, recalling knowledges, searching elementary variation, predictive-pattern discovery, confirming a predictive-pattern, combining patterns, and selecting a pattern. In addition, pattern-discovering process involves a systemic process of element, elementary variation, relative prior knowledge, generating and confirming predictive-pattern, and selecting final pattern-knowledge. The processes were shown the abductive and deductive reasoning as well as inductive reasoning. This study also discussed the implications of these findings for teaching and evaluating in science education.

• Journal of KIISE:Software and Applications
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• v.35 no.3
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• pp.189-196
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• 2008

To build autonomous agents who can make a decision on behalf of humans in time-critical complex environments, the formulation of operational knowledge base could be essential. This paper proposes the methodology of how to formulate the knowledge base and evaluates it in a practical application domain. We analyze threat data received from the multiple sensors of Aircraft Survivability Equipment(ASE) for Korean helicopters, and integrate the threat data into the inductive model through compilation technique which extracts features of the threat data and relations among them. The compiled protocols of state-action rules can be implemented as the brain of the ASE. They can reduce the amounts of reasoning, and endow the autonomous agents with reactivity and flexibility. We report experimental results that demonstrate the distinctive and predictive patterns of threats in simulated battlefield settings, and show the potential of compilation methods for the successful detection of threat systems.

• 한국정보교육학회:학술대회논문집
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• 2005.08a
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• pp.69-77
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• 2005

본 연구는 초등학생들의 논리적 사고력을 신장시키기 위해 지식 기반 프로그램인 선언적 프로그램을 통해 교육현장에서도 적용할 수 있는 프로그래밍 교육을 제언하고자 한다. 학생들에게 논리적 사고 중에서도 협의의 논리적 사고 즉, 기호적 사고, 분석적 사고, 추론적 사고, 종합적 사고를 분석적 방법을 통해 실제 프로그래밍을 해 봄으로써 연역적 사고 또는 귀납적 사고를 보다 효과적이고 체계적인 프로그래밍을 할 수 있도록 지도함으로써 제 8차 교육과정에서의 컴퓨터 교육과정의 일부분으로서의 프로그래밍의 마인드를 제시하였다. 따라서 본 연구는 선언적 프로그램을 통해서 초등학교 학생들의 논리적 사고력 신장를 위하여 프로그래밍 교수학습의 방법적인 측면을 제시하고자 한다.