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

• Journal of Korean Philosophical Society
• /
• v.129
• /
• pp.267-290
• /
• 2014

The slippery slope argument means that if we accept a type of action A, we are committed to accepting B, C and eventually N. Then, N is situation which we must not accept morally. It works causal mechnism that B because A is raised, C because B is raised. But in the logic textbooks and treatises, the slippery slope argument is classified as fallacy. The reason is that the argument is not a causal argument. Actually, it is a probable. Also it is argued that the argument is wrong because it fears about the future extremely. But We can not say all slippery slope argument is fallacy even though a slippery slope argument is sometimes fallacy. I think it is persuasive argument in a significant place. Therefore I argue that the argument is not simple logic as a form of thinking, but practical reasoning applied the context of dialogue. So in order to find it to be practical reasoning we demand the new understanding to fallacy theory. In traditionally, fallacy is defined to wrong reasoning logically, but according to Walton, fallacy means a verbal tactic or deceptive trick that can be used to cause someone to fall down in argument. That is to say, whether or not the argument is successful depends on how it uses as argument tactic in a given context of dialogue. Therefore I argue that whether or not the argument is successful, because of it is practical problem used in a context of dialogue, is to be approached to pragma and dialectical method, not semantic.

• Journal of Educational Research in Mathematics
• /
• v.24 no.1
• /
• pp.1-27
• /
• 2014

In the present study, we analyze the four participating 9th grade students' mathematical reasoning processes in their dragging activities while solving open-ended geometry problems in terms of abduction, induction and deduction. The results of the analysis are as follows. First, the students utilized 'abduction' to adopt their hypotheses, 'induction' to generalize them by examining various cases and 'deduction' to provide warrants for the hypotheses. Secondly, in the abduction process, 'wandering dragging' and 'guided dragging' seemed to help the students formulate their hypotheses, and in the induction process, 'dragging test' was mainly used to confirm the hypotheses. Despite of the emerging mathematical reasoning via their dragging activities, several difficulties were identified in their solving processes such as misunderstanding shapes as fixed figures, not easily recognizing the concept of dependency or path, not smoothly proceeding from probabilistic reasoning to deduction, and trapping into circular logic.

• Korean Journal of Logic
• /
• v.17 no.1
• /
• pp.197-217
• /
• 2014

In my previous papers, I have argued that the so-called 'Uncontested Principle' does not hold for indicative conditionals based on inductive reasoning. This is mainly because if we accept that a material conditional '$A{\supset}C$' can be inferred from an indicative conditional based on inductive reasoning '$A{\rightarrow}_iC$', we get an absurd consequence such that we cannot distinguish between claiming 'C' to be probably true and claiming 'C' to be absolutely true on the assumption 'A'. However, in his recent paper "Uncontested Principle and Inductive Argument", Eunsuk Yang objects that my argument is unsuccessful in disputing the Uncontested Principle. In this paper, I show that his objections are irrelevant to my argument against the Uncontested Principle.

• The Mathematical Education
• /
• v.49 no.2
• /
• pp.223-246
• /
• 2010

Goos(2004) introduced educational researchers' demand for change on the way that mathematics is taught in schools and the series of curriculum documents produced by the National council of Teachers of Mathematics. The documents have placed emphasis on the processes of problem solving, reasoning, and communication. In Korea, the national curriculum documents have also placed increased emphasis on mathematical activities such as reasoning and communication(1997, 2007).The purpose of this study is to analyze the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities containing communication and reasoning for science high school students. In this paper, we introduce an inquiry-oriented instruction containing Polya's plausible reasoning, Freudenthal's guided reinvention, Forman's sociocultural approach of learning, and Vygotsky's zone of proximal development. We analyze the impact of mathematical findings from inquiry-oriented instruction on students' mathematical activities containing communication and reasoning.

• Proceedings of the KIEE Conference
• /
• 2006.04a
• /
• pp.141-143
• /
• 2006

한국을 비롯한 동양 금석학 정보 인식의 중요한 매체인 탁본을 디지털 영상데이터로 변환하여 영상 특성을 분석하고 수학적 모델을 구현한다. 이를 위해 역사적으로 유명한 대표적 탁본을 포함한 50여개의 탁본영상 샘플을 작위로 선택하였고, 샘플영상 속에 내재되어 있는 영역특성을 중심으로 통계분석을 시도하였다. 탁본 원영상은 흑백의 두 영역으로 분할되는 완벽한 이진영상인데 반하여, 관측영상은 탁본뜨기 수작업과정을 거치면서 영역간 색도의 혼재와 얼룩무늬와 문양이 전체 영상에 분포한다. 본래의 두 영역은 정보영역과 바탕영역으로 구분되나 이들 얼룩무늬들은 또 다른 영역들로 치부되어 주로 바탕영역에 산발적으로 분포되어 영상인식을 저해하는 요인으로 작용한다. 관측영상 속에 내재되어 있는 영역 본래의 특성과 본뜨기 수작업 과정에서 새로 생성되는 영역들 사이의 기하학적 차이를 통계적으로 분류 처리함으로 관측 탁본영상의 영역 특성의 추이를 추론할 수 있다. 분석 결과, 탁본영상은 영역간 극단적인 확률적 차이를 보였으며, 이 양극성은 곧 탁본 원영상의 속성이 수작업과 관측이라는 훼손 과정을 거치면서도 보존됨을 의미한다. 이를 근거로 영역 특성과 훼손 과정을 수학적으로 모델링하였고 정보영역 추출의 일차적 개연성을 제시하였다.

• Journal of Educational Research in Mathematics
• /
• v.22 no.1
• /
• pp.101-115
• /
• 2012

Analogy, a plausible reasoning on the basis of similarity, is one of the thinking strategy for concept formation, problem solving, and new discovery in many disciplines. Statistics educators argue that analogy can be used as an useful thinking strategy in statistics as well. This study investigated the characteristics of students' analogical thinking in statistics. The mathematically gifted were asked to construct similar problems to a base problem which is a statistical problem having a statistical context. From the analysis of the problems, students' new problems were classified into five types on the basis of the preservation of the statistical context and that of the basic structure of the base problem. From the result, researchers provide some implications. In statistics, the problems, which failed to preserve the statistical context of base problem, have no meaning in statistics. However, the problems which preserved the statistical context can give possibilities for reconceptualization of the statistical concept even though the basic structure of the problem were changed.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2006.05a
• /
• pp.1460-1464
• /
• 2006

강수량의 특성 및 계절적인 양상은 지협적인 원인이기 보다는 해수면 온도(sea surface temperature)와 같은 기상 현상에 주로 영향을 받는다. 이러한 관점에서 강수량과 같은 수문변량의 장기적인 거동을 기상인자로부터 유추하고자 하는 연구는 무엇보다 중요하며 이러한 추론을 바탕으로 강수량의 장기예측 및 모의를 위한 기본적인 도구로 활용을 가능케 한다. 따라서 본 연구의 주요 목적은 해수면 온도를 기본으로 강수량과 기온의 변동성 및 상관성을 분석하고자 하며, 무엇보다 한반도 근해의 해수면 온도와의 직 간접적인 개연성을 살펴봄으로서 보다 효과적인 강수량 예측을 위한 하나의 변수로서의 가능성을 평가하고자 한다. 이를 위해 다양한 분석 방법 즉, 연주기를 제거하지 않은 자료의 선형적인 지체 상관 분석, 연주기를 제거하기 위해 표준화 된 자료의 지체 상관 분석 및 비모수적 상관분석을 수행하였다. 연주기를 제거하지 않은 자료의 경우 매우 강한 상관관계를 나타내었지만 이는 주로 계절 특성으로 인한 것으로 사료된다. 그러나 연주기를 제거한 Anomaly는 상대적으로 매우 작은 상관성을 보이고 있으나 유의성 검토를 통해 통계적으로 유의한 관계가 존재함을 확인 할 수 있었다. 따라서 강수량의 예측을 하나의 변수로서 이용이 가능할 것으로 사료되나 근해뿐만 아니라 한반도 기상의 연관성을 갖는 타 지역기상인자와의 보다 통합적인 검토가 필요하다 하겠다.

• KOMUNHWA
• /
• no.61
• /
• pp.95-128
• /
• 2003

Shell middens, so called waste sites, are the remains made by files of wastes after the sources are used from the natural and artificial environment. The relic things, excavated in shell middens are usually found to be broken and hard to recognize the ori

• Journal of Educational Research in Mathematics
• /
• v.23 no.3
• /
• pp.335-351
• /
• 2013

This research assumes that abduction is so important as much as all the creative plausible reasoning to be based upon. We expect it to be deeply appreciated and be taught positively in school mathematics. We are noticing that every problem solving process must contain some steps of abduction and thus, we believe that those who are afraid of abduction cannot solve any newly faced problem. Upon these thoughts, we are looking into the middle school mathematics textbooks to see that how strongly various abductions are emphasized to solve problems in it. We modified types of abduction those were suggested by Eco(1983) or by Bettina Pedemonte, David Reid (2011) and investigated those books to see if, we may regard, various types of abduction be intended to be used to solve their problems. As a result of it, we found that more than 92% of the problems were not supposed to use creative abduction necessarily to solve it. And we interpret this as most authors of the textbooks have emphasis more on the capturing and understanding of basic knowledge of school mathematics rather than the creative reasoning through them. And we believe this need innovation, otherwise strong debates are necessary among the professionals of it.