• Communications of Mathematical Education
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• v.25 no.3
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• pp.537-556
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• 2011

This paper focuses on proportional reasoning being emphasized in today's elementary math, and analyzes the way students use their proportional reasoning abilities and strategies according to their academic achievement levels in solving proportional problems. For this purpose, various types of proportional problems were presented to 173 sixth-grade elementary school students and they were asked to use a maximum of three types of proportional reasoning strategies to solve those problems. The experiment results showed that upper-ranking students had better ability to use, express and perceive more types of proportional reasoning than their lower-ranking counterparts. In addition, the proportional reasoning strategies preferred by students were shown to be independent of academic achievement. But there was a difference in the proportional reasoning strategy according to the types of the problems and the ratio of the numbers given in the problem. As a result of this study, we emphasize that there is necessity of the suitable proportional reasoning instruction which reflected on the difference of ability according to student's academic achievement.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.1-17
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• 2014

Recently a student's mathematical thinking and problem-solving skills are emphasized. Nevertheless, the students solved the problem associated with a given type of problem solving using mechanical algorithms. With this algorithm, It's hard to achieve the goal that are recently emphasized. Furthermore It may be formed error or misconception. However, consistent errors have positive aspects to identify of the current cognitive state of the learner and to provide information about the cause of the error. Thus, this study tried to analyze the error happening in the process of solving gearwheel-involved problem and to propose the correct teaching method. The result of student's error analysis, the student tends to solve the gear-wheel problem with proportional expression only. And the student did not check for the proportional expression whether they are right or wrong. This may be occurred by textbook and curriculum which suggests only best possible conditioned problems. This paper close with implications on the discussion and revision of the concepts presented in the curriculum and sequence related to the gearwheel-involved problem as well as methodological suggested of textbook.

• Journal of the Korean Chemical Society
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• v.46 no.6
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• pp.569-580
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• 2002

The purpose of this study was to analyze the problem-solving process of student's compensation con-cept.For this purpose, verbal interactions during activities were audio-taped, transcribed, and analyzed. And classroom observation and interview with students were carried out. Students who were superior in mathematical operations tended to explain compensation concept using proportionality. On the other hand, students who had low level of conservation concept can not connect 'relation of two variables' with 'conservation of equilibrium' at the formation process of com-pensation concept. Students who succeed in the formation of compensation concept showed high level of conservation concept. To promote the formation of compensation concept, it is necessary that how to develop proportional concept and conservation concept as closely related with compensation concept should be studied.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.283-290
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• 1998

A solution method is presented to solve the eigenproblem arising in tile dynamic analysis of non-proportional damping systems with symmetric matrices. The method is based on tile use of Lanczos method to generate a Krylov subspace of trial vectors, witch is then used to reduce a large eigenvalue problem to a much smaller one. The method retains the η order quadratic eigenproblem, without the need to the method of matrix augmentation traditionally used to cast the problem as a linear eigenproblem of order 2n. In the process, the method preserves tile sparseness and symmetry of the system matrices and does not invoke complex arithmetics, therefore, making it very economical for use in solving large problems. Numerical results are presented to demonstrate the efficiency and accuracy of the method.

• 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.

• School Mathematics
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• v.9 no.4
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• pp.447-466
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• 2007

Math education in schools have to enable students to understand the importance of math and nurture the capacity to resolve various problems in daily life with reasoning, which is therefore, always applicable to the actual world. Proportional reasoning capacity is being often used in daily life, and some kind of unit is not fixed. So students are considering it very difficult. This study looks into the difficulties that students have in proportional reasoning, what kind of problem solving strategy is being used, what the problems are in current textbooks, etc. Based on this, it tried to check the concept changes in students' proportional reasoning by developing the instruction program for 'proportional expression' unit in the 6th grade. Based on the results, this study analyzes the features of proportional reasoning instruction programs and the instruction results. Also it analyzes in-advance & after examination papers of the experimental class and comparison class to contribute to the instruction method and instruction contents improvement of 'proportional expression' unit.

• 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 Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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• pp.172-181
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• 2019

This paper deals with the problem of generating the energy optimal trajectory which is intended to enhance the target tracking performance of a passive homing missile. Noticing that the essence of passive target tracking is the range estimation problem, the target information gathered by passive measurements can be readily analyzed by introducing the range estimator designed in line-of-sight(LOS) frame. Moreover, for the linear filter structure of the suggested range estimator, the cost function associated with the target information is clearly expressed as a function of the line-of-sight rate. Based on this idea, the optimal missile trajectory maximizing the target information is obtained by solving the saddle point problem for an indefinite quadratic cost which consists of the target information and the energy. It is shown that, different from the previous heuristic approaches, the guidance command producing the optimal passive homing trajectory is produced by the modified proportional navigation guidance law whose navigation constant is determined by the weighting coefficient for target information cost.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.1
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• pp.32-45
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• 2007

The T-50 advanced supersonic jet trainer employs the Relaxed Static Stability (RSS) concept to improve the aerodynamic performance while the flight control system stabilizes the unstable aircraft and provides adequate handling qualities. The T-50 flight control laws employ a proportional-plus-integral type controller based on a dynamic inversion method in longitudinal axis and a proportional type controller based on a blended roll system with simple roll rate feedback and beta-betadot feedback system. These control laws are verified by flight tests with various maneuver set flight envelopes and the control laws are updated to resolve flight test issues. This paper describes several concepts of flight control laws used in T-50 to resolve those flight test issues. Control laws for solving the roll-off problem during pitch maneuver in asymmetric loading configurations, improving the departure resistance in negative angle of attack conditions and enhancing the fine tracking performance in air-to-air tracking maneuvers are described with flight test data.

• 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.