• 제목/요약/키워드: combinatorial reasoning

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중학교 1학년 학생들의 '경우의 수' 문제 해결과정에서 나타나는 표현기호와의 상호작용을 통한 곱셈추론 양식의 변화 (An Investigation of Two Seventh Graders' Modification of their Multiplicative Reasoning for Solving Combinatorial Problems and their Reciprocal Interactions with Represented Symbols)

  • 신재홍;이중권
    • 대한수학교육학회지:학교수학
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    • 제11권3호
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    • pp.351-368
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    • 2009
  • 본 연구는 일 년간 행해진 두 명의 중학교 1학년 학생들과의 교육실험 자료로부터 '경우의 수'를 다룬 문제를 푸는 과정에서 어떻게 두 학생들이 자신들의 곱셈 추론양식을 수정, 변경해 나가며, 표현된 기호들과 상호작용을 해 나가는 지 보여주고 있다. Damon은 그의 곱셈적 추론방식을 수정하여 순환적 곱셈 추론의 구성단계에 있으며, Carol은 여전히 이원적 곱셈 추론 도식에 머물러 있는 것으로 보여 졌다. 이 연구는, 학생들이 그들 자신이 구성한 또는 교사에 의해 제시된 기호들을 다루는 과정에서 두 학생들이 겪는 어려움을 통해, 교사의 관점에서 잘 구성된 기호양식이라 하더라도, 그것이 반드시 학생들의 수학적 능력향상으로 연결되지 않을 수도 있음을 보여주고 있다.

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우리나라 중학생들의 논리적 사고 능력에 대한 메타 분석 - 1980 ${\sim}$ 2000년까지의 학술지 게재 논문을 중심으로 - (A Meta-analysis on the Logical Thinking Ability of Korean Middle-School Students - Meta-analysis of the researches between 1980 and 2000 -)

  • 김영민;김수현
    • 한국과학교육학회지
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    • 제29권4호
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    • pp.437-449
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    • 2009
  • 이 연구의 목적은 한국 중학생들의 논리적 사고에 대해 메타분석을 통해 평균적인 논리 형성 정도를 알아보는 것이다. 1980년대부터 2000년까지 학술지에 게재된 논리적 사고 하위 논리를 조사한 연구는 6편이며, 이들에 대해 메타 분석해 본 결과, 우리나라 중학생들의 GALT 검사에 의한 논리적 사고 형성자 비율은 32% 정도이며, 하위 논리별로 보면, 보존 논리 48%, 비례 논리 42%, 변인통제 논리 29%, 확률 논리 33%, 상관 논리 10%, 조합논리 35% 정도로 나타났다. 우리나라 중학생들의 논리 형성자 비율 평균은, 비슷한 시기에 다른 연구자들에 의해 조사된 미국 학생들의 수준(31%)과는 비슷하고 일본 중학생들의 수준(50%)에 비해서는 많이 떨어지는 것으로 나타났다.

영재교육 프로그램이 논리적 사고와 창의성에 미치는 효과 (The Effect of GEIK Programs for the Gifted Children upon Logical Thinking and Creativity.)

  • 신현숙
    • 영재교육연구
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    • 제5권2호
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    • pp.139-156
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    • 1995
  • The purpose of the study is to examine the effects of Gifted Education Isnstitute of Korea (GEIK) programs for gifted children especially in the areas of reasoning skills and creativity, thereby proving the effectiveness of the program. The subjects are 136 (103 boys and 33 girls) fourth, fifth, and sixth grade gifted children, who have participated in GEIK programs for more than six moths. They were stratified by the length of participation in GEIK programs. Ninety four children have participated for more than one year. Forty-two children have participated for less than one year. Both groups are rather homogeneous in IQ scores and school achievement levels at the time of enterance into GEIK programs. Both a Group Assessment of Logical Thinking (GAIT) and a Creativity test were used for the study on reasoning skills and creativity. GALT, developed by V. Roadranka, R. H. Yeany and M. J. Padilla in 1983, consists of 12 questions. It is classified into six subscales: conservation, proportional reasoning, controlling variables, provability reasoning, correlational reasoning, and combinatorial reasoning. The reliability of this test is .85. This test recommends to classify the stages of child development as follows according to the total test score. 0-4 point: Concrete Stage, 5-7 points: Transitional Stage, and 8 and above points: Formal stage. The Creativity Test was developed by Y. Lee and W. Chung (1971). It consists of four components: fluency, flexibility, originality, and openness. Only both fluency and openness were used in this study. In order to analyze data, T-Test, Intercorrelational Analyses, ANOVA, and Nultiple Regression were used. Followings are the results deduced from the above analoyses of the data. First, 43.48% of the subjects were on Concrete Stage, 36.78% were on the Transitional Stage, and 19.86% were on the Formal Stage in the developmental level classified by Piaget. Second, the students who have participated in GEIK programs more than one year acquired significantly higher score in GALT than the students who have participated in GEIK programs less than one year. Third, boys showed higher score in GALT than girls did. Fourth, there were statistically significant intercorrelations between six subscales of GALT. Fifth, the students who have participated in GEIK programs more than one year acquired significantly higher score in openness of creativity test than the students who have participated in GEIK programs less than one year. There were no significant differences in openness of creativity test between boys and girls. Sixth, the students who have participated in GEIK programs more than one year acquired significantly higher score in fluency of creativity test than the students who have participated in GEIK programs less than one year. Girls showed higher score in fluency of creativity test than boys did. Seventh, the students who acquired higher score in GALT showed higher score in both openness and fluency of creativity test. Followings are the conclusions deduced form the above results. First, the developmental level of reasoning skills of the fourth grade students participationg in GEIK programs is the same as that of 7th grade of normal Korean students and the same as those of 10th grade of U.S.A. and Philipoine students. Second, the GEIK programs are effective in improving reasoning skills. Third, the GEIK programs are effective in improving creativity. Fouth, reasoning skills and creativity can be improved by well planned programs. In conclusion, this study suggests that beyond reasoning skills and creativity, other areas such as areas in science skills, mathmatical skills, or verbal skills, etc., should be studied in the future.

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Logo를 이용한 정보과학적 사고 기반의 알고리즘 학습이 예비 초등교사에게 미치는 영향 (The Effects of Computational Thinking of Algorithm Learning using Logo for Primary Pre-service Teachers)

  • 김태훈;김병수;김종훈
    • 정보교육학회논문지
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    • 제16권4호
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    • pp.463-474
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    • 2012
  • 정보과학기술의 발달로 급변하는 사회에서 정보교육의 필요성에 대한 목소리가 높아지고 있다. 하지만 초등학교의 대부분의 교사들은 정보교육의 필요성을 체감하지 못하고 핵심원리인 정보과학적 사고에 대하여 인지하지 못하고 있는 실정이다. 본 연구에서는 예비 초등교사들이 정보교육의 필요성을 체감하고 정보과학적 사고를 올바로 인지할 수 있도록 Logo를 이용한 정보과학적 사고 기반의 알고리즘 학습 프로그램을 설계하고 시행하였다. 사전, 사후검사를 분석한 결과 예비교사의 논리적 사고력 중 상관논리, 조합논리와 논리적 사고력 합계의 평균이 유의미하게 상승하였다. 또한 정보교육과 정보과학적 사고에 대한 예비교사들의 인식이 긍정적으로 변화한 것으로 나타났다.

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중학생의 논리적 사고력과 통합적 과학탐구 능력에 관한 한.일 비교연구 (A Comparative Study of the Logical Thinking Skills and Integrated Process Skills of Junior High School Students in Korea and Japan)

  • 소원주;우종옥
    • 한국과학교육학회지
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    • 제14권3호
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    • pp.312-320
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    • 1994
  • The purpose of this study is to analyze the relationship of logical thinking skills and integrated process skills, and to investigate the differences in general tendency of subskills by grade level and gender between Korean middle school students and Japanese one. The performance level of skills was measured using GALT and TIPS II. The results are compared with those of Japan (Mattheis et al., 1992). Summary of the results are as follow. 1. Percentages of formal and transitional stage of males are more than females in developmental level. It has been found out that the males attained significantly higher scores of logical thinking skills than the females in middle school stage. The significant differences in scores by gender show a good correlation with those for Japanese middle school students. Developmental level of Korean middle school students shows a remarkable improvement as they move up from 8th grade to 9 one. The significant differences in developmental level by grade also show a good correlation with those for Japanese middle school students. Total scores of GALT for Japanese middle school students are higher than Korean one, but it has been found nearly same scores for 9th grade in both countries. Scores of subskills of logical thinking skills, except correlational reasoning, for Korean students show lower than those for Japanese students. It could be noted that the combinatorial reasoning is considered to be easiest and the correlational reasoning to be most difficult in both countries. 2. It also has been found out similar pattern for integrated process skills in both countries because the males and females did not examplify significant differences, although males gain somewhat higher scores than females in Korea. Scores of subskills of integrated process skills for Japanese middle school students show higher them Korean one. It could be noted that the identifying variables is considered to be easiest and stating hypothesis to be most difficult in both countries. 3. There was a significant relationship (r= .65) between logical thinking skills and integrated process skills, and there were statistically significant differences of the integrated process skills for developmental level. In integrated process skills, the students who belong to the higher grade levels acquired better score than who belong to the lower grade level. It has been also found remarkable improvement between 8th and 9th grade, and there are significant differences for grade level in both countries.

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정보 교과의 문제해결과정에서 논리적 사고력 구성요소에 대한 조작적 정의 (Operational Definition of Components of Logical Thinking in Problem-solving Process on Informatics Subject)

  • 윤일규;김종혜;이원규
    • 컴퓨터교육학회논문지
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    • 제13권2호
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    • pp.1-14
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    • 2010
  • 지금까지의 정보 교과에서의 논리적 사고력 향상에 관한 연구는 대부분 일반적인 논리적 사고력 검사지를 바탕으로 이루어졌으며, 프로그래밍 학습 결과를 통한 논리적 사고력의 향상에 한정되어 있다. 본 연구에서는 일반적인 논리적 사고력의 특성 및 타 교과에서 논리적 사고력의 특성과 달리 정보 교과의 문제 해결 과정에서의 논리적 사고력의 조작적 정의를 제시하였다. 먼저, 정보 교과의 문제 해결 과정에서 요구되는 논리적 사고력의 구성요소를 선정하고, 각각에 대한 조작적 정의를 개방형식의 전문가 설문과 연구자 숙의 과정을 통하여 제시하였다. 또한, 각각의 조작적 정의를 바탕으로 중등 정보 교과 '문제 해결 방법과 절차' 영역의 내용요소와 연관성을 제시하고, 그에 따른 평가 문항을 개발하였다. 연구 결과, 정보 교과의 문제해결과정에서 요구되는 논리적 사고력의 구성요소는 서열화 논리, 명제 논리, 상관 논리, 변인 통제 논리, 조합 논리, 비례 논리이며, 조작적 정의와 정보교과 내용요소를 바탕으로 논리적 사고력 평가문항을 개발하여 그 실효성을 알아보았다. 본 연구 결과는 정보 교과의 논리적 사고력 신장을 위한 교수학습방법과 평가 방안의 가이드라인을 제공하는 데에서 의의를 찾을 수 있을 것이다.

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확률적 평가에 기반한 컴퓨터 바둑의 후보 생성 시스템 (A Candidate Generation System based on Probabilistic Evaluation in Computer Go)

  • 김영상;유기영
    • 전자공학회논문지CI
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    • 제37권2호
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    • pp.21-30
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    • 2000
  • 바둑이 진행될 때마다 적절한 후보 자리를 계산하는 모델이 있다면, 사례를 이용하지 않고도 후보 생성알고리즘의 표준으로 정립될 수 있다. 본 논문에서는 바둑을 조합 게임론에 따라서 분석하고, 흑, 백간 영역의 차이를 반면의 형세로 나타내는 확률 행렬(PM)을 기반으로 임의의 국면에 대한 후보를 생성하는 후보 본 논문에서 설계된 CGS는 임의의 국면에 돌이 놓여지면 영향력, 안정도, 살아남을 확률 값(PV), 확률행렬(PM)을 계산하고, 현 국면에 대한 적당한 후보를 생성한다. CGS의 기본 전략은 현재의 반면에 대해서 다섯 개의 후보를 생성하고 그 중에서 PV가 높은 지점을 최종 후보로 선정한다. CGS는 공격보다 방어에 주력하였으며 정석 사례를 사용하는 NEMESIS에 비해서 사례를 전혀 구축하지 않은 CGS가 초반에 있어서 다소 우세함을 보여준다.

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보다 정확한 동적 상황인식 추천을 위해 정확 및 오류 패턴을 활용하여 순차적 매칭 성능이 개선된 상황 예측 방법 (Context Prediction Using Right and Wrong Patterns to Improve Sequential Matching Performance for More Accurate Dynamic Context-Aware Recommendation)

  • 권오병
    • Asia pacific journal of information systems
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    • 제19권3호
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    • pp.51-67
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    • 2009
  • Developing an agile recommender system for nomadic users has been regarded as a promising application in mobile and ubiquitous settings. To increase the quality of personalized recommendation in terms of accuracy and elapsed time, estimating future context of the user in a correct way is highly crucial. Traditionally, time series analysis and Makovian process have been adopted for such forecasting. However, these methods are not adequate in predicting context data, only because most of context data are represented as nominal scale. To resolve these limitations, the alignment-prediction algorithm has been suggested for context prediction, especially for future context from the low-level context. Recently, an ontological approach has been proposed for guided context prediction without context history. However, due to variety of context information, acquiring sufficient context prediction knowledge a priori is not easy in most of service domains. Hence, the purpose of this paper is to propose a novel context prediction methodology, which does not require a priori knowledge, and to increase accuracy and decrease elapsed time for service response. To do so, we have newly developed pattern-based context prediction approach. First of ail, a set of individual rules is derived from each context attribute using context history. Then a pattern consisted of results from reasoning individual rules, is developed for pattern learning. If at least one context property matches, say R, then regard the pattern as right. If the pattern is new, add right pattern, set the value of mismatched properties = 0, freq = 1 and w(R, 1). Otherwise, increase the frequency of the matched right pattern by 1 and then set w(R,freq). After finishing training, if the frequency is greater than a threshold value, then save the right pattern in knowledge base. On the other hand, if at least one context property matches, say W, then regard the pattern as wrong. If the pattern is new, modify the result into wrong answer, add right pattern, and set frequency to 1 and w(W, 1). Or, increase the matched wrong pattern's frequency by 1 and then set w(W, freq). After finishing training, if the frequency value is greater than a threshold level, then save the wrong pattern on the knowledge basis. Then, context prediction is performed with combinatorial rules as follows: first, identify current context. Second, find matched patterns from right patterns. If there is no pattern matched, then find a matching pattern from wrong patterns. If a matching pattern is not found, then choose one context property whose predictability is higher than that of any other properties. To show the feasibility of the methodology proposed in this paper, we collected actual context history from the travelers who had visited the largest amusement park in Korea. As a result, 400 context records were collected in 2009. Then we randomly selected 70% of the records as training data. The rest were selected as testing data. To examine the performance of the methodology, prediction accuracy and elapsed time were chosen as measures. We compared the performance with case-based reasoning and voting methods. Through a simulation test, we conclude that our methodology is clearly better than CBR and voting methods in terms of accuracy and elapsed time. This shows that the methodology is relatively valid and scalable. As a second round of the experiment, we compared a full model to a partial model. A full model indicates that right and wrong patterns are used for reasoning the future context. On the other hand, a partial model means that the reasoning is performed only with right patterns, which is generally adopted in the legacy alignment-prediction method. It turned out that a full model is better than a partial model in terms of the accuracy while partial model is better when considering elapsed time. As a last experiment, we took into our consideration potential privacy problems that might arise among the users. To mediate such concern, we excluded such context properties as date of tour and user profiles such as gender and age. The outcome shows that preserving privacy is endurable. Contributions of this paper are as follows: First, academically, we have improved sequential matching methods to predict accuracy and service time by considering individual rules of each context property and learning from wrong patterns. Second, the proposed method is found to be quite effective for privacy preserving applications, which are frequently required by B2C context-aware services; the privacy preserving system applying the proposed method successfully can also decrease elapsed time. Hence, the method is very practical in establishing privacy preserving context-aware services. Our future research issues taking into account some limitations in this paper can be summarized as follows. First, user acceptance or usability will be tested with actual users in order to prove the value of the prototype system. Second, we will apply the proposed method to more general application domains as this paper focused on tourism in amusement park.