• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권2호
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• pp.325-344
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• 2010

본 연구는 중학생을 대상으로 학생들이 경험적 증명과 연역적 증명에 대한 선호를 결정할 때 영향을 미치는 요인을 분석하였다. 47명의 중학생에게 설문지를 통하여 자료를 수집하고 응답들을 분석한 결과, 경험적 증명과 연역적 증명의 선호에 영향을 미치는 요인들로 측정, 수학적 원리, 다양한 예를 통한 검증과정에 대한 인식들이 공통적으로 나타났다. 이 요소들은 경험적 증명과 연역적 증명의 선호와 비선호를 결정짓는 요인으로써, 선호하는 증명에 따라 상호 배타적으로 나타나지 않고 증명 선호에 영향을 미쳤다. 이를 통해 본 연구에서는 학생들이 특정 증명을 선호할 때, 한 증명에 대한 비선호와 다른 증명에 대한 선호가 동시에 작용할 수 있다는 결론과 함께 한 증명에 대한 선호요인을 보는 것만으로는 학생들의 증명 선호 이유를 정확히 파악할 수 없을 것이라는 가능성을 제언한다.

• 대한수학교육학회지:수학교육학연구
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• 제9권1호
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• 대한수학교육학회지:수학교육학연구
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• 제9권2호
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• pp.419-438
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• 1999

This paper explored the impact of dynamic geometry software such as CabriII, GSP on student's understanding deductive justification, on the assumption that proof in school mathematics should be used in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof. The following results have been drawn: Dynamic geometry provided positive impact on interacting between empirical justification and deductive justification, especially on understanding the necessity of deductive justification. And teacher in the computer environment played crucial role in reducing on difficulties in connecting empirical justification to deductive justification. At the beginning of the research, however, it was not the case. However, once students got intocul-de-sac in empirical justification and understood the need of deductive justification, they tried to justify deductively. Compared with current paper-and-pencil environment that many students fail to learn the basic knowledge on proof, dynamic geometry software will give more positive ffect for learning. Dynamic geometry software may promote interaction between empirical justification and edeductive justification and give a feedback to students about results of their own actions. At present, there is some very helpful computer software. However the presence of good dynamic geometry software can not be the solution in itself. Since learning on proof is a function of various factors such as curriculum organization, evaluation method, the role of teacher and student. Most of all, the meaning of proof need to be reconceptualized in the future research.

• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.385-402
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• 2001

The purpose of this study is to conceptualize 'proof' school mathematics. We based on the assumption the following. (a) There are several different roles of 'proof' : verification, explanation, systematization, discovery, communication (b) Accepted criteria for the validity and rigor of a mathematical 'proof' is decided by negotiation of school mathematics community. (c) There are dynamic relations between mathematical proof and empirical theory. We need to rethink the nature of mathematical proof and give appropriate consideration to the different types of proof related to the cognitive development of the notion of proof. 'proof' in school mathematics should be conceptualized in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof 'proof' has not been taught in elementary mathematics, traditionally, Most students have had little exposure to the ideas of proof before the geometry. However, 'proof' cannot simply be taught in a single unit. Rather, proof must be a consistent part of students' mathematical experience in all grades, in all mathematics.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제27권1호
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• pp.75-92
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• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• 통상정보연구
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• 제8권4호
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• pp.159-175
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• 2006

This paper that explain exchange rate determination using Korea's economy data moment investigate whether each theory cause effect that is some on exchange rate showdown analyzing actual proof relation between foreign exchange fluctuation and financing part variance examine wish to. Because korea economic enters in the 1990s and the 2000s and the change is notable, foreign exchange fluctuation by such change is real condition that is changing. In this paper, I wish to enforce actual proof analysis if change such as him is grasped by form that is some about foreign exchange fluctuation. First, the second chapter investigates exchange rate decision theory that is used on actual proof interpretation, and executes actual proof Test in reply in subsequent the third chapter. And finally, the fourth chapter wishes to drive conclusion of this paper.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권3호
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• pp.217-233
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• 2009

The purpose of this study is to describe how dynamic geometry systems can be useful in proof activity; teaching sequences based on the use of dynamic geometry systems and to analyze the possible roles of dynamic geometry systems in both teaching and learning of proof. And also dynamic geometry environments can generate powerful interplay between empirical explorations and formal proofs. The point of this study was to show that how using dynamic geometry software can provide an opportunity to link between empirical and deductive reasoning, and how such software can be utilized to gain insight into a deductive argument.

• 대한수학교육학회지:수학교육학연구
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• 제21권2호
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• pp.135-148
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• 2011

우리나라 중학교 수학 2에서는 공리의 역할을 하는 명제를 공리라는 명시 없이, 실험에 의해 확인한 옳은 결과로만 받아들여 증명에 사용한다. 그러나 공리 개념은 경험적 입증과 연역적 증명, 직관기하와 논증기하, 증명과 증명이 아닌 것의 차이를 이해하는데 매우 중요한 것이다. 본 연구의 교과서 분석과 영재학생들을 대상으로 한 인식조사 결과는, 공리와 증명의 취급에 대하여 우리나라 교과서가 가진 한계와 문제점을 보여주고 있다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제25권1호
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• pp.65-89
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• 2022

Despite its recognition in the field of mathematics education and mathematics, students' understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers' judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제7권2호
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• pp.85-99
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• 2003

In this paper, firstly examined various proofs types that cover informal empirical justifications by Balacheff, Miyazaki, and Harel ＆ Sowder and Tall. Using these theoretical frameworks, justification activities by 5th graders were analyzed and several conclusions were drawn as follow: 1) Children in 5th grade could justify using various proofs types and method ranged from external proofs schemes by Harel & Sowder to thought experiment by Balacheff This implies that children in elementary school can justify various mathematical statements of ideas for themselves. To improve children's proving abilities, rich experience for justifying should be provided. 2) Activities that make conjectures from cases then justify should be given to students in order to develop a sense of necessity of formal proof. 3) Children have to understand the meaning and usage of mathematical symbol to advance to formal deductive proofs. 4) New theoretical framework is needed to be established to provide a framework for research on elementary school children's justification activities. Research on proof mainly focused on the type of proof in terms of reasoning and activities involved. But proof types are also influenced by the tasks given. In elementary school, tasks that require physical activities or examples are provided. To develop students'various proof types, tasks that require various justification methods should be provided. 5) Children's justification type were influenced not only by development level but also by the concept they had. 6) Justification activities provide useful situation that assess students'mathematical understanding. 7) Teachers understanding toward role of proof(verification, explanation, communication, discovery, systematization) should be the starting point of proof activities.