• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.6
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• pp.1996-2011
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• 2021

To understand a trend is to explore the intricate process of how something or a particular situation is constantly changing or developing in a certain direction. This exploration is about observing and describing an unknown field of knowledge, not testing theories or models with a preconceived hypothesis. The purpose is to gain knowledge we did not expect and to recognize the associations among the elements that were suspected or not. This generally requires examining a massive amount of data to find information that could be transformed into meaningful knowledge. That is, looking through the lens of big-data analytics with an inductive reasoning approach will help expand our understanding of the complex nature of a trend. The current study explored the trend of well-being in South Korea using big-data analytic techniques to discover hidden search patterns, associative rules, and keyword signals. Thereafter, a theory was developed based on inductive reasoning - namely the hook, upward push, and downward pull to elucidate a holistic picture of how big-data implications alongside social phenomena may have influenced the well-being trend.

• 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.

• 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.

• Journal of Korean Elementary Science Education
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• v.37 no.4
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• pp.372-390
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• 2018

The purpose of this research is to know the scientific reasoning ability of elementary students. In order to find it, 320 elementary students wrote a report about germination of the 700 or 2,000 years old seeds. Their writings were analyzed by scientific writing analysis frameworks, Scientific Reasoning Types and Scientific Reasoning Level Criteria developed by Lim (2018). Minto Pyramid Principles was used to show statements and relations of statements related to scientific reasoning. This paper showed scientific reasoning statements of elementary students about germination of seeds. The characteristics of scientific reasoning of elementary students were as follows. In the process of logical writing by the types of scientific reasoning, many students showed various characteristics and different levels. In the writings based on inductive reasoning, they did not distinguish between common features and differences of cases, and did not derive the rules based on common features and differences of the cases. In the writings based on deductive reasoning, there were cases where the major premise corresponding to the principle or rule was omitted and only the phenomenon was described, or the rule was presented but not connected with the case. In the writings based on abductive reasoning, the ability to selectively use the background knowledge related to the question situation was not sufficient, and borrowing of similar background knowledge, which was commonly used in other situations, was very rare.

• 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 Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.

• 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.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.241-245
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• 1989

A knowledge based expert system is a computer program that emulates the reasoning process of a human expert in a specific problem domain. This paper presents an expert system to diagnose the various faults in power system. The developed expert system is represented considering two points; the possibility of solution and the fast processing speed. As uncertainties exist in the facts and rules which comprise the knowledge base of the expert system, Certainty Factor, which is based on the confirmation theory is used for the inexact reasoning. Also, as the diagnosis problem requires the inductive reasoning process in nature, the solution is imperfect and not unique in general. So the expert system is designed to generate all the possible hypothesis in order of the possibility and also it can explain the propagation procedure of the faults for each solution using the built in backtracking mechanism. In realization of the expert system, the processing speed is greatly dependent upon the problem representation, reasoning scheme and search strategy. So, in this paper the fault diagnosis problem itself is analysed from the view point of Artificial Intelligence and as a result, the expert system has the following basic features. 1) The certainty factor is adopted in the inference engine for inexact reasoning. 2) Problem apace is represented using the problem reduction technique. 3) Bidirectional reasoning scheme is used. 4) Best first search strategy is adopted for rapid processing. The expert system was developed us ing PROLOG language.