• Korean Journal of Logic
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• v.12 no.2
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• pp.59-88
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• 2009

According to David Hume, a deductive demonstration for inductive inference is not possible, because inductive inference is not deductive; and an inductive demonstration for inductive inference is not possible either, because such a demonstration is circular. Thus, on his view, there is no way of justifying inductive inference. Ever since Hume raised this problem of induction, a fair number of philosophers have tried to solve it. Nevertheless there is still no solution which is plausible enough to receive wide endorsement. According to Wilfrid Sellars, we cannot justify inductive inference by any theoretical reasoning; we can vindicate it only by a certain sort of practical reasoning. In this paper, I defend this Sellarsian proposal by developing and explaining it.

• 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.

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

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.405-422
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• 2017

Nim games were divided into three stages : one file, two files and three files game, and inquiry activities were conducted for middle school mathematically gifted students. In the first stage, students easily found a winning strategy through deductive reasoning. In the second stage, students found a winning strategy with deductive reasoning or inductive reasoning, but found an error in inductive reasoning. In the third stage, no students found a winning strategy with deductive reasoning and errors were found in the induction reasoning process. It is found that the tendency to unconditionally generalize the pattern that is formed in the finite number of cases is the cause of the error. As a result of visually presenting the binary boxes to students, students were able to easily identify the pattern of victory and defeat, recognize the winning strategy through game activities, and some students could reach a stage of justifying the winning strategy.

• 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.

• Journal of The Korean Association For Science Education
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• v.37 no.6
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• pp.1037-1049
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• 2017

The purpose of this study is to explore how the flow of discourse move and their reasoning process in dialogic argumentation during group modeling on excretion. Five groups of three to four students in the second grade of a middle school participated in the modeling practice of a Gifted Center. Analysis was conducted on argumentation during the modeling activity in which students should explain how the waste product (ammonia) leaves the body. It was found that there was a sequential argumentative process-tentative consensus, solving the uncertainty, and consensus. There were several discourse moves - 'claim' and 'counterclaim' in the stage of tentative consensus, 'query' and 'clarification of meaning' in the stage of solving the uncertainty, and 'change of claim' in the stage of consensus. Students participated in the dialogic argumentation by constructing argument collaboratively for reaching a consensus. Critical questioning in the stage of solving the uncertainty and reasoning in the stage of consensus were the impact factors of dialogic argumentation. By answering the critical questions, students changed their claims or suggested new claims by defending or rebutting previous claims. Students justified group claims with diverse argumentation scheme and scientific reasoning to reach a group consensus. These findings have implication for science educators who want to adopt dialogic argumentation in science classes.

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.155-171
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• 2024

This study compared and analyzed students' reasoning processes and justification methods when introducing the concept of "the sum of angles in a triangle" in mathematics classes with a focus on both measurement and geometric aspects. To confirm this, the research was conducted in a 4th-grade class at H Elementary School in Suwon, Gyeonggi-do, South Korea. The conclusions drawn from this study are as follows. First, there is a significant difference when introducing "the sum of angles in a triangle" in mathematics classes from a measurement perspective compared to a geometric perspective. Second, justifying the statement "the sum of angles in a triangle is 180°" is more effective when explained through a measurement approach, such as "adding the sizes of the three angles gives 180°," rather than a geometric approach, such as "the sum of the angles forms a straight angle." Since elementary students understand mathematical knowledge through manipulative activities, the level of activity is connected to the quality of mathematics learning. Research on this reasoning process will serve as foundational material for approaching the concept of "the sum of angles in a triangle" within the "Geometry and Measurement" domain of the Revised 2022 curriculum.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.459-479
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• 2006

The purpose of this study is to investigate the applicability of DGS(dynamic geometry software) for the assessment of reasoning ability and the influence of DGS on the process of assessing students' reasoning ability in middle school geometry. We developed items for assessing students' reasoning ability by using DGS in the connected form of 'construction - inductive reasoning - deductive reasoning'. And then, a case study was carried out with 5 students. We analyzed the results from 3 perspectives, that is, the assessment of students' construction ability, inductive reasoning ability, and justification types. Items can help students more precisely display reasoning ability Moreover, using of DGS will help teachers easily construct the assessment items of inductive reasoning, and widen range of constructing items.

• 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.