• 대한수학교육학회지:학교수학
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• 제14권4호
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• pp.445-468
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• 2012

본 연구는 산술적 바탕 위에 있는 학생들이 형식적인 대수 추론으로 자연스럽게 이행하는 것을 돕고자, 초등학생들이 대수 문제를 접하였을 때 사용하는 대수 추론 전략을 조사하였다. 총 839명을 대상으로 초등학생의 대수 추론 방법을 조사한 결과, 초등학생들이 연립 일차방정식과 관련된 문장제의 해결에서 기존의 교과서에 제시된 방법 이외의 다양한 산술적 추론과 전형식적 대수 추론을 사용하는 것이 파악되었다. 또한, 대수 문제의 구조에 따라 학생들이 사용하는 추론 전략의 차이가 있음을 밝혔으며, 학생들의 대수 문제해결에서 나타나는 추론상의 오류의 원인을 분석하였다. 특히, 초등학생들이 사용하는'양적 추론'과 '비례적 추론'과 같은 전략들은 비형식적인 대입법, 이항법임을 밝혔다. 마지막으로, 이러한 전형식적 대수 추론들을 형식적 대수 추론으로 연결할 수 있는 가능성에 대하여 논의하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권3호
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• pp.291-318
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• 2002

We investigated on the primary school children's abilities of formal reasoning. Seventy students in grade 5 participated in the study. They responsed their best reactions on the problems constituted of three parts requiring the informal or formal reasoning and generalization. Their reactions are classified by some criteria depending the level of reasoning. About 10 students showed that they constructed a kind of scheme for solving the problems, similar to formal reasoning and beyond naive informal reasoning. And about 30 students did so partially. We concluded that the teaching and learning of reasoning by the progressive increasing the degree of rigor from grade 5 is possible.

• 대한수학교육학회지:수학교육학연구
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• 제16권2호
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• pp.95-113
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• 2006

본 연구는 학교 수학에서 추론 지도의 수준을 보다 상세히 구분해 보고자 한 것이다. 수학의 특징으로부터, 대상에서 분리된 순수한 형식적 관점은 새로운 지식의 창안에서 한계를 지닌다는 점을 알 수 있으며, 수학교육에서도 이를 반영할 필요가 있다고 본다. 이런 점에서 귀납 추론과 형식적 연역 추론의 매개 단계로서 구체적 조작이나 감각 경험과 관련된 직관적 증명의 수준을 설정하는 것이 적절할 것으로 생각되며, 이 수준의 핵심적인 활동은 경험으로부터 일반성을 통찰하는 것이다. 이 수준은 낮은 수준의 귀납 추론보다는 대상과 분리되며 보다 형식적인 논리의 개입을 필요로 하는 과정에 있다. 이와 같이 보다 점진적으로 대상으로부터 분리되고 형식적 논리를 학습할 수 있도록 추론 지도 수준을 구분하고, 이에 따라 수학적 추론을 지도하는 것이 필요할 것이다.

• 한국과학교육학회지
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• 제11권2호
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• pp.23-30
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• 1991

The purpose of this study is to investigate the interrelationships on integrated science process skills and Piagetian cognitive modes for high school students according to the different cognitive reasoning levels. About 509 high school students were randomly selected for the samples of this study. They were identified as concrete, transitional and formal operational stage with the scores of GALT(Group Assessment of Logical Thinking) developed by Roadrangka, Yeaney and Padilla(1982), and TIPS II(Test of Integrated Process Skills) developed by Burns, Wise and Okey(1983). The result of this study were showed that about 11.8% of the samples were in the concrete operational stage and about 24.4% of the samples were in the transitional stage, while about 63.8% of them were in the formal operational stage. It was also found that the achivement scores of the science process skills increase in accordance with the cognitive reasoning levels. The value of the correlation coefficient between science process skills and cognitive reasoning abilities was 0.49, which was significant at the 0.05 level. This finding seems to support previous research that the student's cognitive reasoning abilities appeared to have influenced student's scores of the science process skills No differences to the logical reasoning ability between male and female students according to each cognitive level were found except formal operational stage.

• 한국과학교육학회지
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• 제9권1호
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• pp.19-37
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• 1989

The purpose of this study was to investigate the development of logical thinking and scientific reasoning pattern of Korean high school students. To carry out this study subjects were selected about 2,000 Junior high school students, and about 4,100 senior high school students throughout the nation. They were identified as concrete, transitional or formal operational stage with the use of TOLT(the Test of Logical Thinking) by Tobin and Capie(1980), and TOSR(the Test of Scientific Reasoning) by W.A Farmer(1986). This study turned out that more than 76% of Junior high school students were classified as the concrete operational stage and about 44% of senior high school students were classified as the formal operational stage, while about 26% of them were still in the concrete operational level. This study showed that the main factor of the intellectual development of students is learning by the gradual advancement of their grades and especially entrance into the senior high school rather than by the physical growth. This study also showed that there are the take-off stage of the development of logical thinking between fourteen and fifteen years of their ages. Less than 25% of junior high school students were in the formal operational stages which are capable of control of variables, probabilistic, correlation and combinational logic in problem-solving situation, while 33-54% of senior high school students were in the formal operational levels. 38% of junior high school students were in the formal operational stage which is capable of proportional logic, while about 55% of senior high school students were in the formal operational stage. Less than 20% of senior high school students were classified as group of highly capable of scientific reasoning, while more than 23% of them were classified as group of poor capability. It also turned out that there are differences or no differences between male and female students of each school in problem-solving situation regarding each logic approach. These differences were proved to be fluctuating depending on the situations and their grades. The other results of this study is similar to those of other researches such as Tomlinson-Keasey 1972, Coleman 1973, Lawson 1973, Lawson and Renner 1974, Neimark 1975, Han 1982, and Kim 1989.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권4호
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• pp.243-266
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• 2013

Accompanied with ongoing calls for reform in statistics curriculum, mathematics and statistics teachers purposefully have been reconsidering the curriculum and the content taught in statistics classes. Changes made are centered around statistical inference since teachers recognize that students struggle with understanding the ideas and concepts used in statistical reasoning. Despite the efforts to change the curriculum, studies are sparse on the topic of characterizing student learning and understanding of statistical inference. Moreover, there are no tools to evaluate students' statistical reasoning in a coherent way. In response to the need for a research instrument, in a series of research study, the researcher developed a reliable and valid measure to assess students' inferential reasoning in statistics (IRS). This paper describes processes of test blueprint development that has been conducted from review of the literature and expert reviews.

• 한국초등수학교육학회지
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• 제19권4호
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• pp.457-484
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• 2015

본 연구에서는 초등학생들이 다양한 비례 추론 과제를 해결할 때 사용하는 비례 추론 전략과 정답률을 분석하여 비례 추론 능력 지도를 위한 시사점을 제공하고자 하였다. 이를 위해 비례식을 학습한 6학년 173명을 대상으로 조사 연구를 실시하였다. 비례 추론 과제는 대수 기하, 양적 질적 추론, 미지값 비교 과제로 구분하고, 선행 연구에서 사용된 비례 추론 문항을 참조하여 다양한 과제 유형을 고려한 문항으로 검사지를 구성하였다. 과제 유형별로 정답률을 살펴보면, 기하 과제보다는 대수 과제, 질적 추론 과제보다는 양적 추론 과제, 비교 과제보다는 미지값 과제의 정답률이 상대적으로 높게 나타났다. 학생들이 사용한 비례 추론 전략을 살펴보면 비례식을 학습하였음에도 불구하고 형식적 전략보다는 인수 전략, 단위 비율 전략과 같은 비형식적 전략을 사용하는 비율이 상대적으로 높게 나타났다. 이와 같은 결과를 바탕으로 비례 추론 능력 지도를 위한 시사점으로 형식적 전략의 약화와 비형식적 전략의 명시적 지도, 질적 추론의 강화 및 질적 양적 추론의 결합, 다양한 과제 유형의 균형있는 취급 등을 제안하였다.

• 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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.719-724
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• 1998

This paper presents a systematic developement of a formal approach to inference in approximate reasoning. We introduce some measures of similarity and discuss their properties. Using the concept of similarity index we formulate two methods for inferring from vague knowledge. In order to illustrate the effectiveness of the proposed technique we use it to develop a vowel recognition system.

• East Asian mathematical journal
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• 제24권5호
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.