• Journal of Science Education
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• v.43 no.1
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• pp.79-93
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• 2019

There have been great concerns on induction, deduction, abduction, and hypothetical deductive method as scientific method and logic behind the method. However, as seen from the similar logic structure of abduction and hypothetical deductive method logic, distinction of those four terms could be unclear. This study investigates statements of science instruction textbooks concerning those terms to analyze their meaning as scientific method or in the context of inquiry. For this purpose, related statements are extracted from seven textbooks to investigate the definitions and examples of those terms and relation among these terms by focusing on coherence of usage of the terms and the possibility of clear distinction among the terms. We find that those terms do not have coherent meanings in the textbooks and many statements make it hard to distinguish the meanings of the terms. Finally the origin of the confusion and educational implication is discussed.

• School Mathematics
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• v.6 no.3
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• pp.283-299
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• 2004

It is a very important objective of mathematical education to lead students to apply mathematics to the problem situations and to solve the problems. Assuming that mathematical modeling is appropriate for such mathematical education objectives, we must emphasize mathematical modeling learning. In this research, we focused what mathematical concepts are learned and what reasoning are applied and used through mathematical modeling. In the process of mathematical modeling, the students used several types of reasoning; deduction, induction and abduction. Although we cannot generalize a fact by a single case study, deduction has been used to confirm whether their model is correct to the real situation and to find solutions by leading mathematical conclusion and induction to experimentally verify whether their model is correct. And abduction has been used to abstract a mathematical model from a real model, to provide interpretation to existing a practical ground for mathematical results, and elicit new mathematical model by modifying a present model.

• Annual Conference on Human and Language Technology
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• 1991.10a
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• pp.171-177
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• 1991

한글 표현에 나타난 부정의 사용의 애매성에서 부터 그 속의 어떠한 종류이던간의 특성을 귀납적으로 추론하는 것은 언어학적으로 중요하나, 부정이 가지고 있는 원초적인 문제를 고찰하는 것이 또다른 측면으로 한글속의 부정을 조명하여 볼 수도 있을 것이다. 그래서 부정의 개념적 구조에서 부터 한글 표현에서의 부정의 사용을 이해하여 보려는 형식적 구조에서 시작하여서 한글 부정의 특성을 살펴 보고자 한다.

• School Mathematics
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• v.18 no.3
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• pp.589-609
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• 2016

In this study, researchers have modernly reinterpreted geometric solving of cubic equations presented by an arabic mathematician, Omar Khayyam in medieval age, and have considered the pedagogical significance of geometric solving of the cubic equations using two conic sections in terms of analytic geometry. These efforts allow to analyze educational application of mathematics instruction and provide useful pedagogical implications in school mathematics such as 'connecting algebra-geometry', 'induction-generalization' and 'connecting analogous problems via analogy' for the geometric approaches of cubic equations: $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$ and $x^3=ax+b$. It could be possible to reciprocally convert between algebraic representations of cubic equations and geometric representations of conic sections, while geometrically approaching the cubic equations from a perspective of connecting algebra and geometry. Also, it could be treated how to generalize solution of cubic equation containing variables from geometric solution in which coefficients and constant terms are given under a perspective of induction-generalization. Finally, it could enable to provide students with some opportunities to adapt similar solving procedures or methods into the newly-given cubic equation with a perspective of connecting analogous problems via analogy.

• Journal of the Korean Geographical Society
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• v.35 no.3
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• pp.455-474
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• 2000

제 7 차 교육과정에서 경제지리 과목이 심화 선택 과목으로 새롭게 설정되었다. 그러나 제 6차 교육과정 한국지리 과목의 경제지리 교육내용을 단순 확대.심화시켜 구성하였기 때문에, 그 동안의 비판과 문제점을 해결하지 못하고 있다. 지리교육에서 경제 지리교육내용의 선정 및 조직 바법은 산업별 분류방법, 주제 중심방법, 경제과정 중심방법으로 분류할 수 있는데, 기존은 교육과정은 산업별 분류방법을 근간으로 하고 있다. 본 연구에서는, 공급자의입장에서 나열적으로 교육내용을 선정.조직하고 있는 기존 방법의 문제점을 개선하고, 실생활에서 학습의 유용성을 확인시켜 학습자의 관심과 흥미를 갖게 하며, 다양한 형태의 교수-학습 활동이 가능하도록 하면서, 심화 선택 과목의 특성을 살릴 수 있는 경제 지리 과목의 교육내용 선정 및 조직 대안으로 지역문제 중심방법을 제안한다.

• School Mathematics
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• v.19 no.1
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• pp.153-170
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• 2017

This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.

• Korean Journal of Logic
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• v.15 no.2
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• pp.223-250
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• 2012

The reference-class problem is known as a problem that frequentism on the nature of probability is supposed to encounter. Alan H$\acute{a}$jek argues that other theories on the nature of probability also meet this problem inevitably and claims that we can resolve the problem by regarding conditional probabilities as primitive. In this paper I shall present an adequate way of understanding the reference-class problem and its philosophical implications by scrutinizing his argument. H$\acute{a}$jek's claim is to be classified into the following two: (i) probability is relative to its reference class and (ii) what is known as the 'Ratio' analysis of conditional probability is wrong. H$\acute{a}$jek believes that these two are to be closely related but I believe these two should be separated. Moreover, I shall claim that we should accept the former but not the latter. Finally, regarding the identity condition of reference class I shall distinguish the extensional criterion from the non-extensional one. I shall claim that the non-extensional criterion is the right one for the identity condition of reference class by arguing that the reference-class problem should be regarded as an instance of the qua-problem.

• 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 the Korean School Mathematics Society
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• v.15 no.3
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• pp.511-533
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• 2012

In order to determine whether there is a significant correlation between relational understanding and creative math. problem finding ability, this study performed relational understanding and problem finding ability tests on a sample of 186 8th grade middle school students. According to the study results, we found a very significant positive correlation between relational understanding and the creativity of the mathematising ability and the combining ability of mathematical concepts in the problem finding ability. Although there was no statistically significant correlation between relational understanding and the extension ability of mathematical facts, the results from analyzing the students response rate and actual scores in each test showed that students with high relational understanding scores also had high response rate and high scores in analogical reasoning and inductive reasoning. Through this study, therefore, relational understanding is found to have a positive impact on the creative mathematics problem finding ability.

• Korean Business Review
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• v.21 no.1
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• pp.1-17
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• 2008

This article examines the establishment of the game theoretic model for the cleaner vehicles and analyzes the established model. We discuss the way to represent the players' preferences over the outcomes to make the model applicable in real practice. In this article we employ the real data to represent the preferences. In the analysis of the model we consider various scenarios and discuss how we can use GAMBIT, which is a game theory analysis software, to find solutions in each proposed scenario.