• 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.

• Journal of The Korean Association For Science Education
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• v.23 no.3
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• pp.286-298
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• 2003

The purpose of this study was to analyze scientific thinking types and processes generated in inductive inquiry by college students. Subjects were three college student. Three inductive tasks were developed: Caminalcules set I which is a task consisted of 6 imaginary animals, a potato task which is a task about the interaction between juiced potato and $H_2O_2$, and Caminalcules set 2. Subjects' thinking types and processes were investigated through thinking-aloud method and interview. Subjects' performances were recorded on videotapes and analyzed. Subjects have shown 5 types of inductive thinking in the first task; observing, discovering commonness, discovering pattern, classifying, discovering hierarchy. The processes of inductive thinking shown by students are followed; observing $\rightarrow$discovering commonness $\rightarrow$classifying $\rightarrow$discovering pattern $\rightarrow$discovering hierachy. The subtypes of inductive thinking on observing were investigated by the analysis of subjects' performance on the second task. In analysis of protocol, student' thinking types on observing have been classified as simple observing and operational observing. Operational observing has been categorized conjectural observing and predictive observing. The subtypes of inductive thinking on classification and hierarchy were investigated by the analysis of subjects' performance on the third task. In analysis of protocol, students' thinking types on classification have been searching criteria for classifying and selecting criteria for classifying. Subtypes of discovering hierarchy have been classifying groups and hierarchical ordering by students. Processes of classifying groups proceeded from searching criteria for classifying to selecting criteria for classifying.

• 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.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.109-124
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• 2004

대학수학에서 수학적귀납법의 원리를 소개하고 풍부한 예를 통해 이해를 돕는다. 특별히 교양수학을 수강하는 1학년 학생 수준에 맞게 매스매티카 프로그램을 이용하여 구체적인 예를 갖고 한단계 한단계 접근하여 수학적귀납법의 증명을 연습할 기회를 준다. 증명을 단계적으로 하는 것을 연습하여 학생들은 논리적인 사고능력을 개발하고 새로운 명제를 발견할 수 있는 기회를 맞보게 한다. 물론, 증명 연습은 1학년 신입생에게는 쉽지 않으나 여러 명제에 대해 연습을 하는 것은 수학적, 논리적 사고 능력을 개발하고 증명문제에 대한 인식을 바꾸는데 매우 중요한 역할을 할 것이다.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.11-15
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• 2008

다각형에서 가장 기본이 되는 삼각형과 사각형의 종이를 접을 때 마다 다양한 규칙성들이 발견될 수 있다. 따라서 본 연구에서는 이런 종이접기를 통한 패턴 탐구를 통해 문제를 형식화거나 일반화 하는 능력과 수학적으로 사고하는 능력 즉, 귀납적 추론력을 길러주고자 함에 목적을 두고 있다.

• 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.14
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• pp.273-295
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• 2001

통계는 연역적 사고를 강조하는 수학의 다른 영역과 달리 귀납적 추론과 직관적 사고를 요구한다. 따라서 학교 수업에서 학생들이 실제적인 상황을 모델링 할 수 있도록 하며, 주어진 상황에서 자료를 올바르게 산출하고 분석 할 수 있도록 적절한 지도 방법이 필요하다. 그렇지만 학교 수업은 대다수 알고리즘 연습 위주의 통계 학습-지도로 통계적 사고 교육이 제대로 이루어지지 못하고 있다. 이로 인해 학생들은 형식적인 통계 처리에는 익숙하지만 통계 교육의 궁극적 목적인 변이성과 자료를 현명하게 다루는 능력이 부족하다. 본고에서는 피상적인 기계적 계산위주의 통계교육에서 실제적인 자료를 수집하고, 이를 적절히 가공 처리하여 정보의 가치를 높일 수 있는 통계 지도 방향을 탐색해 보고자 한다.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.371-392
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• 2009

A lot of researches state mathematical justification is important. Specially, NCTM (2000) mentions that mathematical reasoning and proof should be taught every student from pre-primary school to 12 grades. Some of researches say elementary school students are also able to prove and justify their own solution(Lester, 1975; King, 1970, 1973; Reid, 2002). Balacheff(1987), Tall(1995), Harel & Sowder(1998, 2007), Simon & Blume(1996) categorize the level or the types of mathematical justification. We re-categorize the 4 types of mathematical justification basis on their studies; external conviction justification, empirical-inductive justification, generic justification, deductive justification. External conviction justification consists of authoritarian justification, ritual justification, non-referential symbolic justification. empirical-inductive justification consists of naive examples justification and crucial example justification. Generic justification consists of generic example and visual example. The results of this research are following. First, elementary school teachers in Korea respectively understand mathematical justification well. Second, elementary school teachers in Korea prefer deductive justification when they justify by themselves, while they prefer empirical-inductive justification when they teach students.

• The Mathematical Education
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• v.42 no.5
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• pp.647-672
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• 2003

This study sought to determine the impact of the graphing calculator on prospective math-teachers' mathematical thinking while they engaged in the exploratory tasks. To understand students' thinking processes, two groups of three students enrolled in the college of education program participated in the study and their performances were audio-taped and described in the observers' notebooks. The results indicated that the prospective teachers got the clues in recalling the prior memory, adapting the algebraic knowledge to given problems, and finding the patterns related to data, to solve the tasks based on inductive, deductive, and creative thinking. The graphing calculator amplified the speed and accuracy of problem-solving strategies and resulted partly in students' progress to the creative thinking by their concept development.