• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.585-599
• /
• 2004

본 연구에서는 학교수학에서 증명지도의 문제점을 정당화의 측면에서 분석하고, 정당화의 한 방법으로서 확률론적 정당화를 제시하며, 학교수학에서 정당화 지도의 교육적 가치, 정당화 지도의 방향, 정당화 지도의 예와 지도 방법에 대해 논의한다. 이러한 논의에 근거하여 학교수학에서의 정당화 지도의 필요성 및 가능성에 관하여 살펴본다. 본 연구에서 '증명'은 고전적인 의미에서의 증명, 즉 엄밀한(rigorous) 증명, 수학적(mathematical) 증명이고, '정당화'는 기존의 수학적 증명 개념은 물론, 다양한 논증 기법을 포함하는 넓은 의미이다.

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

• Journal of the Korean School Mathematics Society
• /
• v.24 no.3
• /
• pp.261-282
• /
• 2021

This study identified the meaning of mathematical justification and its characteristics for middle school math gifted students. 17 middle school math gifted students participated in questionnaires and written exams. Results show that the gifted students recognized justification in various meanings such as proof, systematization, discovery, intellectual challenge of mathematical justification, and the preference for deductive justification. As a result of justification exams, there was a difference in algebra and geometry. While there were many deductive justifications in both algebra and geometry questionnaires, the difference exists in empirical justifications: there were many empirical justifications in algebra, but there were few in geometry questions. When deductive justification was completed, the students showed satisfaction with their own justification. However, they showed dissatisfaction when they could not deductively justify the generality of the proposition using mathematical symbols. From the results of the study, it was found that justification education that can improve algebraic translation ability is necessary so that gifted students can realize the limitations and usefulness of empirical reasoning and make deductive justification.

• Journal of Educational Research in Mathematics
• /
• v.19 no.3
• /
• pp.371-392
• /
• 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 Journal of Information Systems
• /
• v.16 no.1
• /
• pp.65-90
• /
• 2007

전통적인 비용수익 분석법 (CBA approach) 과 활동기준원가계산 방법 (ABC approach)과 같은 지금까지의 방법으로는 전략적 정보시스템이나 정보 하부구조를 효과적으로 평가하고 정당화하는데 한계가 있다고 지적되어왔다. 따라서, 본 논문은 정보시스템의 하부구조를 이루고 있는 데이터 웨어하우징을 스물여섯 개의 데이터 웨어하우징 성공사례 분석을 통해서 데이터 웨어하우징이 가치사슬 모델의 각 활동에 어떻게 활용되고 있는지를 분석하고, 경쟁우위적 관점에서 이들 사례들의 공통점을 찾아내어, 데이터 웨어하우징을 경쟁우위적 관점에서 보다 효과적으로 정당화할 수 있는 모델을 제시하고 있다. 이 모델은 기존의 정보시스템 정당화에 사용되어왔던 방법들의 단점을 보완하여, 기업들이 데이터 웨어하우징이나 경쟁우위를 확보하기 위해서 구축하는 다른 정보시스템들을 경쟁우위적 관점에서 정당화하고자 할 때 유용한 도구로써, 기존의 방법들과 병행해서 사용하면 보다 효과적으로 정보시스템들을 평가하고 정당화할 수 있으리라 생각된다.

• Journal of Educational Research in Mathematics
• /
• v.16 no.1
• /
• pp.79-94
• /
• 2006

The purpose of this study is to find out the characteristics of the types(levels) of justification which are appeared by elementary mathematically gifted students in solving the tasks of plane division and spatial division. Selecting 10 fifth or sixth graders from 3 different groups in terms of mathematical capability and letting them generalize and justify some patterns. This study analyzed their responses and identified their differences in justification strategy. This study shows that mathematically gifted students apply different types of justification, such as inductive, generic or formal justification. Upper and lower groups lie in the different justification types(levels). And mathematically gifted children, especially in the upper group, have the strong desire to justify the rules which they discover, requiring a deductive thinking by themselves. They try to think both deductively and logically, and consider this kind of thought very significant.

• Communications of Mathematical Education
• /
• v.15
• /
• pp.189-194
• /
• 2003

급격하게 변하고 있는 이 사회에 맞춰 수학이 변하고 있다. 이에 따라 학교 수학에서의 증명지도가 변해야할 필요성이 있다. 본 연구에서는 기존의 증명 개념을 아우르는 보다 포괄적인 개념으로써 정당화를 소개하고 정당화 지도 방안을 제안한다. 또, 기존의 형식적이고 엄밀한 연역적 증명과 정당화가 어떻게 다른지 비교해 보고 실제 수업하는데 도움을 줄 수 있도록 활용 방안을 간단하게 제시하고자 한다.

• Communications of Mathematical Education
• /
• v.26 no.1
• /
• pp.85-108
• /
• 2012

The comprehensive implication in justification activity that includes the proof in the elementary school level where the logical and formative verification is hard to come has to be instructed. Therefore, this study has set the following issues. First, what is the mathematical justification type shown in the Number and Operations, and Geometry? Second, what are the errors shown by students in the justification process? In order to solve these research issues, the test was implemented on 62 third grade elementary school students in D City and analyzed the mathematical justification type. The research result could be summarized as follows. First, in solving the justification type test for the number and operations, students evenly used the empirical justification type and the analytical justification type. Second, in the geometry, the ratio of the empirical justification was shown to be higher than the analytical justification, and it had a difference from the number and operations that evenly disclosed the ratio of the empirical justification and the analytical justification. And third, as a result of analyzing the errors of students occurring during the justification process, it was shown to show in the order of the error of omitting the problem solving process, error of concept and principle, error in understanding the questions, and technical error. Therefore, it is prudent to provide substantial justification experiences to students. And, since it is difficult to correct the erroneous concept and mistaken principle once it is accepted as familiar content that it is required to find out the principle accepted in error or mistake and re-instruct to correct it.

• School Mathematics
• /
• v.16 no.2
• /
• pp.201-218
• /
• 2014

The purpose of this study is to research the Actual Introduction of Justification that mentioned in the middle school mathematics of 2009 Revised Curriculum. For this, researcher analyzed the new mathematics textbooks for 8th grade that will be applied 2014. Researcher and cooperators analyzed the 8th grade geometry using the criteria of advanced research. The conclusion of this study is following. Frist, Teacher need to present the various types of Justification to be used students of the different levels. Second, Teacher have to lead the activity of Justification to satisfy the needs of students.

• Korean Journal of Logic
• /
• v.22 no.1
• /
• pp.125-150
• /
• 2019

A coherence theory is adequate as a theory of justification only when justification as conceived by the theory is truth-conducive. But it is not clear how coherentist justification is truth-conducive. This is the alleged truth-conduciveness problem of coherentism. In my 2017 paper, I argued that a certain version of the coherence theory, namely a Sellarsian coherence theory combined with the deflationary conception of truth, can cope with this problem. Against this claim, Kiyong Suk argues in his recent paper that my proposed solution fails on the grounds that there is no practical way of distinguishing between intersubjective justification and objective justification. The purpose of this paper is to clarify my view by way of explaining why Suk's criticism is not correct. In particular, I argue that his criticism is based on a wrong assumption, namely that for one to be objectively justified in believing something, one's justification must be qualitatively transformed into the status of having objective justification from the status of having intersubjective justification.