• Title/Summary/Keyword: 수리논리

Search Result 68, Processing Time 0.289 seconds

Patterns of mathematical concepts and effective concept learning - around theory of vectors (수학적 개념의 유형과 효과적인 개념학습 - 벡터이론을 중심으로)

  • Pak, Hong-Kyung;Kim, Tae-Wan;Lee, Woo-Dong
    • Journal for History of Mathematics
    • /
    • v.20 no.3
    • /
    • pp.105-126
    • /
    • 2007
  • The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

  • PDF

An Investigation and Practices on Mathematics Essay Test in University Entrance Examination (대입 수리논술고사에 대한 고찰과 실제)

  • Son, Jung Hwa
    • School Mathematics
    • /
    • v.18 no.3
    • /
    • pp.503-526
    • /
    • 2016
  • The study aimed at determining the identity of mathematics essay test in the university entrance examination. For this purpose, a document research was conducted for higher order thinking and mathematics essay ability and it analyzed the goal of assessment and the tendency of problem settings and looked into mathematics essay problems of twenty-five universities. As a result, the study found out that evaluation factors of mathematics essay test requires higher order thinking ability including mathematical knowledge and essay ability such as mathematical knowledge, understanding, problem solving, logical and critical thinking, creative ability, power of expression, argument skills. Also, problems from previous mathematics essay tests were set mainly to assess mathematical knowledge, understanding and problem solving. Based on the findings, the past mathematics essay tests in university entrance examination in Korea that require logical and critical thinking, creative ability, power of expression, argument skills were a rather small percentage of questions.

Theoretical Prediction for Drying Shrinkage of Concrete (콘크리트 건조수축이 이론적 예측에 관한 연구)

  • 한만엽
    • Magazine of the Korea Concrete Institute
    • /
    • v.5 no.1
    • /
    • pp.157-164
    • /
    • 1993
  • 콘크리트내의 물의 흐름의 양과 방향을 결정하는 수리에너지의 분포는 그양의 변화에 따라 콘크리트의 수축과 팽창을 지배하는 응력의 일종이다. 따라서 이 수리에너지와 건조수축 변형율 사이에는 직접적인 연관관계가 있다. 본 논문에서는 건조수축과 수리에너지 사이의 이론적인 관계를 논리적으로 유도하여 두 개의 변수사이의 상관관계를 밝히는 이론식을 유도하였다. 본 논문에서는 세 개의 건조수축 작동구조(메카니즘)중 평상적인 상대습도하에서, 즉 50%이상에서, 작용하는 작동구조만을 고려하였다. 열전 쌍 싸이크로미터를 콘크리트 슬라브에 매설하여 수리에너지를 측정하고 동시에 건조수축량을 측정하여 두 측정값사이의 상관관계를 밝힘으로서 유도된 이론을 증명하고자 하였다. 측정결과는 본 이론의 타당성을 증명하는 동시에 본 이론이 실제 구조물의 건조수축량의 측정에 이용될수 있는 방법도 동시에 보여 주었다.

The Development of the Compensational Thinking Through the Compensation activities of 'Thinking Science' Program ('생각하는 과학' 프로그램의 보상 논리 활동에 의한 보상적 사고 수준 변화)

  • Kim, sun-Ja;Lee, Sang-Kwon;Park, Jong-Yoon;Kang, Seong-Joo;Choi, Byung-Soon
    • Journal of The Korean Association For Science Education
    • /
    • v.22 no.3
    • /
    • pp.604-616
    • /
    • 2002
  • The purpose of this study was to analyze the development of the compensational thinking by the compensation activities of 'Thinking Science' program. The 138 students were sampled in elementary schools and were divided into two groups, the experimental group of 74 students and the control group of 64 students. Both the compensation activities of the 'Thinking Science' program and a regular science curriculum were implemented to the experimental group, while only a regular science curriculum to the control group. Both experimental and control group were pre-tested with Science Reasoning Task II and compensational thinking test I and were post-tested with compensational thinking test II. This study revealed that the types of strategies used in compensation problem solving were categorized as illogical explanation, rule automation, proportionality, explanation in qualitative terms, additive quantification, inverse proportionality and were related to the context of the items. It was found that compensation activities of the 'Thinking Science' program were effective on the development of the compensational thinking.

High School Students’ Problem-Solving Strategy-Performing Ability Measured by an Essay-Type Test (서술형 검사로 측정한 고등학생의 문제 해결 전략 수행 능력)

  • Jeon, Kyung Moon;Ahn, Choong Hee;Noh, Tae Hee
    • Journal of the Korean Chemical Society
    • /
    • v.45 no.4
    • /
    • pp.370-376
    • /
    • 2001
  • In this study, high school students' problem-solving strategy-performing ability was measured by an essay-type test. The relationship between students' logical thinking ability and strategy-performing ability was also investigated. Four classes (N=187) were selected from two high schools in Seoul, and the strategy performance ability test and the Group Assessment of Logical Thinking (GALT) were administered. Evaluation scheme for strategy-performing ability consists of 7 subcategories - understanding given of problems, recalling related law, setting up subgoals, deriving physical quantities, logical progress, mathematical execution, and reviewing. The intercoder agreement for scaling was .92, which indicated substantial strength of agreement. The results revealed that students' ability of understanding given of problems and mathematical execution was relatively high. However, their ability of setting up subgoals and reviewing was very low. The total scores of the strategy performance ability test and all of the scores of each subcategory were significantly correlated with the GALT scores.

  • PDF

The Ontological Conservativeness of Logic and Mereology (논리학의 존재론적 보수성과 부분전체론)

  • Kang, Soo-Whee
    • Korean Journal of Logic
    • /
    • v.13 no.2
    • /
    • pp.167-201
    • /
    • 2010
  • This paper aims to scrutinize the possibility of mereology as philosophically satisfiable metalogic. Motivation for this is straightforward. As I see, a traditional approach to metalogic presented in the name of mathematical logic posits the existence of mathematical entities such as sets, functions, models, etc. to give definitions of logical concepts like logical consequence. As a result, whenever logic is used in any individual sciences, this set-theoretical metalogic cannot but add these mathematical entities to the domain of them. This fact makes this approach contradict to the ontological conservativeness of logic. Mereology, however, has been alleged to be ontologically innocent, while it is a formal system very similar to set theory. So it may well be that some people thought of mereology as a good substitute for set theoretic metalanguage and concepts for ontologically neutral metalogic. Unfortunately, when we look into argument for the ontological innocence of mereology, we can find that mereological entities such as mereological sums or fusions are not ontologically neutral. Thus we can conclude that mereological approach to metalogic is not promising at all.

  • PDF

인과지도의 타당성 확보와 정보 표현력 향상을 위한 이론적 고찰

  • Jeong, Jae-Un;Kim, Hyeon-Su
    • 한국경영정보학회:학술대회논문집
    • /
    • /
    • pp.817-822
    • /
    • 2007
  • 시스템 다이내믹스에서의 인가지도는 동적 환경의 문제를 분석하고, 분석된 내용을 논의할 수 있는 도구로써 활용되고 있다. 하지만, 인과지도는 복잡도가 높은 문제를 설명함에 있어서 문제에 대한 정보의 표현과 논리적인 전개에 한계가 존재한다. 그리고 인과지도의 작성 과정에서 연구자의 주관성을 배제 하고 오류를 검증하기 위한 객관적 기준이 미흡한 실정이다. 또한, 문제 해결을 위한 세부적인 개체 모델링과의 연계성이 부족하다. 이에 일각에서는 시스템 다이내믹스의 문제분석에 관한 방법론에 지적을 가하는 경우도 있다. 이에 본 연구에서는, 인과지도의 타당성 확보와 정보 표현력 향상을 위한 이론적 연구를 진행하고자 한다. 본문에서는 인과지도가 객관적인 논리에 의해 작성될 수 있도록 수리적, 논리적 근거들을 제시함과 동시에, 인과지도의 정보 표현력 향상을 통한 대화도구로서의 기능적 향상 방안에 대해서 연구를 진행하였다.

  • PDF

비트겐슈타인의 철학과 퍼지 논리 - 언어 사용을 중심으로 -

  • 박창균
    • Journal for History of Mathematics
    • /
    • v.13 no.2
    • /
    • pp.145-150
    • /
    • 2000
  • This paper is intended to show that fuzzy logic can be understood in the context of the late Wittgenstein's philosophy. It introduces the view of language presupposed by fuzzy logic and parallels it with the late Wittgenstein's view of language. To make the parallel clear it contrasts the views of the early Wittgenstein and the late Wittgenstein.

  • PDF

교사양성대학에서의 수학사 및 수리철학 강좌 운영

  • Sin, Hyeon-Yong;Seo, Bong-Geon
    • Communications of Mathematical Education
    • /
    • v.15
    • /
    • pp.1-7
    • /
    • 2003
  • 수학사 및 수리철학에 관한 연구는 교사양성 대학에서 더욱 강조되어야 할 부분임에도 불구하고 그에 관한 연구가 미진하다. 자연대의 수학과는 수학 그 자체가 중요하겠지만, 교사양성 대학에서는 수학 내용자체 뿐만 아니라, 수학의 역사적인 측면과 수학에 관한 인식론적인 측면이 함께 요구되어 진다. 절대적인 것으로 인식되어 온 수학에 대한 잘못된 선입견은 수학교육에도 심각한 악영향을 끼칠 수 있다. 그러나 괴델의 불완전성 정리 등으로 인해 수학에서의 논리체계는 더 이상 절대적이지 않다는 것을 알 수 있다. 본 연구에서는 숱한 오류들의 극복을 통해 발전해 온 수학사적인 측면과 그로 인하여 수학에 관한 인식론적 변화를 수학에서의 큰 사건들을 중심으로 살펴보고자 한다. 구체적으로 유클리드 기하에서 비유클리드 기하의 발견, 칸토어의 무한한 역설의 발생, 역설을 극복하기 위한 수학기토론의 탄생, 괴델의 불완전성 정리로 이어지는 과정들을 살펴보고, 그로 인해 도출되어지는 수학교육적 시사점을 논의해 보며, 이르르 바탕으로 교사양성 대학에서의 수학사 및 수리철학 강좌의 운영 방안을 제시한다.

  • PDF

The Intuition in History of Mathematical Philosophy and Mathematics (수리철학과 수학의 역사에서 직관)

  • Lee Dae Hyun
    • Journal for History of Mathematics
    • /
    • v.18 no.2
    • /
    • pp.23-30
    • /
    • 2005
  • Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.

  • PDF