• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.461-483
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• 2017

The ability to think mathematically and to reason inductively are basics of logical reasoning and the most important skill which students need to acquire through their Math curriculum in elementary school. For these reasons, we need to conduct an analysis in their procedure in inductive reasoning and find difficulties thereof. Therefore, through this study, I found parts which covered inductive reasoning in their Math curriculum and analyzed the abilities and characteristics of students in solving a problem through inductive reasoning.

• Journal of The Korean Association For Science Education
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• v.38 no.6
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• pp.839-851
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• 2018

The purpose of this study is to analyze the science reasoning differences of elementary school students' science writing. For this purpose, science writing activities and analysis frameworks were developed. Science writing data were collected and analyzed. Third to sixth grade elementary students were selected from a middle high level elementary school in terms of a national achievement test in Seoul. A total of 320 writing materials were analyzed. The results of the analysis were as follows. Science writings show science reasoning at 52 % for $3^{rd}$ grade, 68% for $4^{th}$ grade, 85% for $5^{th}$ grade, and 89% for $6^{th}$ grade. Three types of scientific reasoning such as inductive reasoning, deductive reasoning, and abductive reasoning appeared in science writing of the third to sixth graders. The abductive reasoning appeared very low in comparing with inductive and deductive reasoning. Level three appeared the most frequently in the science writing of the elementary students. The levels of inductive and deductive reasoning in science writing increased according to increasing grade and showed statistical differences between grades. But the levels of abductive reasoning did not show an increasing aspect according to increasing grade and also did not show statistical differences between grades. The levels of inductive reasoning and deductive reasoning of the 3rd grade was very low in comparing with the other grades.

• Communications of Mathematical Education
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• v.8
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• pp.137-150
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• 1999

본 연구의 목적은 아동들의 수학 교과에 대한 정의적 특성과 수학적 문제 해결력, 추론 능력간의 상호 관계를 구명하고, 이러한 관계들은 아동의 지역적인 환경에 따라 차이가 있는지를 분석하는 것이다. 본 연구를 통하여 얻은 결론은 다음과 같다. 정의적 특성의 하위 요인 중 수학적 문제 해결력과 귀납적 추론 능력에 대한 설명력이 가장 높은 요인은 수학교과에 대한 자아개념인 것으로 나타났으며, 연역적 추론 능력에 대한 설명력은 학습 습관이 가장 높은 것으로 나타났다. _그리고 귀납적 추론 능력이 연역적 추론 능력 보다 수학적 문제 해결력에 대한 설명력이 더 높은 것으로 나타났으며, 수학적 문제 해결력과 귀납적 추론 능력은 지역별로 유의한 차가 나타났으나 연역적 추론 능력은 지역간 유의한 차이가 나타나지 않았다.

• School Mathematics
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• v.14 no.1
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• pp.85-107
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• 2012

Problem solving is important in school mathematics as the means and end of mathematics education. In elementary school, inductive reasoning is closely linked to problem solving. The purpose of this study was to examine ways of improving problem solving ability through analysis of inductive reasoning process. After the process of inductive reasoning in problem solving was analyzed, five different stages of inductive reasoning were selected. It's assumed that the flow of inductive reasoning would begin with stage 0 and then go on to the higher stages step by step, and diverse sorts of additional inductive reasoning flow were selected depending on what students would do in case of finding counter examples to a regulation found by them or to their inference. And then a case study was implemented after four elementary school students who were in their sixth grade were selected in order to check the appropriateness of the stages and flows of inductive reasoning selected in this study, and how to teach inductive reasoning and what to teach to improve problem solving ability in terms of questioning and advising, the creation of student-centered class culture and representation were discussed to map out lesson plans. The conclusion of the study and the implications of the conclusion were as follows: First, a change of teacher roles is required in problem-solving education. Teachers should provide students with a wide variety of problem-solving strategies, serve as facilitators of their thinking and give many chances for them ide splore the given problems on their own. And they should be careful entegieto take considerations on the level of each student's understanding, the changes of their thinking during problem-solving process and their response. Second, elementary schools also should provide more intensive education on justification, and one of the best teaching methods will be by taking generic examples. Third, a student-centered classroom should be created to further the class participation of students and encourage them to explore without any restrictions. Fourth, inductive reasoning should be viewed as a crucial means to boost mathematical creativity.

• 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.

• The KIPS Transactions:PartB
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• v.11B no.1
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• pp.83-90
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• 2004

Strategic games are missing special qualities of genre these days. Game engines neither reason about behaviors of computer objects nor have learning ability that can prepare countermeasure in variously command user's strategy. This paper suggests a strategic game engine that applies non-monotonic reasoning and inductive machine learning. The engine emphasizes three components -“user behavior monitor”to abstract user's objects behavior,“learning engine”to learn user's strategy,“behavior display handler”to reflect abstracted behavior of computer objects on game. Especially, this paper proposes two layered-structure to apply non-monotonic reasoning and inductive learning to make behaviors of computer objects that learns strategy behaviors of user objects exactly, and corresponds in user's objects. The engine decides actions and strategies of computer objects with created information through inductive learning. Main contribution of this paper is that computer objects command excellent strategies and reveal differentiation with behavior of existing computer objects to apply non-monotonic reasoning and inductive machine learning.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.299-327
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• 2023

In this study, we tried to find out the level of inductive reasoning ability and the aspects of visualization components shown in students in the class using exploratory software for the 'congruence and symmetry' unit in the second semester of the 5th grade of elementary school. To this end, classes using GeoGebra, one of the exploratory software, were conducted for a total of 19 students in one class of fifth graders in elementary school, and the results of the students' activities were analyzed. As a result of this study, the level of inductive reasoning ability of students remained at a similar level or developed, and it was shown that students inferred new properties of shapes using various functions of software inductively. In addition, in terms of visualization, students were able to quickly and easily draw shapes that met the conditions, and unlike the paper-and-pencil environment, using the 'measurement' and 'symmetry' functions, they transformed and manipulated complex yet precisely congruent and symmetrical external representations. Based on these analysis results, implications for the use of exploratory software in the area of figures were derived.

• 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 Cognitive Science
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• v.25 no.3
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• pp.233-257
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• 2014

Category-based induction is one of major inferential reasoning methods used by humans. This research tested the effect of perceived within-category variability on the inductive generalization. Experiment 1 manipulated variability by directly presenting category exemplars. After displaying low variable (low variability condition) or highly variable exemplars (high variability condition) depending on condition, participants performed inductive generalization task about a category in question. The results showed that participants have greater confidence in generalization when category variability was low than when it was high. Rather than directly presenting category exemplars in Experiment 2, participants performed induction task after they formed category variability impression by categorization task of identifying category exemplars. Experiment 2 also found the tendency that participants have greater inductive confidence when category variability was low. The variability effect discovered in this research is distinct from the diversity effect in previous research and the category-based induction model proposed by Osherson et al. (1990) cannot fully account for the variability effect in this research. Test of variability effect in category-based induction is discussed in the general discussion section.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.461-472
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• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.