• 아동학회지
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• 제35권3호
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• pp.49-69
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• 2014

The purposes of this study were (1) to investigate children's moral judgment, justification reasoning in terms of aggressive behavior, and (2) it examined the relationship to false belief understanding. Children aged between 3 to 5 years(N = 120) participated in this study. Each child was interviewed individually and responded questions designed to measure his/her moral judgment and justification reasoning and false belief understanding. The 12 pictorial tasks consisted of selfish and altruistic intentions and three different types of acts (physical, verbal, relational) as responses to aggressive behavior. The results indicated that the kind of moral judgment used was different according to the intention and the types of acts. There were significant differences in children's justification reasoning according to the age and the types of acts. There was a positive relationship between false belief understanding and moral judgment, justification reasoning. This paper also provided a detailed discussion of the results and recommendations in the context of more general cognitive developmental changes.

• 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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• 제13권2호
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• pp.159-178
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• 2003

본 연구는 초등 수학 교재에서 정당화 과점이나 문제 해결 과정에서 활용되는 추론을 분석한 것이다. 본 연구의 분석 결과, 한 가지 전형적인 예에 대한 국소적 연역 추론이 가장 전형적인 특징으로 드러났으며, 사각형에 대한 몇 가지 명제는 연역 추론으로 정당화할 뿐 아니라 일반성을 요구하고 있는 것으로 드러났다. 또한, 열거에 의한 귀납 주론은 그리 많이 활용되고 있지 않으며, 구체물을 통한 유추가 밭이 활용되고 있음을 알 수 있었다. 전형적인 한 가지 예에 대한 설명은 Miyazaki가 제시한 예에 의한 설명이나 Semadeni가 제시한 활동 증명과 유사한 면을 지니고 있지만, 학생들의 학년 단계가 높아지더라도 계속 낮은 수준 머물러 있는 점이 문제점으로 부각되었다. 또한, 사각형의 일반적인 성질을 다루는 몇몇 명제는 Piaget의 이론에 비추어 너무 어려운 것으로 분석되었다. 본 연구에서는 이러한 문제점을 해결할 수 있는 방한으로서 보다 점진적인 추론의 지도를 제안하였는바, 전형적인 예에 대한 경험적 정당화, 전형적인 예에 대한 경험으로부터 추측의 구성, 다양한 예에 대한 추측의 타당성 조사, 일반성에 대한 스키마 형성, 함의 관계의 이해를 위한 기초 경험의 다섯 가지 수준이다.

• 아동학회지
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• 제36권5호
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• pp.135-153
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• 2015

The purpose of this study was to investigate false belief understanding and justification reasoning according to information of reality amongst children aged 3, 4 and 5. Children aged 3 to 5 years (N = 176) participated in this study. Each child was interviewed individually and responded to questions designed to measure his/her false belief understanding. Every child responded to the false belief task under two different information conditions of reality(reality known vs reality unknown). For more specific analysis, children's reasoning responses were also recorded. The major findings of this study are as follows. Children could understand false belief more easily under reality unknown conditions. Specifically, the influences of information conditions were crucial to 3-year-olds but not to 4- and 5-year-olds. Although 3 year olds were able to avoid the systematical errors inherent in the false belief task, they still did not understand the false belief itself. This study provides specific aspects of false belief understanding and its relevance to general changes in cognitive development.

• 대한수학교육학회지:수학교육학연구
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• 제19권3호
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• pp.371-392
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• 2009

본 연구는 초등학교 교사들의 수학적 정당화에 관한 인식을 설문 조사와 면담을 통하여 연구한 것이다. 초등학교 교사를 수학 관련 교과를 전공한 교사(수학 관련교사)와 그 밖의 교과를 전공한 교사(비관련 교사)로 구분하여 두 집단 간의 수학적 정당화의 인식과 정당화의 선호도를 조사 연구하였다. 조사 결과, 다음과 같은 결론을 내릴 수 있다. 첫째, 우리나라 초등학교 교사들은 비교적 수학적 정당화에 대해 대체로 잘 이해하고 있다. 수학적 정당화는 필요하며 이는 논리적 사고를 기르거나 수학적 지식을 이해시키는 데에 좋은 방법이라는 것에 대해 잘 인식하고 있으며, 권위적 정당화를 선호하지 않고, 형식적 정당화나 귀납적 정당화를 더 가치 있게 여기고 있다. 둘째, 우리나라 초등학교 교사들은 자기 자신이 증명을 할 경우에는 형식적인 수학적 정당화를 선호하나, 학생들을 가르칠 경우 학생들의 이해를 위해 형식적 증명보다는 귀납적 정당화나 그림과 같은 단서를 이용하는 것이 더 효과적이라고 생각하고 있었다.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권3호
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• pp.291-318
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• 2002

We investigated on the primary school children's abilities of formal reasoning. Seventy students in grade 5 participated in the study. They responsed their best reactions on the problems constituted of three parts requiring the informal or formal reasoning and generalization. Their reactions are classified by some criteria depending the level of reasoning. About 10 students showed that they constructed a kind of scheme for solving the problems, similar to formal reasoning and beyond naive informal reasoning. And about 30 students did so partially. We concluded that the teaching and learning of reasoning by the progressive increasing the degree of rigor from grade 5 is possible.

• 한국학교수학회논문집
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• 제24권3호
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• pp.261-282
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• 2021

이 연구는 중학교 수학 영재학생의 수학적 정당화에 대한 의미 인식과 수학적 정당화의 특성을 파악하여 정당화 교육을 위한 시사점을 얻고자 한 것이다. 이를 위해 17명의 중학교 수학 영재학생을 대상으로 설문지와 검사지를 투입하여 분석한 결과, 영재학생들은 수학적 정당화에 대하여 입증, 체계화, 발견, 지적 도전과 같은 다양한 의미로 정당화를 인식하였고, 연역적 정당화의 선호도가 높았다. 실제 정당화 활동의 결과, 대수와 기하 문항 모두에서 연역적 정당화가 많았지만 대수 문항에서는 경험적 정당화도 많은 반면 기하 문항에서는 매우 낮음을 알 수 있었다. 연역적 정당화를 완성한 경우, 자신의 정당화에 만족함을 보였지만 수학적 문자와 기호를 사용하여 명제의 일반성을 연역적으로 정당화를 하지 못한 경우에는 불만족을 보였다. 연구 결과는 영재학생들이 경험적 추론의 유용성과 한계를 깨닫고 연역적 정당화를 할 수 있도록 하며 특히 대수적 번역 능력을 향상시킬 수 있는 정당화 교육이 필요함을 시사한다.

• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.351-364
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• 1998

This thesis analyzes the nature of proof in the perspective on the philosophy of mathematics. such as absolutism, quasi-empiricism and social constructivism. And this thesis searches for the improvement of teaching proof in the light of the result of those analyses of the nature of proof. Though the analyses of the nature of proof in the perspective on the philosophy of mathematics, it is revealed that proof is a dynamic reasoning process unifying the way of analytical thought and the way of synthetical thought, and plays remarkably important roles such as justification, discovery and conviction. Hence we should teach proof as a dynamic reasoning process unifying the way of analytic thought and the way of synthetic thought, avoiding the mistake of dealing with proof as a unilaterally synthetic method. At the same time, we should make students have the needs of proof in a natural way by providing them with the contexts of both justification and discovery simultaneously. Finally, we should introduce the aspect of proof that can be represented as conviction, understanding, explanation and communication to school mathematics.

• East Asian mathematical journal
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• 제37권2호
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• pp.149-167
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• 2021

The six core competencies included in the mathematics curriculum revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the reasoning is very important for students' enhancing much higher mathematical thinking. Based on this competency, this study selected the four elements of investigation and fact guess, justification, the logical performance of mathematical content and process, reflection of reasoning process, And also this study selected the domain of function which is comprised of the content of the coordinate plane, the graph, proportionality in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the four elements of the reasoning competency were shown in each textbook.

• 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.