• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.505-516
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• 2013

The purpose of this paper is to analyse the essence of proportional reasoning and to analyse the contents of the textbooks according to the mathematics curriculum revised in 2007, and to seek the direction for developing the proportional reasoning in the elementary school mathematics focused the task variables. As a result of analysis, it is found out that proportional reasoning is one form of qualitative and quantitative reasoning which is related to ratio, rate, proportion and involves a sense of covariation, multiple comparison. Mathematics textbooks according to the mathematics curriculum revised in 2007 are mainly examined by the characteristics of the proportional reasoning. It is found out that some tasks related the proportional reasoning were decreased and deleted and were numerically and algorithmically approached. It should be recognized that mechanical methods, such as the cross-product algorithm, for solving proportions do not develop proportional reasoning and should be required to provide tasks in a wide range of context including visual models.

• Journal of KIISE:Computing Practices and Letters
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• v.7 no.3
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• pp.248-259
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• 2001

This paper proposes a human action recognition scheme to recognize nonverbal human communications automatically. Based on the principle that a human body action can be defined as a combination of multiple articulation movements, we use the method of inferencing stochastic grammars to understand each human actions. We measure and quantize each human action in 3D world-coordinate, and make two sets of 4-chain-code for xy and zy projection plane. Based on the fact that the neighboring information among articulations is an essential element to distinguish actions, we designed a new stochastic inference procedure to apply the neighboring information of hands. Our proposed scheme shows better recognition rate than that of other general stochastic inference procedures. ures.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.609-627
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• 2008

The purpose of this research was to investigate the relationship between the students' strategy types and the recognition for proportional situations. The students' strategy types which were based on the results of ratio and proportion tests were divided into an additive type, a multiplicative type, and a formal type. This research analyzed the students' activities of categorization when were given the proportional problems and nonproportional problems to the students. And it also explored how to develop students' recognizing for the discrimination between the proportional situations and nonproportional situations. The results was the following. First, the students didn't discriminate the proportional situations and the nonproportional situations in the initial state but they came to discriminate little by little. Secondly, the students didn't discriminate the direct proportions and the inverse proportions until the last stage. Third, the multiplicative type was outperformed more than the formal type in solving the ratio and proportion problems but the formal type was outperformed more than the multiplicative type in discriminating between proportional situations and nonproportional situations. These results are interpreted as showing that solving ratio and proportion tasks and recognizing proportional situations are different aspects of proportional reasoning and it is necessary to understand multiplicative strategy with formal strategy in recognizing proportional situations.

• Journal of The Korean Association For Science Education
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• v.31 no.4
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• pp.587-599
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• 2011

The purpose of this study was to analyze variable-controlling strategy (below vcs) and the ability to infer the effect of variables in Middle school students who experienced 'Thinking Science' activities in a CASE program. For this study, 71 9th grade students experienced in CASE program for 2 years were selected as the experimental group and 72 students were selected as the control group. All students were tested with Science Reasoning TaskVII. The five types of variable-controlling strategy were extracted from students' response. According to the result of this study, the students experienced in CASE program was more successful in the variable-controlling strategy of length, quality, and shape than the control group. The types of reasoning ability of the variable effect intuitively were categorized as possibility of reasoning, impossibility of reasoning, and impossibility of reversible thinking. It has shown that the reasoning ability of the experimental group was higher than that of the control group in the length and thickness variable effect. The results of this study implied that the variable controlling activities in CASE program could be effective for learning variable controlling, and eventually, for the development of reasoning ability of the variable controlling effect. In the ability to infer the effects of variables to get difficult Intuitively, both groups were similar to the rate of cognitive level reached to the formal operation in generalization, and the student of experimental group was 1.5 times faster than the control group.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.117-132
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• 2009

The purpose of this study was analysis on types of strategies and errors when the sixth grade students were solving proportion problems of mathematics textbooks. For this study, proportion problems in mathematics textbooks were investigated and 17 representative problems were chosen. The 277 students of two elementary schools solved the problems. The types of strategies and errors in solving proportion problems were analyzed. The result of this study were as follows; The percentage of correct answers is high if the problems could be solved by proportional expression and the expression is in constant rate. But the percentage of correct answers is low, if the problems were expressed with non-constant rate.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06a
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• pp.282-285
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• 2011

서술논리를 기반으로 하는 OWL 온톨로지는 표준화된 형식적 언어로써 실세계의 도메인 지식을 표현하는데 적합하다. 따라서 논리를 바탕으로 명시적으로 정의된 지식 속에 내재되어 있는 새로운 지식의 추론이 가능하다. 그러나 OWL이 가지는 Open World Assumption(OWA)의 특성은 근거가 불완전하거나 완전한 정보획득이 불가능한 상황에서의 추론을 제한한다. 더불어 OWL이 가지는 또 다른 특성으로 Unique Name Assumption(UNA)의 비지원은 실제적 지식표현을 지원하는 반면, 표현의 불충분으로 인해 결과 도출의 불능을 야기한다. 이러한 특징을 고려하여, 본 논문에서는 지능형 에이전트 구성을 위한 서술논리 기반 지식 표현 방법을 제안한다. 이는 논리적 정당성을 유지하고 올바른 결과를 이끌어 낼 수 있도록 하며, 항상 논리적 결론 도출이 가능한 지식모델을 구성할 수 있도록 돕는다. 이를 통해, 지식모델에 정의된 불완전한 개념에 있어서 OWL이 가지는 특징으로 인하여 발생할 수 있는 문제점에 대한 해결방안을 제시한다. 이에 있어서, 모바일 온톨로지의 예를 통하여 OWA와 UNA에 따른 추론의 제약을 보이며, 이를 해결할 수 있는 방안을 논리적으로 표현함으로써 본 제안의 정당성을 증명한다.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.275-292
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• 2010

In this study, we discussed the way to teach algebra earlier through investigating to research trends of Early Algebra and researching about nature of subject involving algebra. There is a strong view that arithmetic and algebra have analogous forms and that algebra is on extension to arithmetic. Nevertheless, it is also possible to present a perspective that the fundamental goal and role of symbols and letters are difference between arithmetic and algebra. And, we could recognize that geometry was starting point of algebra trough historical perspectives. To consider these, we extracted some of possible directions to approaches to teach algebra earlier. To access to teaching algebra earlier, following ways are possible. (1) To consider informal strategy of young children. (2) Arithmetic reasoning considered of the algebraic relation. (3) Starting to algebraic reasoning in the context of geometrical problem situation. (4) To present young students to tool of letters and formular.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.791-810
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• 2017

This study explored the possibility of using visual models in teaching proportional reasoning based on the review of previous studies. Many studies on proportional reasoning emphasize that students tend to simply apply formal procedures without understanding the meaning behind them and that using visual models may be an alternative to help students develop informal strategies and proportional reasoning. Given these, we re-constructed and implemented the unit of a textbook to teach sixth graders proportional reasoning with ratio table, double number line, and double tape diagram. The results of this study showed that such visual models helped students understand the meaning of proportion, explore the properties of proportion, and solve proportional problems. However, several difficulties that students experienced in using the visual models led us to suggest cautionary notes when to teach proportional reasoning with visual models. As such, this study is expected to provide empirical information for textbook developers and teachers who teach proportional reasoning with visual models.