• Title/Summary/Keyword: combinatorial reasoning

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

  • Shin, Jae-Hong;Lee, Joong-Kweon
    • School Mathematics
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    • v.11 no.3
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    • pp.351-368
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    • 2009
  • This study presents data from a year-long teaching experiment which illustrate how two seventh graders modified their multiplicative thinking and interacted with their representing symbols in the context of combinatorial problem situations. Damon was at the process of construction of recursively multiplicative thinking by modifying his multiplicative reasoning, but Carol appeared to remain at the stage of a binary multiplicative scheme. The two students' struggles with their representing symbols or represented symbols by the teacher show that even well-organized symbolic systems from teachers' perspective do not necessarily help students advance their mathematical capacity.

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

  • Kim, Young-Min;Kim, Soo-Hyun
    • Journal of The Korean Association For Science Education
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    • v.29 no.4
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    • pp.437-449
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    • 2009
  • The purpose of the study is to meta-analyze research results on Korean students' logical thinking ability. The results of meta-analysis on the research studies between the year 1980 and the year 2000 show that about 40-50% of Korean middle school students have conservation reasoning, proportional reasoning and combinatorial reasoning abilities, and that about 25-30% of them have control of variables and probability reasoning abilities. In addition, only 8% of the Korean middle-school students have correlational ability. When comparing their logical thinking ability results with those of Japanese and American middle-school students, The ratio (32.6%) of Korean middle-school students who have formal thought ability is a little higher than that of American students (30.6%), but much lower than that of Japanese students (50.1%).

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

  • 신현숙
    • Journal of Gifted/Talented Education
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    • v.5 no.2
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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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The Effects of Computational Thinking of Algorithm Learning using Logo for Primary Pre-service Teachers (Logo를 이용한 정보과학적 사고 기반의 알고리즘 학습이 예비 초등교사에게 미치는 영향)

  • Kim, Tae-Hoon;Kim, Byeong-Su;Kim, Jong-Hoon
    • Journal of The Korean Association of Information Education
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    • v.16 no.4
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    • pp.463-474
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    • 2012
  • The necessity of computer science education has been increased in the society which has been changing rapidly by the development of information science. But most elementary school teachers don't realize its necessity and don't recognize the notion of computational thinking which is the fundamental principle of computer science. In this research, we designed and implemented an algorithm learning program based on computational thinking with using Logo, which was for pre-service elementary school teachers to be able to realize the necessity of computer science education and recognize computational thinking. As the findings analyzed between pre- and post-test, the averages of correlational reasoning, combinatorial reasoning and the sum of overall logical thinking increased significantly. Also, participants' awareness of computer science education and computational thinking changed positively.

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

  • Soh, Won-Joo;Woo, Jong-Ok
    • Journal of The Korean Association For Science Education
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    • v.14 no.3
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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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Operational Definition of Components of Logical Thinking in Problem-solving Process on Informatics Subject (정보 교과의 문제해결과정에서 논리적 사고력 구성요소에 대한 조작적 정의)

  • Yoon, Il-Kyu;Kim, Jong-Hye;Lee, Won-Gyu
    • The Journal of Korean Association of Computer Education
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    • v.13 no.2
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    • pp.1-14
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    • 2010
  • Previous researches on the improvement of logical thinking in Informatics subject have used general logical thinking test and only limited improvement of logical thinking by programming learning result. In this study, the operational definition of the logical thinking in problem-solving process on Informatics education is different from the general logical thinking and the logical thinking of the other subjects. Firstly, we suggested the operational definition of components of logical thinking using the open questionnaire by expert and research team discussion. Also, we suggested the relationship between the operational definition and contents of the 'problem-solving methods and procedure' section in secondary Informatics subject. Finally, this study developed the evaluation contents based on the operational definition of components of logical thinking. The components of logical thinking which was required in problem-solving process on Informatics subject were ordering reasoning, propositional logic, controlling variables, combinatorial logic, proportional reasoning. We suggested the relationship between operational definition and problem-solving process and assessment of logical thinking in problem-solving process on Informatics subject. This paper will give meaningful insight to supply the guideline of the teaching strategy and evaluation methods for improving the logical thinking in Informatics education.

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

  • Kim, Yeong-Sang;Yu, Gi-Yeong
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.37 no.2
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    • pp.21-30
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    • 2000
  • If there exists a model that calculates the proper candidate position whenever the game of Go is in progress, it can be used for setting up the prototype of the candidate generation algorithm without using case-based reasoning. In this paper, we analyze Go through combinatorial game theory and on the basis of probability matrix (PM) showing the difference of the territory of the black and the white. We design and implement a candidate generation system(CGS) to find the candidates at a situation in Go. CGS designed in this paper can compute Influence power, safety, probability value(PV), and PM and then generate candidate positions for a present scene, once a stone is played at a scene. The basic strategy generates five candidates for the Present scene, and then chooses one with the highest PV. CGS generates the candidate which emphasizes more defence tactics than attack ones. In the opening game of computer Go, we can know that CGS which has no pattern is somewhat superior to NEMESIS which has the Joseki pattern.

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

  • Kwon, Oh-Byung
    • Asia pacific journal of information systems
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    • v.19 no.3
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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.