• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.863-882
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• 2013

Shanghai has been reported as the highest performing countries(economies) in PISA 2009 and PISA 2012. In this reason, we reviewed literatures related to educational system of Shanghai focusing on the mathematics education. Additionally, we analysed the results of PISA 2009 of mathematics domain between Korea and Shanghai to compare some differences between two countries. As a result, we discovered the followings: 1) Comparing with Shanghai students, Korea students attained low performance in every sub-categories of mathematics abilities indicated in the PISA framework. 2) In PISA 2009 Framework, Korea students produced low achievement than Shanghai students in sub-categories of "reflection". 3) In PISA 2012 Framework. Korea students attained low performance than Shanghai students in sub-categories of "formulating". Consequently, it gave us insight into the idea that school mathematics in Korea should use authentic context to help students improve their competencies "reflection" and "formulating".

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.215-227
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• 2006

After reviewing China's appearance and research on the Math open-ended problems, together with the application of those problems in mathematics test of Shanghai Senior Middle School Entrance Exams (SSMSEE) since 1999, this paper points out the difficulty in establishing an evaluation system for such problem. Through comparative study, the paper gives an operational definition of open-ended problem, and it attempts to establish an evaluation system and non-systematic competence targets that are appropriate to Math open-ended problems. Meanwhile, it describes the performance feature of those targets. By applying the standard international grading system of difficulty, it discusses the elements of difficulty in Math open-ended problems, and puts forward an evaluation as well as a level-of-difficulty forecasting system that is appropriate to the Middle School Entrance Exam.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.185-188
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• 2010

In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.641-653
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• 2020

To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: $${\max}\{X:X=X^*,\;\(\array{A&V&X\\V&B&W\\X&W&C}\){\geq}0\}$$. We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1483-1495
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• 2016

The notion of int-soft (implicative) filters in lattice implication algebras is introduced, and related properties are investigated. Characterizations of int-soft (implicative) filters are discussed. Conditions for an int-soft filter to be an int-soft implicative filter are provided. Extension property for int-soft implicative filters is established.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.227-237
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• 2015

By employing certain extended classical summation theorems, several surprising ${\pi}$ and other formulae are displayed.

• Research in Mathematical Education
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• v.11 no.3
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• pp.165-176
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• 2007

From the perspective of phenomenongraphy(根据登的象式), two videotaped mathematics lessons were observed, compared and analyzed, and the features of those times were extracted. The quantitative and qualitative analysis of the global structure and the questioning in the lessons etc. showed that in teaching behaviors there were some essential differences reflecting the impact of new beliefs and principles of teaching. Evidences also show that excellent teachers did keep and carry on the good tradition teaching for basic knowledge and basic skills were seen as the most important thing in mathematics teaching in China.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.601-611
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• 1996

In this paper, we introduce the notion of weakly associative BCI-algebras and investigate structure of it. Some of characterizations of elements of the quasi-associative part Q(X) of a BCI-algebra X are shown.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.431-439
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• 2012

Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.

• Research in Mathematical Education
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• v.26 no.4
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• pp.291-310
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• 2023

In this paper, we propose a theoretical framework for Chinese high school mathematics teachers use new textbooks based on the work of Remillard (1999) and Chau (2014). Based on this framework, a multiple case approach was used to investigate how two high school mathematics teachers from Shanghai use new textbooks. The results suggest that in the curriculum mapping arena, both the novice teacher and the expert teacher often planned to appropriate the unit content, and sometimes planned to add supplemental content. When organizing the unit content, novice teacher always planned to follow the new textbook in sequence, while expert teacher often would follow the new textbook in sequence, but sometimes planned to rearrange the unit content. In the design arena, both the novice teacher and the expert teacher tended to appropriate the introduced tasks and definitions. The novice teacher often planned to appropriate the example problems and exercise problems, while the expert teacher often intended to flexibly use the example problems and exercise problems. In the construction arena, the novice teacher seldom adjusted the planned tasks; in contrast, the expert teacher adjusted the planned tasks more frequently. In the reflection arena, the novice teacher often thought she should improve the mathematics tasks, while the expert teacher almost always thought he needed to improve the mathematics tasks. The framework shown in this paper provides a tool to investigate how mathematics teachers use textbooks.