• The Journal of Korean Association of Computer Education
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• v.5 no.3
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• pp.79-87
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• 2002

Theorema system is built on top of Mathematica to automate deductive reasoning processes as the combination of computer algebra system and deductive system. Theorema system that was developed at RISC in Austria provides three modes based on rewriting techniques; computation, problem solving and proving. This paper shows how the computation mode of Theorema can simulate Derive part for TI-92 graphic calculators to produce TI-92 manuals. Moreover, it also describes how such manuals can be converted to web-based learning materials via Java servlet.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.927-941
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• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• The Journal of Korean Institute for Practical Engineering Education
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• v.5 no.1
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• pp.1-13
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• 2013

For a basic engineering education the confirmation and verification of the deductive Inference was studied and the principle of probability inference was applied. The background of introduction of deductive Inference and its test method was mentioned, and historic arguments on the compatibility of deductive statistical inference was summarized and analyzed. Philosophical arguments on the deductive confirmation for engineering experiments was introduced. Premise, procedure, and control of the experiments are studied. As an example of the deductive probability inference three groups of experimental data were used in order to find successful inferences respectively.

• The Mathematical Education
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• v.41 no.3
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• pp.273-289
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• 2002

It tends to be emphasized that mathematics is the important discipline to develop students' mathematical reasoning abilities such as deduction, induction, analogy, and visual reasoning. This study is aimed for investigating the present state about mathematical reasoning in secondary school. We survey teachers' opinions and analyze the results. The results are analyzed by frequency analysis including percentile, t-test, and MANOVA. Results are the following: 1. Teachers recognized mathematics as knowledge constructed by deduction, induction, analogy and visual reasoning, and evaluated their reasoning abilities high. 2. Teachers indicated the importances of reasoning in curriculum, the necessities and the representations, but there are significant difference in practices comparing to the former importances. 3. To evaluate mathematical reasoning, teachers stated that they needed items and rubric for assessment of reasoning. And at present, they are lacked. 4. The hindrances in teaching mathematical reasoning are the lack of method for appliance to mathematics instruction, the unpreparedness of proposals for evaluation method, and the lack of whole teachers' recognition for the importance of mathematical reasoning

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.123-148
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• 2014

The purpose of this study is to figure out the perceptional characteristics of mathematically gifted elementary students by comparing the mathematical reasoning ability and errors between mathematically gifted elementary students and non-gifted students. This research has been targeted at 63 gifted students from 5 elementary schools and 63 non-gifted students from 4 elementary schools. The result of this research is as follows. First, mathematically gifted elementary students have higher inductive reasoning ability compared to non-gifted students. Mathematically gifted elementary students collected proper, accurate, systematic data. Second, mathematically gifted elementary students have higher inductive analogical ability compared to non-gifted students. Mathematically gifted elementary students figure out structural similarity and background better than non-gifted students. Third, mathematically gifted elementary students have higher deductive reasoning ability compared to non-gifted students. Zero error ratio was significantly low for both mathematically gifted elementary students and non-gifted students in deductive reasoning, however, mathematically gifted elementary students presented more general and appropriate data compared to non-gifted students and less reasoning step was achieved. Also, thinking process was well delivered compared to non-gifted students. Fourth, mathematically gifted elementary students committed fewer errors in comparison with non-gifted students. Both mathematically gifted elementary students and non-gifted students made the most mistakes in solving process, however, the number of the errors was less in mathematically gifted elementary students.

• 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.

• Korean Journal of Logic
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• v.7 no.2
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• pp.121-146
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• 2004

본 논문은 베이즈주의가 확률론을 이용해서 제거적 귀납을 정교하게 발전시키고 있다고 주장한다. 이를 위해 본 논문은 두 가지 작업을 진행한다. 하나는 제거적 귀납이 무엇인가 하는것이고 다른 하나는 제거적 귀납이 베이즈주의에 기여하는 바가 무엇인가 하는 것이다. 먼저 본 논문은 제거적 귀납이 참인 가설을 포함하는 가능한 가설들의 총체로부터 경쟁가설들을 연역적 또는 귀납적으로 제거하고 남는 가설을 선택하는 추론형식임을 밝히고, 이 때 베이즈주의는 제거적 귀납을 정교하게 발전시킨 모습이기 때문에 제거적 귀납으로부터 기술적으로 도움 받을 측면은 없다고 주장한다. 그 대신 본 논문은 베이즈주의가 과학방법론으로 발전되는 데에서 직면하는 여러 가지 문제점을 해결하는 방법에 대해 제거적 귀납으로부터 조언을 얻을 수 있다고 주장한다. 이와 같은 논의를 통해 본 논문은 베이즈주의와 제거적 귀납주의의 결합은 유용한 과학방법론을 만들 수 있을 것으로 전망한다.

• 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.

• East Asian mathematical journal
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• v.24 no.5
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.417-435
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• 2011

Mathematical justification is essential to assert with reason and to communicate. Students learn mathematical justification in 8th grade in Korea. Recently, However, many researchers point out that justification be taught from young age. Lots of studies say that students can deduct and justify mathematically from in the lower grades in elementary school. I conduct questionnaire to know awareness and steps of elementary school students and middle school students. In the case of 9th grades, the rate of students to deduct is highest compared with the other grades. The rease is why 9th grades are taught how to deductive justification. In spite of, however, the other grades are also high of rate to do simple deductive justification. I want to focus on the 6th and 5th grades. They are also high of rate to deduct. It means we don't need to just focus on inducing in elementary school. Most of student needs lots of various experience to mathematical justification.