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

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

• 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.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.207-219
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• 2007

Students have a hard time with a formal proof, which is one of most important part in mathematics education. They were taught the proof with algebraic visual materials using technology and specialized visual materials. But, they experienced the difficulty in justifying due to the lack of experimental recognition with the representation using technology. The specialized visual materials limited the extension of mathematics thinking of students because it worked only for the case that is fixed. In order to solve this type of problem, we made algebraic visual materials for 9th graders using technology and generalized visual materials so that students experience for themselves to help them to experience experimental justification, thus we recognized that they were improved in enhancing mathematical thinking.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.159-178
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• 2003

This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

• School Mathematics
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• v.10 no.1
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• pp.23-42
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• 2008

The purpose of this study was to describe characteristics of thinking in elementary gifted students' solutions to algebraic tasks. Especially, this paper was focused on the students' strategies to develop generalization while problem solving, the justifications on the generalization and metacognitive thinking emerged in stildents' problem solving process. To find these issues, a case study was conducted. The subjects of this study were four 6th graders in elementary school-they were all receiving education for the gifted in an academy for the gifted attached to a university. Major findings of this study are as follows: First, during the process of the task solving, the students varied in their use of generalization strategies and utilized more than one generalization strategy, and the students also moved from one strategy toward other strategies, trying to reach generalization. In addition, there are some differences of appling the same type of strategy between students. In a case of reaching a generalization, students were asked to justify their generalization. Students' justification types were different in level. However, there were some potential abilities that lead to higher level although students' justification level was in empirical step. Second, the students utilized their various knowledges to solve the challengeable and difficult tasks. Some knowledges helped students, on the contrary some knowledges made students struggled. Specially, metacognitive knowledges of task were noticeably. Metacognitive skills; 'monitoring', 'evaluating', 'control' were emerged at any time. These metacognitive skills played a key role in their task solving process, led to students justify their generalization, made students keep their task solving process by changing and adjusting their strategies.

• Korean Journal of Legislative Studies
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• v.15 no.1
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• pp.261-290
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• 2009

The primary purpose of this study is to explain the changing nature of Korean Democratic Labor Party, namely the revealed characteristics contrary to the party's original identity, based on empirical framework of so-called "Korean Democratic Labor Party' as a Parliamentary Party". This paper focuses on the unanticipated phenomenon that Korean Democratic Labor Party, in spite of its expectancy as an alternative party model to overcome the challenges of Korean party politics, has lost its characteristics as a mass party but has revealed the characteristics of parliamentary party since it took parliamentary seats in National Assembly.

• School Mathematics
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• v.6 no.1
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• pp.59-90
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• 2004

This study has been established with two purposes. The first one is to development the learning-teaching model for enhancing students' creative proof capacities in the domain of demonstrative geometry as subject content. The second one is to aim at experimentally testing its effectiveness. First, we develop the learning-teaching model for enhancing students' proof capacities. This model is named the generative-convergent model based instruction. It consists of the following components: warming-up activities, generative activities, convergent activities, reflective discussion, other high quality resources etc. Second, to investigate the effects of the generative-convergent model based instruction, 160 8th-grade students are selected and are assigned to experimental and control groups. We focused that the generative-convergent model based instruction would be more effective than the traditional teaching method for improving middle school students' proof-writing capacities and error remediation. In conclusion, the generative-convergent model based instruction would be useful for improving middle grade students' proof-writing capacities. We suggest the following: first, it is required to refine the generative-convergent model for enhancing proof-problem solving capacities; second, it is also required to develop teaching materials in the generative-convergent model based instruction.

• 한국지구과학회:학술대회논문집
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• 2010.04a
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• pp.19-19
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• 2010

현재 과학교육의 목표는 과학적 소양의 함양이며 이를 구현하기 위해서는 교실에서의 과학탐구의 실현을 필수로 하고 있다. 과학자들이 경험하는 과학탐구는 "실질적 과학탐구(ASI)"라고 하여 필수적인 5가지 탐구요소(문제제기, 자료수집, 설명형성, 설명평가, 발표 및 정당화)를 포함하고 있다. 현재 사용하고 있는 지구과학내용의 교과서를 이 ASI 관점으로 분석하여 5가지 탐구요소의 분포도를 분석하고 이를 이용하여 지구과학탐구를 가르치는 초임교사를 대상으로 탐구에 대한 인식 및 교수실천을 같은 ASI관점으로 분석하였다. 탐구요소 2,3,4 에 해당하는 '증거수집', '설명형성' 그리고 '설명평가'는 빈번하게 나타났으나 탐구요소 1에 해당하는 '문제제기'나 5에 해당하는 '발표 및 정당화'의 기회는 나타나지 않았다. 특히 다른 과학(화학)과목 경우에 '증거수집'이 가장 빈번한 것에 비해 지구과학의 경우에는 '설명형성'이 주를 이루는 것은 지구과학탐구의 특징이라 할 수 있겠다. 또한 교과서 탐구기능은 SAPA로 분석한 결과 일반화, 의사소통, 예상, 그래프작성, 자료해석이 주를 이루었다. 과학적 소양을 함양을 위한 실질적인 과학탐구의 실현하기 위해서는 자유탐구와 같은 부차적인 기회를 통해서 경험하지 못한 ASI의 탐구요소의 기회를 학생들에게 부여해야 할 것이다. 또한 이 연구에 참여한 지구과학 초임교사의 과학탐구 인식 및 교수실천 또한 ASI로 분석한 결과 탐구요소 2번째에 치우친 경향을 보여주고 있었다. 실질적인 과학탐구의 실현을 위해서는 교과서에서 강조되는 탐구요소뿐만 아니라 다른 탐구요소를 경험할 수 있는 자유탐구를 개발하여 실용화해야 할 것이며, 관련 초임교사연수를 통해 초임교사들의 과학탐구에 대한 인식 및 교수실천의 반영 및 이들의 새로운 형성이 추진되어야 할 것이다.