• School Mathematics
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• v.14 no.4
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• pp.565-577
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• 2012

In this study, we investigated the process of constructing the geometrical solutions to quadratic equation, through proportions between lengths of similar triangles in a dynamic environment. To do this, we provided one task to 4 ninth grades students and observed the process of the students' activities and strategies. As a result of this pilot lesson study, our research shows the advantage and possibility of geometrical method in learning and teaching quadratic equation.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.117-130
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• 2009

This study shows how to use effectively construction and solution of the quadratic equation developed by mathematicians such as Gyung Sun-jing, Hong Jung-ha, Hong Dae-yong, Lee Sang-hyuk, and Nam Byung-gil through mathematics history of Chosun Dynasty. Mathematics history of Chosun Dynasty can be used in order to enhance comprehension and increase interest in an introduction to the quadratic equation. It also can be used to help motivate middle school students to solve the quadratic equation with much interest during the development phase, and develope conceptual thinking and reflective thinking in the practical phase.

• 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.

• Journal of Korea Multimedia Society
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• v.6 no.5
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• pp.870-875
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• 2003

We Present digital watermarking using a quadratic equation embedding method in wavelet transform domain in order to improve the invisibility. Generally, embedding watermark used a simple equation form, but we extended a quadratic equation form in this paper. We performed a computer simulation in order to compare proposed method to other methods using LENA, GOLDHILL, BARBARA, and MAN images By computer experiments, invisibility of the proposed method better than the conventional methods at 100 % normalized similarity.

• 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 for History of Mathematics
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• v.24 no.4
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• pp.143-155
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• 2011

The discriminant is one of the important concepts in school mathematics according to second degree polynomials. In this paper we survey the history of development to discriminant of any higher degree polynomials and investigate how the discriminant works for determining the graph of polynomials.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.655-659
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• 2008

본 연구에서는 3차원 수치모의를 통하여 횡방향 하상형상 및 격자형 이차흐름 구조의 생성 메커니즘을 분석하였다. 이를 위해 곡선좌표계에서의 지배방정식을 구성하고, 난류 폐합을 위해 Speziale(1987)가 제안한 비등방성 k-$\varepsilon$모형을 이용하였다. 또한 Exner 방정식을 이용하여 시간에 따른 하상변동을 예측하였다. 그 결과 바닥과 측벽 사이에서 발생되는 바닥 이차흐름의 하향류에 의해 측벽 부근부터 하상이 침식되고, 침식된 유사량은 이차흐름의 횡방향 유속에 의해 이동되어 퇴적되어, 결국 횡방향으로 연속적인 언덕 및 저면과 같인 하상형상이 생성되는 것으로 나타났다. 또한 시간에 따른 이차흐름 및 바닥 전단력, 하상고의 변화에 대해 살펴보았다.

• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.381-385
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• 2004

본 인구에서는 레이놀즈응력모형을 이용하여 직사각형 개수로 흐름을 수치모의 하고 이차흐름의 생성 메커니즘을 제시하였다. 수치모의 결과 자유수면과 측벽의 접합부 근처에서 inner secondary flow가 발생하였다. 이는 최근 Grega 등(1995)과 Hsu 등(2000)에 의해 밝혀진 새로운 이차흐름이다. 또한 측벽에서의 전단력 분포를 계산한 결과 inner secondary flow에 의하여 수면 근처에서의 전단력 값이 증가하는 것으로 나타났다. 계산된 결과를 이용하여 와도 방정식에서 각 항의 크기를 비교하여 이차 흐름의 생성 메커니즘을 살펴보았다. 그 결과 벽 및 측벽 경계 부근에서는 난류의 비등방성에 의한 와도 생성항에 의해 이차 흐름이 생성되고, 경계와 멀리 떨어진 영역에서는 레이놀즈응력에 의한 와도 생성항이 이차흐름을 생성시키는데 중요한 역할을 하는 것으로 나타났다.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.505-514
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• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.