• Communications of Mathematical Education
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• v.26 no.1
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• pp.137-154
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• 2012

Approximation' is one of central conceptions in calculus. A basic conception for explaining 'approximation' is 'tangent', and 'tangent' is a 'line' with special condition. In this study, we will study pedagogically these mathematical knowledge on the ground of a viewpoint on the teaching of secondary geometry, and in connection with these we will suggest the teaching program and the chief end for the probable teaching. For this, we will examine point, line, circle, straight line, tangent line, approximation, and drive meaningfully mathematical knowledge for algebraic operation through the process translating from the above into analytic geometry. And we will construct the stream line of mathematical knowledge for approximation from a view of modern mathematics. This study help mathematics teachers to promote the pedagogical content knowledge, and to provide the basis for development of teaching model guiding the mathematical knowledge. Moreover, this study help students to recognize that mathematics is a systematic discipline and school mathematics are activities constructed under a fixed purpose.

• Communications of Mathematical Education
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• v.29 no.1
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• pp.91-110
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• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.263-269
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• 1996

The somplest approximate confidence interval for the probability of success is the one based on the normal approximation to the binomial distribution, It is widely used in the introductory teaching, and various guidelines for its use with "large" sample have appeared in the literature. This paper suggests a guideline when to use it as an approximation to the exact confidence interval, and comparisons with existing guidelines are provided. provided.

• The Mathematical Education
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• v.59 no.3
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• pp.271-294
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• 2020

The purpose of this study was to explore the possibility of digital simulation by which pre-service teachers (PSTs) can approximate the core teaching practice of eliciting student thinking. This study examined PSTs' questions to elicit student thinking, their use of "pause" session and peer feedback, and their reflections on doing a digital simulation. We analyzed a two-hour digital simulation session with 13 PSTs who enrolled in the elementary mathematics methods course. The results showed that PSTs shifted their general questions to more content-specific questions throughout the simulation and made a quick transition to comparing students' strategies. The number of lead PST-initiated "pause" ranged one to four times for various reasons. Their peer-coaches did not voluntarily "pause" the simulation session but actively shared what they noticed from the student work samples and suggested the next teaching moves. Without utilizing the pause session, the dramatic improvement of questioning was not observed. Even though the PSTs felt overwhelmed with interacting with the student-avatars in real-time, they highlighted the benefits of simulations, appreciated the opportunity to learn the core teaching practice, and viewed this digital simulation as "real" and "authentic" experience. The findings of this study provide implications for re-designing a practice-based teacher education program.

• The Mathematical Education
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• v.37 no.1
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• pp.101-114
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• 1998

In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

• East Asian mathematical journal
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• v.34 no.4
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• pp.463-486
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• 2018

This study identifies elements involved in designing rehearsals for improving preservice teachers' capacity to teach mathematics. Observation of a secondary mathematics methods course and regular interviews with the teacher educator following each class were used in this research. After characterizing what is considered and enacted in rehearsals as a way to help preservice teachers practice the work of teaching mathematics, I illustrate them with examples from the observations and interviews. I then discuss the challenge of dual contexts-the teacher education classroom and the secondary mathematics classroom-and dual perspectives-the mathematical and pedagogical-in designing and enacting rehearsals. I conclude with implications for mathematics teacher education.

• Archives of Plastic Surgery
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• v.43 no.3
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• pp.248-253
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• 2016

Background Financial, clinical, and psychological considerations have made same-day surgery an attractive option for a variety of procedures. This article aimed to analyse the postoperative results of same-day primary unilateral cleft nasolabial repair. Methods This study was performed from 2011 to 2014. Unilateral cleft lip patients fulfilling the inclusion criteria were preoperatively classified as mild, moderate, and severe. All patients underwent same-day surgery and were discharged after satisfying the appropriate clinical criteria, receiving thorough counselling, and the establishment of a means of communication by phone. Postoperative outcomes were assessed and stratified according to preoperative severity and the type of repair. Results A total of 423 primary unilateral cleft lip patients were included. Fisher's anatomical subunit approximation technique was the most common procedure, followed by Noordhoff's technique. The postoperative outcome was good in 89.8% of cases, fair in 9.9% of cases, and poor in 0.2% of cases. The complication rate was 1.18% (n=5), and no instances of mortality were observed. The average hospital stay was 7.5 hours, leading to a cost reduction of 19% in comparison with patients who stayed overnight for observation. Conclusions Mild unilateral cleft lip was the most common deformity for which Fisher's anatomical subunit approximation technique was performed in most of the cases, with satisfactory postoperative outcomes. Refinements in the cleft rhinoplasty techniques over the course of the study improved the results regarding cleft nasal symmetry. Single-day primary unilateral cleft cheiloplasty was found to be a cost-effective procedure that did not pose an additional risk of complications.

• Smart Structures and Systems
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• v.24 no.2
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• pp.233-242
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• 2019

In this paper, an inverse approach based on uniform load surface (ULS) is presented for structural damage localization and quantification. The ULS is excellent approximation for deformed configuration of a structure under distributed unit force applied on all degrees of freedom. The ULS make use of natural frequencies and mode shapes of structure and in mathematical point of view is a weighted average of mode shapes. An objective function presented to damage detection is discrepancy between the ULS of monitored structure and numerical model of structure. Solving this objective function to find minimum value yields damage's parameters detection. The teaching-learning based optimization algorithm has been employed to solve inverse problem. The efficiency of present damage detection method is demonstrated through three numerical examples. By comparison between proposed objective function and another objective function which make use of natural frequencies and mode shapes, it is revealed present objective function have faster convergence and is more sensitive to damage. The method has good robustness against measurement noise and could detect damage by using the first few mode shapes. The results indicate that the proposed method is reliable technique to damage detection in structures.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.11
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• pp.56-65
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• 1993

This paper presents the design consideration of the MFNNs(Multilayer Feed forward Neural Networks) based on the distribution of the given teching patterns. By extracting the feature points from the given teaching patterns, the structure of a network including the netowrk size and interconnection weights of a network is initialized. This network is trained based on the modified version of the EBP(Error Back Propagation) algorithm. As a result, the proposed method has the advantage of learning speed compared to the conventional learning of the MFNNs with randomly chosen initial weights. To show the effectiveness of the suggested approach, the simulation result on the approximation of a two demensional continuous function is shown.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.743-765
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• 2019

Conceptual and procedural knowledge of integration is necessary not only in calculus but also in real analysis, complex analysis, and differential geometry. However, students show not only focused understanding of procedural knowledge but also limited understanding on conceptual knowledge of integration. So they are good at computation but don't recognize link between several concepts. In particular, Riemann sum is helpful in solving applied problem, but students are poor at understanding structure of Riemann sum. In this study, we try to investigate understanding on conceptual and procedural knowledge of integration and to analyze errors. Conducting experimental class of Riemann sum, we investigate the understanding of Riemann sum structure and so present the implications about improvement of integration teaching.