• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• 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.

• Proceedings of the Technology Innovation Conference
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• 1992.12a
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• pp.97-118
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• 1992

To date, the implementation and adoption of new manufacturing technologies has been retarded despite their technical advances and strategic virtues such as flexibility and synergy effect. This phenomenon is partly attributable to the lack of commensurate development and widespread dissemination of adequate selection and justification procedures. Many strategically vital automation projects have been rejected and/or seemingly promising proposals have turned out to be fiascos since the justification process has been solely based on the traditional capital budgeting or engineering economy methods. As the degree of system automation/integration increases, a variety of benefit/cost attributes, both quantitative and qualitative, should be taken into account and more comprehensive and analytic justification methods should be applied in the justification process. This paper points out the distinct characteristics of advanced technologies and presents an illustrative set of procedures that can be used in the justification process. It outlines the algorithmic structure of each procedure and also describes the advantages/disadvantages of each procedure and the conditions under which it is most appropriate to employ. The selection of appropriate justification technique is situation-specific. In general, it is recommended that more complex and sophisticated procedures be used as the degree of integration increases. Nonetheless, traditional procedures may be used as well to make in-depth analyses of the local impact.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Education of Primary School Mathematics
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• v.16 no.3
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• pp.267-283
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• 2013

Mathematical justification is the process through which one's claim is validated to be true based on proper and trustworthy data. But it serves as a catalyst to facilitate mathematical discussions and communicative interactions among students in mathematics classrooms. This study is designed to investigate the effects of mathematical justification on students' problem-solving and communicative processes occurred in a mathematics classroom. In order to fulfill the purpose of this study, mathematical problem-solving classes were conducted. Mathematical justification processes and communicative interactions recorded in problem understanding activity, individual student inquiry, small and whole group discussions are analyzed. Based on the analysis outcomes, the students who participated in mathematical justification activities are more likely to find out various problem-solving strategies, to develop efficient communicative skills, and to use effective representations. In addition, mathematical justification can be used as an evaluation method to test a student's mathematical understanding as well as a teaching method to help develop constructive social interactions and positive classroom atmosphere among students. The results of this study would contribute to strengthening a body of research studying the importance of teaching students mathematical justification in mathematics classrooms.

• The Mathematical Education
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• v.51 no.4
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• pp.377-393
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• 2012

The understanding demands the different degree of the understanding according to student's learning situation. In this paper, we investigate what is the foundation for the complete understanding for the generalization in the generalization-process and justification of some concepts or some theories, through a case. We discovered that the completeness of the understanding in the generalization-process and justification requires 'the meaningful-mental object' which can give the meaning about the concept or theory to students. Students can do the generalization-process through the construction of 'the meaningful-mental object' and confirm the validity of generalization through 'the meaningful-mental object' which is constructed by them. And we can judge the whether students construct the completeness of the understanding or not, by 'the meaningful-mental object' of the student. Hence 'the meaningful-mental object' are vital condition for the generalization-process and justification.

• Korean Journal of Child Studies
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• v.35 no.3
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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.

• Education of Primary School Mathematics
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• v.7 no.2
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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.

• The Mathematical Education
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• v.48 no.2
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• pp.149-167
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• 2009

This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

• The Journal of Industrial Distribution & Business
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• v.11 no.8
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• pp.39-49
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• 2020

Purpose: Current study aimed at exploring the roles of system justification in the effects of consumers' self-identification with the threatened social in-group on the within-domain versus across-domain consumption. It focused on whether there are positive effects of both of the self-definition and the self-investment on the in-group system justification, and also explored whether the system justification, in turn, could make positive effects on the consumption. Research design, data and methodology: The self-identification was approached in view of self-definition and self-investment when the in-group was threatened by members of their out group. The empirical study was performed with the single factor within-subject design based on the feeling of the consumers' being threatened when the in-group was criticized by the others. The in-group threatened was accessed from the memory of each of the undergraduate students participating in the empirical study by asking them to remember the events by which their important in-group was perceived to be threatened in their past life. Questionnaire data collected from the undergraduate students were used to verify research hypotheses by structural equation model in Amos 21.0 program. Results: First, the self-definition positively affected the within-domain versus across-domain consumption, but did not affect the in-group system justification. Second, the self-investment positively affected the in-group system justification. Third, the system justification made positive effects on the within-domain versus the across-domain consumption. Therefore, this article could contribute to the development of the theory related to compensatory consumption in the view that there could be the positive mediation roles of system justification in the effects of consumers' self-investment to their in-group on the within-domain versus across-domain consumption when the in-group is threatened. Conclusions: The results of this study could give managerial implications to brand or product marketing managers. How to vitalize consumers' self-definition with, and self-investment to, the threatened in-group is at issue to the marketers when consumers' important in-group was threatened by others. By evoking the in-group-based self-investment to consumers when the in-group was threatened, the marketers should increase the level of the system justification, and the marketers should promote the consumers to recognize that their products or brands are included into the within-self domain.