• Communications of Mathematical Education
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• v.23 no.3
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• pp.923-951
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• 2009

In this paper, we have analyzed the term examinations on quadratic equations and functions in middle schools based on the object of evaluations given by the ministry of education, science and technology of Korea.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.545-567
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• 2023

This study investigates effective ChatGPT prompts for solving mathematical problems, focusing on the chapters of quadratic equations and quadratic functions. A structured prompt was designed, following a sequence of 'Role-Rule-Example Solution-Problem-Process'. In this study, an artificial intelligence model combining GPT-4, Wolfram plugin, and Advanced Data Analysis was utilized. Wolfram was used as the primary tool for calculations to reduce computational errors. When using the structured prompt, the accuracy rate for problems from nine high school mathematics textbooks on quadratic equations and quadratic functions was 91%, showing higher performance compared to zero-shot prompts. This confirmed the effectiveness of the structured prompts in solving mathematical problems. The structured prompts designed in this study can contribute to the development of intelligent information systems for personalized and customized education.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.883-898
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• 2013

The purpose of this study is to examine that high school students recognize mathematical situation when they are requested for changing identical mathematics situations into different situations. The results of the study are followings. First, percentage of correct answers to the questions of turning equal mathematical situation into function is higher than the one of turning equal mathematical situation into equation and inequality. As a result of individual interview for comprehensibility of the students on these relations, it is found that if degree goes up and there is different expressions of questionaries although mathematical situation is identical, it affects comprehensibility of the subjects. Second, we found that they cannot understand identical mathematics situations because they have trouble in drawing graph or applying to get the answer while many students understand a point of intersection on the graph as a correct answer. Third, As a result of individual interview for comprehensibility of the students on relation between equation, inequality and function, we found that students manage to get correct answer even without perfect comprehensibility on this relation.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.525-547
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• 2015

This study analyzed the written texts of textbook and the teacher's discourse explaining 'the relationship between quadratic functions and quadratic equations' in the 9th grade high school mathematics class. Data consisted of the lecture recordings and the textbooks were analyzed based on the Halliday's systemic functional linguistics. According to the results, the written texts of the textbook used lexico-grammatical strategies such as generalization using hyponomy of meanings, mathematical objectification through nominalization and materialization of meaning through change in themes to compose mathematical concepts. The textbook generalized from an example in the description of formulating mathematical concepts, and in this process the organizational interactions of discourse-semantic level and lexico-grammartical level appeared. On the other hand, the teacher's doscourse appeared the change in transitivity and the addition of the reasons and the process. Also the teacher used explanation process of formulating the relationship between quadratic functions and quadratic equations. The linguistic characteristics of the teacher were linguistic implication and omission of lexemes due to contextual ommission. And there was no use of structural lexico-grammatical resources that influence the discourse-semantic level. This results provide a new framework for analyzing mathematical discourse, and suggest the lexico-grammatical strategies that can be used to explain mathematical concepts by teachers in math classrooms.

• Computational Structural Engineering
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• v.7 no.3
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• pp.115-122
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• 1994

Design sensitivity analysis of the second order perturbed eigenproblems for random structural system is presented. Dynamic response of random system including uncertainties for the design variable is calculated with the first order and second order perturbation method to original governing equation. In optimal design methods, there is fundamental requirement for design gradients. A method for calculating the sensitivity coefficients is developed using the direct differentiation method for the governing equation and first order and second order perturbed equation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.4
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• pp.501-507
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• 2021

Neural networks with differentiable activation functions are differentiable with respect to input variables. We improve the approximation capability of neural networks by using the gradient and Hessian of neural networks to satisfy the differential equations of the problems of interest. We apply differential neural networks to the pricing of financial options, where stochastic differential equations and the Black-Scholes partial differential equation represent the differential relation of price of option and underlying assets, and the first and second derivatives of option price play an important role in financial engineering. The proposed neural network learns - (a) the sample paths of option prices generated by stochastic differential equations and (b) the Black-Scholes equation at each time and asset price. Experimental results show that the proposed method gives accurate option values and the first and second derivatives.

• Communications of Mathematical Education
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• v.10
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• pp.505-517
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• 2000

수학 학습에서 컴퓨터와 계산기의 활용은 시각화의 강화로부터 직관력과 사고력의 향상을 가져왔다. 컴퓨터 대수체계(Computer Algebra System)가 탑재된 수학 학습용 컴퓨터 프로그램과 계산기가 활발히 사용되고 있으며, 교수매체로서의 활용은 지식 정보전달 체계와 학습자의 지식 구성방법에 새로운 패러다임을 형성하였다. 특히 수학학습용 그래픽 계산기(Graphing Calculator)는 휴대형(Hand-held Technology)으로 학습공간의 이동(Mobil Education)이 가능하며, 수학학습 전용기라는데 의미를 둘 수 있다. Symbolic Graphing Calculator를 활용한 수업에서 학습자는 계산기를 가지고, 기호연산 실행 조작을 통해 자신의 사고과정을 표현하고, Symbolic Graphing Calculator는 실행 조작에 즉각적으로 과정과 결과를 제공하며, 다른 표상과 상호작용을 함으로써 학습자 스스로의 규제가 강화된 과정을 통해 지식을 구성하게 된다. 이때 교사는 지식 정보전달 체계인 대화형 실행매체(IMTs)를 작성하여 학습자의 지식 형성에 안내자의 역할을 하게 된다. 이번 워크샵에서는 CASIO fx 2.0을 활용한 교실 수업모형을 그래프 표상과 연계한 방정식의 풀이과정을 통해 알아본다.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.43-52
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• 2007

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's, Godunov's, Osher's(physical order and natural order), Roe's, HLLE, AUSM, AUSM+, AUSMPW+ and M-AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.5
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• pp.1196-1202
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• 2013

This paper have analyzed the change of breakdown voltage for channel doping concentration and device parameters of double gate(DG) MOSFET using two dimensional potential model. The low breakdown voltage becomes the obstacle of power device operation, and breakdown voltage decreases seriously by the short channel effects derived from scaled down device in the case of DGMOSFET. The two dimensional analytical potential distribution derived from Poisson's equation have been used to analyze the breakdown voltage for device parameters such as channel length, channel thickness, gate oxide thickness and channel doping concentration. Resultly, we could observe the breakdown voltage has greatly influenced on device dimensional parameters as well as channel doping concentration, especially the shape of Gaussian function used as channel doping concentration.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1163-1170
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• 1992

A computer program was developed to analyze the two-dimensional unsteady incompressible viscous flow behind a rectangular bluff body between two parallel plates. The Peaceman-Rachford alternating direction implicit numerical method and Wachspress parameter were adopted to solve the governing equations in vorticity-transport and stream function formulation. The steady state flow and the vortex flow behind a rectangular bluff body in a chemical were investigated for Reynolds numbers of 200 and 500. The vortex shedding was generated by a physical pertubation numerically imposed at the center of the flow field for a short time. It was observed that the perturbed flow became periodic after a transient period.