• Structural Engineering and Mechanics
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• v.34 no.3
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• pp.377-390
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• 2010

This paper studies fracture initiation direction of two parallel non-coplanar cracks of equal length. Using the dislocation pile-up modelling, singular integral equations for two parallel cracks subjected to mixed-mode loading are derived and the crack-tip field including singular and non-singular terms is obtained. The kinking angle is determined by using the maximum hoop stress criterion, or the ${\sigma}_{\theta}$-criterion. Results are presented for simple uniaxial tension and biaxial loading. The biaxiality ratio has a noticeable influence on crack growth direction. For the case of biaxial tension, when neglecting the T-stress the crack branching angle is overestimated for small crack inclination angles relative to the largest applied principal stress direction, and underestimated for large crack inclination angles.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1495-1506
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• 2021

The growth of solutions of second order complex differential equations f" + A(z)f' + B(z)f = 0 with transcendental entire coefficients is considered. Assuming that A(z) has a finite deficient value and that B(z) has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.55-75
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• 2005

As part of development research of a gender-neutral mathematics program, this paper provides a discussion of the fearures of the developed mathematics program. Based on the theory of feminist pedagogy and critical theories about women' ways of knowing, this mathematics program for girls pursues the mathematical empowerment of girls. Specifically, this mathematics program facilitates girls' awareness of their mathematical potentials, encourage them to position women at a center of mathematics in order for th equity in mathematics education. For the purpose, this program emphasizes constructive learning through girls' active participation. Thus, the instructions will value girls' own cognitive resources such as their experiential knowledge and ways of mathematical justification and provide an environment to support the growth of girls' own mathematical potential. This developmental research will be furthered to the systematic program evaluation to extend this program to support the equity for the marginalized poppulations as well as girls in mathematics education.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.369-393
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• 2019

The purpose of this study is to find the commonality between process-focused assessment and existing performance evaluation and to find out whether the process-focused assessment is effective for the development of the character of school mathematics. By analyzing the previous research, this study defined the meaning of process-focused assessment as an evaluation that can improve students' growth and quality of class through immediate feedback by introducing various performance tasks and evaluation methods. The character of school mathematics refers to personality factors that are easily expressed and cultivated during math classes. Therefore, this study presented examples of the feasibility of process-focused assessment focusing on geometry and vector subjects and examined the effectiveness of mathematics and character development through process-based evaluation. Four course-based assessments (math experiments, logic, proof, and communication) aimed at cultivating the character of school mathematics were conducted from March to June 2019 for the third year of high school. The index was measured. Analysis of the results using the corresponding variable t-test showed that the process-based evaluation in this study had a significant effect on the character of school mathematics development.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.249-256
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• 2010

We research the properties of solutions of general higher order homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1079-1086
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• 2013

This paper is devoted to solving one dimensional backward stochastic differential equations (BSDEs). We prove the existence of the solutions to BSDEs if the generator satisfies the general growth and discontinuous conditions.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.415-435
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• 2007

A transition from elementary to secondary school, and among grades, among learning contents is a essential problem in education. A connectivity between learning contents is important in student's growth and development. A gap between lower grades and higher grades in elementary school is no less extensive than a gap between elementary mathematics and secondary mathematics. In this paper, we start with a critical mind about a transition and connectivity between lower grades and higher grades in elementary school. In order to compare between elementary grades, we firstly focus 4th grade mathematics which finish lower grades and start higher grades at the same time. First, we make up a questionnaire to 4th grade students and teachers in charge 4th grade. A questionnaire is composed of questions about the degree of difficulty in the learning(and teaching) of 4th grade mathematics comparing with 3rd grade mathematics. Second, we compare to lower grades lessons(1st grade) and 4th grade lessons using a qualitative method. we analyze the lesson contents, activities and time through 'analysis of the learning course'. And we compare the pattern of eliciting questions, question patterns, nomination patterns and feedback patterns between 1st grade and 4th grade lessons. We hope that this paper is a fundamental sources in investigating a connectivity between lower grades and higher grades in elementary mathematics in the future.

• School Mathematics
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• v.15 no.4
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• pp.867-888
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• 2013

The purpose of this paper was to investigate mathematics gifted educational methods based on STEAM education by Delphi study. As a result by total 3 round Delphi method, the concept of STEAM education for mathematics gifted students was education of developing capacity of Holistic Growth that can communicate diverse people through self-monitoring study as they can find and solve problems with integrative thinking and creative thinking. Thus this elicited the consensual agreements of experts about mathematics gifted educational goals, methods, contents, and evaluations etc. As a follow-up research will be developed mathematics gifted educational model based on STEAM education.

• The Mathematical Education
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• v.53 no.3
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• pp.413-434
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• 2014

Logic lays the foundation of Mathematics and the development of Mathematics is dependent on critical thinking. So it is important that school mathematics helps students develop their logical and critical thinking ability for both mathematics learning and problem solving in general. MINDSTORMS, a LEGO based programming activity kit, is an effective teaching and learning tool that can be used to enhance logical and critical thinking in students. This study focused on measuring the growth of students' ability to think logically and critically when they used MINDSTORMS activities to learn programming. In addition, we investigated how the students' logical and critical thinking changed from the MINDSTORMS learning experience. The study confirmed that the programming activities using MINDSTORMS help to enhance logical and critical thinking in students. The students attitude about logical and critical thinking became more positive and the activities helped to engage students to think logically and critically. This type of programming activities should be valuable in mathematics education and it should be included in a general mathematics curriculum.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.137-147
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• 2015

Let f be a transcendental meromorphic function of finite order in the plane such that $f^{(m)}$ has finitely many zeros for some positive integer $m{\geq}2$. Suppose that $f^{(k)}$ and f share a CM, where $k{\geq}1$ is a positive integer, $a{\neq}0$ is a finite complex value. Then f is an entire function such that $f^{(k)}-a=c(f-a)$, where $c{\neq}0$ is a nonzero constant. The results in this paper are concerning a conjecture of Bruck [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.