• School Mathematics
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• v.14 no.4
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• pp.445-468
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• 2012

This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

• The Mathematical Education
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• v.41 no.3
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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.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• Journal of The Korean Association For Science Education
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• v.11 no.2
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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.

• Journal of The Korean Association For Science Education
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• v.9 no.1
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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.

• Research in Mathematical Education
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• v.17 no.4
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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.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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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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• v.24 no.5
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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.