• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.461-488
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• 2005

This article presents new perspectives for classification of students' mathematical errors on the basis of experiential structuralism. Experiential structuralism's mechanism gives us new insights on mathematical errors. The hard core of mechanism is consist of 6 autonomous capacity spheres that are responsible for the representation and processing of different reality domains. There are specific forces that are responsible for this organization of mind. There are expressed in terms of a set of five organizational principles. Classification of mathematical errors is ascribed by the theory to the interaction between the 6 autonomous capacity spheres. Different types of classification require different autonomous capacity spheres. We can classify mathematical errors in the domain of linear function problem solving comparing cognitive psychological mechanism of experiential structuralism.

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

• The Mathematical Education
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• v.46 no.4
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• pp.357-369
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• 2007

Teachers and students' knowledge of zero was investigated through data collected from 16 preservice secondary mathematics teachers and 20 gifted secondary school students. Results showed that these teachers and students had an inadequate knowledge about zero. They exhibited a reluctance to accept zero as an attribute for classification, confusion as to whether or not zero is a number, and stable patterns of computational error. Although leachers and researchers have long recognized the value of analyzing student errors for diagnosis and remediation, students have not been encouraged to take advantage of errors as learning opportunities in mathematics instruction. The article suggests using errors as springboards for inquiry in action, discusses its potential contributions to mathematics instruction by analyzing students and preservice teachers errors related to zero.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.699-718
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• 2012

The purpose of mathematics eduction is to develop the ability of thinking mathematically. It informs method to solve problem through mathematical thinking that teach mathematical ability. Errors in the problem solving can be thought as those in the mathematical thinking. Therefore analysis and classification of mathematics errors is important to teach mathematics. This study researches the preceding studies on mathematics errors and presents the characteristic of them with analyzed models. The results achieved by analysis of the process of problem solving are as follows : ▸ Students feel much harder to solve words problems rather than multiple-choice problems. ▸ The length of sentence make some differences of understanding of the words problems. Students easy to understand short sentence problems than long sentence problems. ▸ If students feel difficulties on the pre-learned mathematical content, they feel the same difficulties on the words problems based on the pre-learned mathematics content.

• Journal of applied mathematics & informatics
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• v.2 no.2
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• pp.13-20
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• 1995

The goal of this paper is to show that the linear approxi-mation in evaluation of functions may be effectively replaced by the ex-ponential approximation formulas obtained by numerical quadratures and in the instance the relative errors can be estimated without know-ing the true values.

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

• IEMEK Journal of Embedded Systems and Applications
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• v.12 no.5
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• pp.277-286
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• 2017

This paper introduces mathematical modelling and control algorithm of expendable mine disposal vehicle. This vehicle has two longitudinal thrusters, one vertical thruster and internal mass moving system which can control pitch rate. Also, the vehicle has an optical camera and forward looking sonar for underwater mine detection and classification. The vehicle is controlled via an optical cable connected with operating console on the mother ship. We describe the vehicle's 6DOF dynamic model and controller which can track the desired trajectory for the way-point tracking. These simulation results shows guidance and maneuvering performance which has other sensor data or not.

• Korean Journal of Geomatics
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• v.4 no.1
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• pp.23-30
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• 2004

This study aims to establish interior orientation for various types of sensors including frame cameras, panoramic cameras, line cameras, and whisk-broom scanners. To do so, this study suggests the classification of components of interior orientation of which elements are different according to the sensors. This is entailed by incorporation of sensor characteristics into mathematical models of interior orientation parameters are suggested for being used as guidelines in recovering systematic distortions. Finally, the potential errors resulted from the assumption of regarding sensor model of whisk-broom scanner model as that of push-broom scanner are discussed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.632-638
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• 2002

In novelty detection, one attempts to discriminate abnormal patterns from normal ones. Novelty detection is quite difficult since, unlike usual two class classification problems, only normal patterns are available for training. Auto-Associative Multi-Layer Perceptron (AAMLP) has been shown to provide a good performance based upon the property that novel patterns usually have larger auto-associative errors. In this paper, we give a mathematical analysis of 2-layer AAMLP's output characteristics and empirical results of 2-layer and 4-layer AAMLPs. Various activation functions such as linear, saturated linear and sigmoid are compared. The 2-layer AAMLPs cannot identify non-linear boundaries while the 4-layer ones can. When the data distribution is multi-modal, then an ensemble of AAMLPs, each of which is trained with pre-clustered data is required. This paper contributes to understanding of AAMLP networks and leads to practical recommendations regarding its use.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.2
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• pp.147-161
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• 2002

In novelty detection, one attempts to discriminate abnormal patterns from normal ones. Novelty detection is quite difficult since, unlike usual two class classification problems, only normal patterns are available for training. Auto-Associative Multi-Layer Perceptron (AAMLP) has been shown to provide a good performance based upon the property that novel patterns usually have larger auto-associative errors. In this paper, we give a mathematical analysis of 2-layer AAMLP's output characteristics and empirical results of 2-layer and 4-layer AAMLPs. Various activation functions such as linear, saturated linear and sigmoid are compared. The 2-layer AAMLPs cannot identify non-linear boundaries while the 4-layer ones can. When the data distribution is multi-modal, then an ensemble of AAMLPs, each of which is trained with pre-clustered data is required. This paper contributes to understanding of AAMLP networks and leads to practical recommendations regarding its use.