• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.217-231
• /
• 2010

We consider a class of elliptic problems of a logistic type $$-div(|{\nabla}_u|^{m-2}{\nabla}_u)\;=\;w(x)u^q\;-\;(a(x))^{\frac{m}{2}}\;f(u)$$ in a bounded domain of $\mathbf{R}^N$ with boundary $\partial\Omega$ of class $C^2$, $u|_{\partial\Omega}\;=\;+{\infty}$, $\omega\;\in\;L^{\infty}(\Omega)$, 0 < q < 1 and $a\;{\in}\;C^{\alpha}(\bar{\Omega})$, $\mathbf{R}^+$ is non-negative for some $\alpha\;\in$ (0,1), where $\mathbf{R}^+\;=\;[0,\;\infty)$. Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.

• School Mathematics
• /
• v.10 no.2
• /
• pp.199-222
• /
• 2008

The present study was conducted to review the definitions and methods of teaching reflection and then suggest the criteria for analyzing mathematics teaching reflection. The reason for addressing the teaching reflection, which recently attracts considerable attention, was that it would enhance the professional growth of mathematics teachers. The review of the prior studies shows that the hitherto proposed criteria which could be used for analyzing mathematics teaching reflection are inadequate and unsystematic. Further, it was revealed that the self-assessment checklists put forward by previous studies were overly ramified, and thus it seems that an integrative approach should be taken in order to establish the relevant criteria for analyzing mathematics teaching reflection. Considering these findings, the present study suggests the pre-lesson, in-lesson, and post-lesson criteria for analyzing leaching reflection for the subject of mathematics and the attendant questions posed to teachers.

• The Mathematical Education
• /
• v.63 no.1
• /
• pp.19-33
• /
• 2024

This study investigates longitudinal patterns in middle school students' mathematics interest and achievement using panel data from the 4th to 6th year of the Gyeonggi Education Panel Study. Results from the multivariate growth mixture model confirmed the existence of heterogeneous characteristics in the longitudinal trajectory of students' mathematics interest and achievement. Students were classified into four latent classes: a low-level class with weak interest and achievement, a high-level class with strong interest and achievement, a middlelevel-increasing class where interest and achievement rise with grade, and a middle-level-decreasing class where interest and achievement decline with grade. Each class exhibited distinct patterns in the change of interest and achievement. Moreover, an examination of the correlation between intercepts and slopes in the multivariate growth mixture model reveals a positive association between interest and achievement with respect to their initial values and growth rates. We further explore predictive variables influencing latent class assignment. The results indicated that students' educational ambition and time spent on private education positively affect mathematics interest and achievement, and the influence of prior learning varies based on its intensity. The perceived instruction method significantly impacts latent class assignment: teacher-centered instruction increases the likelihood of belonging to higher-level classes, while learner-centered instruction increases the likelihood of belonging to lower-level classes. This study has significant implications as it presents a new method for analyzing the longitudinal patterns of students' characteristics in mathematics education through the application of the multivariate growth mixture model.

• The Mathematical Education
• /
• v.38 no.2
• /
• pp.189-197
• /
• 1999

Discrete mathematics allows students to examine and explore unique, special problem situations which were not used to solve problems by paper-and-pencil procedures or applying common formulas. The use and integration of accessible computer-related technologies such as 'Mathematics' or 'Maple' software programs enables students to explore problem situation dramatically. This study shows that it is possible to introduce computer-based discrete mathematics focused on the Leslie matrix model as modeling age-specific population growth to high school students.

• Education of Primary School Mathematics
• /
• v.24 no.3
• /
• pp.135-156
• /
• 2021

Achievement pressure and enthusiasm affecting mathematics academic achievement are constantly changing and affecting academic achievement. Therefore, a longitudinal study is needed to examine the influence of the change patterns of teachers' achievement pressure and enthusiasm on the change patterns of academic achievement. This study utilized student data from the 5th grade of elementary school (2013 year) to the third grade of middle school (2017 year) of the Korean Education Longitudinal Study 2013. The longitudinal change patterns of mathematics academic achievement were classified into similar subgroups and the influence of the longitudinal change patterns of the achievement pressure and enthusiasm of each group on the longitudinal change pattern of mathematics academic achievement and the path were compared and analyzed. As a result of the analysis, in all four subgroups with similar longitudinal changes in mathematics academic achievement, the teacher's achievement pressure showed little change from the fifth grade, while the teacher's enthusiasm continued to decline from the fifth grade. In addition, the influence of teachers' achievement pressure and enthusiasm perceived by students in each group on mathematics academic achievement was different. This suggests that in order to improve mathematics academic achievement, it is necessary to support teaching and learning reflecting the characteristics and dispositions of students.

• School Mathematics
• /
• v.4 no.3
• /
• pp.513-537
• /
• 2002

The aim of this study is to investigate the purpose of the performance assess-ment, to develop and to apply it's task. By reviewing previous study, I conclude that the performance assessment is sug-gested to evaluate mathematical thinking and attitude in the purpose of school mathematics. To develop the task to fit the purpose of the performance assessment, I refer to the middle and high level in Van den Heuvel's classification the task "Find the number in the star" and about the assess-ment of school mathematics. Then I apply the performance assessment task developed according to this level, analyse the responses of children to "Let's make the problem" and suggest it's assessment rubric and anchor papers for each level for illustrating the process of developing a rubric. Finally, considerations to improve the performance assessment are discussed.

• The Mathematical Education
• /
• v.48 no.1
• /
• pp.61-80
• /
• 2009

The purpose of this study was to develop case-based pedagogy in mathematics for elementary school teachers and to investigate how they participate in the course employing case-based pedagogy. The 13 cases were developed and employed in pre-service teacher education. As such, the cases covered all content areas across grades, and included detailed description of mathematics instruction, questions for discussion, theoretical review related to each case, focus analysis and additional analysis, etc. This paper describes in what ways the participant teachers discussed cases, how case-based pedagogy had an influence on the teachers' own instruction during the practicum period, and how they assessed case-based pedagogy. This paper provides issues and suggestions for the professional development of mathematics teachers on the basis of empirical background.

• East Asian mathematical journal
• /
• v.39 no.2
• /
• pp.199-227
• /
• 2023

The Korean government initiated an educational policy regulating academic acceleration in schools (e.g., regulating teaching or assessing above-grade-level content) in order to normalize public education and prevent the growth of private tutoring. To analyze whether the policy is achieving its intended goals, this study examined how high school mathematics teachers responded to the policy. The findings indicate four distinct teacher responses: the teachers would teach above-grade-level lessons in classes, but not assess them on a test; the teachers sought academic acceleration to prevent excessive private tutoring, although the policymakers thought that teachers' academic acceleration results in an excessive demand for private tutoring; the teachers were willing to teach above-grade-level content for students, but they were reluctant to teach below-grade-level content due to the time constraints; and the teachers recognized that the policy limited their curricular autonomy, even though it was intended to ensure their autonomy. Implications for mathematics teacher educators and policymakers are discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.597-607
• /
• 2019

In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.513-522
• /
• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.