• Journal of Korean Society of Transportation
• /
• v.12 no.3
• /
• pp.5-13
• /
• 1994

In the fields of rail and road design, most vertical alignment design have been thus far heavily dependent upon trial-and-errors of experienced engineers. However, it has long been inefficient in productivity of designing process. In order to overcome this inefficiency, this paper presents the optimal vertical alignment design method using mathematical optimization techniques. For optimization, mathematical model to minimize the construction cost is formulated and the separable programming technique and the Zoutendijk method are introduced to solve it. As result, it is shown that this optimization technique can give efficient solutions to all vertical alignment design fields with properly-estimated cost function.

• The Mathematical Education
• /
• v.46 no.4
• /
• pp.423-443
• /
• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• The Mathematical Education
• /
• v.62 no.1
• /
• pp.35-55
• /
• 2023

The purpose of this study is to examine not only students' cognition in the mathematical error-finding activity of the concept of irrational numbers, but also the students' learning stance regarding the use of errors and a teacher's questioning strategies that lead to changes in the level of mathematical discourse. To this end, error-finding individual activities, group activities, and additional interviews were conducted with 133 middle school students, and students' cognition and the teacher's questioning strategies for changes in students' learning stance and levels of mathematical discourse were analyzed. As a result of the study, students' cognition focuses on the symbolic representation of irrational numbers and the representation of decimal numbers, and they recognize the existence of irrational numbers on a number line, but tend to have difficulty expressing a number line using figures. In addition, the importance of the teacher's leading and exploring questioning strategy was observed to promote changes in students' learning stance and levels of mathematical discourse. This study is valuable in that it specified the method of using errors in mathematics teaching and learning and elaborated the teacher's questioning strategies in finding mathematical errors.

• Industrial Engineering and Management Systems
• /
• v.13 no.2
• /
• pp.231-249
• /
• 2014

This paper discusses a green supply chain with a manufacturer and a collection trader, and it proposes an optimal production planning for remanufacturing of parts in used products with quality classification errors made by the collection trader. When a manufacturer accepts an order for parts from a retailer and procures used products from a collection trader, the collection trader might have some quality classification errors due to the lack of equipment or expert knowledge regarding quality classification. After procurement of used products, the manufacturer inspects if there are any classification errors. If errors are detected, the manufacturer reclassifies the misclassified (overestimated) used products at a cost. Accordingly, the manufacturer decides to remanufacture from the higher-quality used products based on a remanufacturing ratio or produce parts from new materials. This paper develops a mathematical model to find how quality classification errors affect the optimal decisions for a lower limit of procurement quality of used products and a remanufacturing ratio under the lower limit and the expected profit of the manufacturer. Numerical analysis investigates how quality of used products, the reclassification cost and the remanufacturing cost of used products affect the optimal production planning and the expected profit of a manufacturer.

• Journal of the Korean School Mathematics Society
• /
• v.13 no.1
• /
• pp.23-43
• /
• 2010

This study is to investigate how much highschool students, who have learned functional concepts included in the Middle school math curriculum, understand chapters of the function, to analyze the types of errors which they made in solving the mathematical problems and to look for the proper instructional program to prevent or minimize those ones. On the basis of the result of the above examination, it suggests a classification model for teaching-learning methods and teaching material development The result of this study is as follows. First, Students didn't fully understand the fundamental concept of function and they had tendency to approach the mathematical problems relying on their memory. Second, students got accustomed to conventional math problems too much, so they couldn't distinguish new types of mathematical problems from them sometimes and did faulty reasoning in the problem solving process. Finally, it was very common for students to make errors on calculation and to make technical errors in recognizing mathematical symbols in the problem solving process. When students fully understood the mathematical concepts including a definition of function and learned procedural knowledge of them by themselves, they did not repeat the same errors. Also, explaining the functional concept with a graph related to the function did facilitate their understanding,

• Communications of Mathematical Education
• /
• v.2
• /
• pp.181-191
• /
• 1997

The purpose of this study is to provide the primary sources to improve the problem solving performance by analyzing the errors and the strategies selection of the high school students when solving given algebraic problems. To attain the purpose of this study, the questions for investigation in this study are : 1. What are the differences / similarities in the patterns of errors committed by successful and unsuccessful problem-solvers when solving particular algebraic problems ? 2. What are the error types chosen by unsuccessful problem-solvers when solving particular algebraic problems? 3. Do students utilize checking, either locally or globally, when solving particular algebraic problems? Twenty students were drawn out of 10th grade students in J girls' high school in Yengi -gun, Chung-Nam, for this study. The problem-solving test was used as a test instrument. From the data, the verbal protocols and the written protocols were analyzed by the patterns. The conclusions drawn from the results obtained in the present study are as follows: First, in solving particular algebraic problems, when the problems were solved with one strategy, most students didn't give any consideration to other strategies. So mathematics teachers should teach them to use the various strategies, and should develop the problems to be used the various strategies. Second, in solving particular algebraic problems, errors on notions or transformations of equations were found. Thus, the basic knowledges related to equation should be taught. In addition, most unsuccessful students seleted the strategies inadequately to solve the problems because of misunderstanding the problems. So, to improve the problem solving performance the processes of 'understanding problem' should be emphasized to students. Third, although the unsuccesful students used the 'checking' processes when solving the problems, most of them did not find the errors because of misconceptions related to the problems, carelessness, and unskillfulness of checking. Thus, students must be taught more carefully and encouraged to use the checking.

• Journal of Korean Society for Quality Management
• /
• v.17 no.2
• /
• pp.17-26
• /
• 1989

This paper is concerned with forecasting the existing number of errors in the computer software and optimizing the stopping time of the software test based upon the forecasted number of errors. The most commonly used models have assessed software reliability under the assumption that the software failure late is proportional to the current fault content of the software but invariant to time since software faults are independents of others and equally likely to cause a failure during testing. In practice, it has been observed that in many situations, the failure rate decrease. Hence, this paper proposes a mathematical model to describe testing situations where the failure rate of software limearly decreases proportional to testing time. The least square method is used to estimate parameters of the mathematical model. A cost model to optimize the software testing time is also proposed. In this cost mode two cost factors are considered. The first cost is to test execution cost directly proportional to test time and the second cost is the failure cost incurred after delivery of the software to user. The failure cost is assumed to be proportional to the number of errors remained in the software at the test stopping time. The optimal stopping time is determined to minimize the total cost, which is the sum of test execution cast and the failure cost. A numerical example is solved to illustrate the proposed procedure.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.459-466
• /
• 2009

In this paper, a numerical scheme is introduced to solve the Cauchy problem for one-dimensional hyperbolic equations. The mesh points of the proposed scheme are distributed along characteristics so that the solution on the stencil can be easily and accurately computed. This is very important in reducing errors of the scheme because many numerical errors are generated when the solution is estimated over grid points. In addition, when characteristics intersect, the proposed scheme combines corresponding grid points into one and assigns new characteristic to the point in order to improve computational efficiency. Numerical experiments on the inviscid Burgers' equation have been presented.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.1211-1215
• /
• 2003

Accurate mathematical models of spacecraft components are an essential of spacecraft attitude control system design, analysis and simulation. Gyro is one of the most important spacecraft components used for attitude propagation and control. Gyro errors may seriously degrade the accuracy of the calculated spacecraft angular rate and of attitude estimates due to inherent drift and bias errors. In order to validate this model, nominal case simulation has been performed and compared for the low range mode and high range mode, respectively. In this paper, a mathematical model of gyro containing the relationships for predicting spacecraft angular rate and disturbances is proposed.

• East Asian mathematical journal
• /
• v.27 no.1
• /
• pp.35-49
• /
• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].