• Communications of Mathematical Education
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• v.25 no.3
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• pp.577-591
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• 2011

In this study, in order to use computer in mathematical learning effectively, we investigate application of computer shown textbooks in geometry unit of middle school mathematics. First, we analyzed about status of computer application and method of computer application in 27 textbooks. We presented concrete example of mathematics activity using computer that can be used by teachers. Also, we tried to find out the direction to use computer more effectively in teaching and learning geometry. Through this process, we do not simply use computer to play for interest but to use it more meaningfully.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.121-131
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• 1999

Recently our educational methodologies have been changed to an open, student-centered structure. Mathematics is now learned through experiential interaction and less emphasis is placed on abstract theories. For example, the axioms of the geometry in the middle school curriculum have been expressed by using symbolic letters. Students find these abstractions very difficult and it hinders their ability to grasp the significance of geometrical concepts. In an effort to simplify these abstract concepts and enhance the students interest and ability to learn, the GSP (Geometry Sketchpad) is proving to be a useful and effective tool. First, Second and third grade students have found the GSP to be extremely useful. While the pad has no sound function it still enables the students to freely change diagrams without disrupting the integrity of the program. There is also a running order of instructions at the bottom of the screen to facilitate the step by step understanding of mathematical procedures. This function makes the program ideal for use by teachers, students and even beginners. Anyone experiencing difficulty can get immediate assistance from the guidebook which is located at the back of each program. Allowing individuals to manipulate and actually see the changing deductions and axiom proofs on the computer screen provides them with immediate feedback and reinforcement. It also enhances their overall interest in learning geometry. The use of the GSP is proving to be an innovative and effective tool in facilitating the transition of mathematics into an open, student-centered educational forum.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.310-316
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• 2003

One of the significant subject in the automatic arc welding is to establish control system of the welding parameters for controlling bead geometry as a criterion to evaluate the quality of arc welding. This paper proposes an inference algorithm for bead geometry in CMA Welding using Neuro-Fuzzy algorithm. The characteristic welding parameters are measured by the circuit composed of hall sensor, voltage divider tachometer, etc. and then the bead geometry of each weld pool is calculated and detected by an image processing with CCD camera and a measuring with microscope. The relationships between the characteristic welding parameters and the bead geometry have been arranged empirically. From the result of experiments, membership functions and fuzzy rules are tuned and determined by the learning of neural network, and then the relationship between actual bead geometry and inferred bead geometry are concluded by fuzzy logic controller. In the applied inference system of bead geometry using Neuro-Fuzzy algorithm, the inference error percent is within -5%∼+4% in case of bead width, -10%∼+10% in bead height, -5%∼+6% in bead area, -10%∼+10% in penetration. Use of the Neuro-Fuzzy algorithm allows the CMA Welding system to evaluate the quality in bead geometry in real time as the welding parameters change.

• School Mathematics
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• v.1 no.1
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• pp.109-122
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• 1999

In this paper we give a description of students' obstacles in their learning of geometry, especially resulted from their confusing a physical drawing with a figure, a geometrical object which a physical drawing represents. In computer-based teaching-learning environment, we could relieve such obstacles through providing students for experiences in which they must focus on elements of a figure and relations of them. But there may be potential in computer-based environment if we offer students only visual experience for validity of geometrical gacts: students' lack of understanding for need of proof and experience of cognitive obstacles which is very important for students to reflect their thinking and activities. Thus an didactical treatment must follows, which we also give an example.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1721-1737
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• 2020

Human apparent age estimation has become a popular research topic and attracted great attention in recent years due to its wide applications, such as personal security and law enforcement. To achieve the goal of age estimation, a large number of methods have been pro-posed, where the models derived through the cumulative attribute coding achieve promised performance by preserving the neighbor-similarity of ages. However, these methods afore-mentioned ignore the geometric structure of extracted facial features. Indeed, the geometric structure of data greatly affects the accuracy of prediction. To this end, we propose an age estimation algorithm through joint feature selection and manifold learning paradigms, so-called Feature-selected and Geometry-preserved Least Square Regression (FGLSR). Based on this, our proposed method, compared with the others, not only preserves the geometry structures within facial representations, but also selects the discriminative features. Moreover, a deep learning extension based FGLSR is proposed later, namely Feature selected and Geometry preserved Neural Network (FGNN). Finally, related experiments are conducted on Morph2 and FG-Net datasets for FGLSR and on Morph2 datasets for FGNN. Experimental results testify our method achieve the best performances.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.643-671
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• 2012

The purpose of this study was to examine How the exploratory activities using Excel and GSP which are exploratory software, in learning analytic geometry affected on the underachievers' analytic geometry concept development process. The subjects of 5 students who received the 8th~9th grades from their examination of the last semester, participated in a total of 7 units based on Skemp's intelligent learning model. The results of the study showed that there were two important cases found to nearly achieve the category $R_2$. One was reflective thinking could happen through exploratory software in category $R_1$. The other was the exploratory activities which could have the same effectiveness as the relational understanding in category $I_2$, as Skemp mentioned that there is a room to be achieved in the elementary level when such relational understanding is achieved.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.691-708
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• 2010

The purpose of this study is to analyze 'datum' of 'The Data' in the textbooks of middle school on the basis of 'The Data of Euclid' and develop datum. For this, the followings are conducted. First, the distinctive structure of datum of 'The Data' is considered. Second, some learning materials the contents of geometry in the textbooks of middle school are analyzed and the mathematical meanings are explored. Third, the applicable datum to geometry education of middle school are developed and the way of educational use is studied. The hopefully, the result of this study will make school mathematics education more plentiful and give meaningful implications to revision of mathematics education curriculum and the improvement of teaching and learning.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.299-314
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• 2008

The purposes of this study were to investigate what attitudes students have toward learning proofs and what difficulties they have in learning proofs, and to examine how the use of dynamic geometry software, the Geometer's Sketchpad, helps students' proof learning. The study involved 117 9th graders in 2 high schools. According to questionnaire data, over 50 percent of the total respondents(116) indicated negative attitudes toward learning proofs, on the other hand, only 16 percent of the total respondents indicated positive attitudes toward the learning. Memorizing and remembering many kinds of theorems, definitions, and postulates to use in proving statements was the most difficult part in learning proofs, which the largest proportion of the total respondents indicated. The study found that the use of the Geometer's Sketchpad played positive roles in developing students' understanding of proofs and stimulating students' interests in learning proofs.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.4
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• pp.132-139
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• 2002

In GMAW(Gas Metal Arc Welding) processes, bead geometry (penetration, bead width and height) is a criterion to estimate welding quality. Bead geometry is affected by welding current, arc voltage and travel speed, shielding gas, CTWD (contact-tip to workpiece distance) and so on. In this paper, welding process variables were selected as welding current, arc voltage and travel speed. And bead geometry was reasoned from the chosen welding process variables using neuro-fuzzy algorithm. Neural networks was applied to design FL(fuzzy logic). The parameters of input membership functions and those of consequence functions in FL were tuned through the method of learning by backpropagation algorithm. Bead geometry could be reasoned from welding current, arc voltage, travel speed on FL using the results learned by neural networks. On the developed inference system of bead geometry using neuro-furzy algorithm, the inference error percent of bead width was within $\pm$4%, that of bead height was within $\pm$3%, and that of penetration was within $\pm$8%. Neural networks came into effect to find the parameters of input membership functions and those of consequence in FL. Therefore the inference system of welding quality expects to be developed through proposed algorithm.

• The Journal of Korean Association of Computer Education
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• v.4 no.1
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• pp.99-107
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• 2001

One of the main objects of geometry in mathematics education is to improve students' geometric intuition capability and logical reasoning capability based on them. A visual element related to intuition plays an important role in teaching and learning of geometry. Therefore, in this research, we focus on the development of multimedia title available to dynamic operation about visual elements and verify of effect of its application. This title for the learning of "the Pythagorean theorem and its practical use" in the third grade of middle school is designed and implemented by an authoring tool, Toolbook. And it enables learners to study mathematics individually and can be applied to the educational field, too. And we taught two groups, the applied group and the compared one of the second grade of middle school and surveyed Questions and evaluated study achievement. We calculated study achievement of two groups on t-test using SPSS. As the result, we knew that the applied group is higher than the compared one in the study achievement and provision of dynamic operation possibility on visual elements make students know very high learning effect and help improvement of intelligent capability.