• Research in Mathematical Education
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• v.9 no.4 s.24
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• pp.317-328
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• 2005

The aim of this study is to investigate future teachers' skills that can make problem solving methods concrete for 7-11 year old students. For the students in the concrete operations level, solutions of word problems should also be taught by concreting. But most of teacher candidates can not solve the problems without algebra because they got used to solve the word problems with algebra during their high school and university education. In this study, whether the teacher candidates have the skills of solving the primary school level problems without using algebra or not are being observed. At the end of this observation it is determinated that primary level teacher candidates generally prefer using algebra operations because of their former habits. The results show that in the education of the primary level teacher candidates, there is the need of developing the solving skills using figures and diagrams without algebra rather than algebraic solutions in word problems.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1047-1067
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• 2016

In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denoted by ${\overrightarrow{D}}_{r,s}(x)$, where $r,s{\in}{\mathbb{N}}$ and x is an indeterminate are introduced. A presentation of walled signed Brauer algebras in terms of generators and relations is given. The cellularity of a walled signed Brauer algebra is established. Finally, ${\overrightarrow{D}}_{r,s}(x)$, is quasi- hereditary if either the characteristic of a field, say p, p = 0 or p > max(r, s) and either $x {\neq}0$ or x = 0 and $r{\neq}s$.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.367-372
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• 1995

In 1955 Singer and Wermer [12] proved that every bounded derivation on a commutative Banach algebra maps into its radical. They conjectured that the continuity of the derivation in their theorm can be removed. In 1988 Thomas [13] proved their conjecture ; Every derivation on a commutative Banach algebra maps into its radical. For noncommutative versions, in 1984 B. Yood [15] proved that the continuous derivations on Banach algebras satisfing [D(a),b] $\in$ Rad(A) for all a, b $\in$ A have the radical range, where [a,b] will be denote the commutator ab-ba. In 1990 M.Bresar and J.Vukman [1] have generlized Yood's result, that is, the continuous linear Jordan derivation on Banach algebra that satisfies [D(a),a] $\in$ Rad(A) for all a $\in$ A has the radical range. In next year Mathieu and Murphy [5] proved that every bounded centralizing derivation on Banach algebras has its image in the radical. Mathieu and Runde [6] removed the boundedness of that.

• Research in Mathematical Education
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• v.9 no.1 s.21
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• pp.59-68
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• 2005

We are introducing a new learning environment for linear algebra at Sungkyunkwan University, and this is changing our teaching methods. Korea's e-Campus Vision 2007 is a program begun in 2003, to equip lecture rooms with projection equipment, View cam, tablet PC and internet D-base. Now our linear algebra classes at Sungkyunkwan University can be taught in a modem learning environment. Lectures can easily being recorded and students can review them right after class. At Sungkyunkwan University almost $100\%$ of all large and medium size lecture rooms have been remodeled by Mar. 2005 and are in use. We introduce this system in detail and how this learning environment changed our teaching method. Analysis of the positive effect will be added.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.315-324
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• 2011

In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.

• Research in Mathematical Education
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• v.7 no.1
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• pp.59-67
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• 2003

In linear algebra course, the theory of vector space is usually presented in a very formal setting, which causes severe difficulties to many students. In this study, the effect of teaching the theory of vector space in linear algebra from the geometrical point of view on students' learning was investigated. It was found that the teaching of the theory of vector space in linear algebra from the geometrical point of view increases the meaningful loaming since it increases the visualization.

• Research in Mathematical Education
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• v.12 no.3
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• pp.215-233
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• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.293-300
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• 1995

Let $R = k[y_1,\cdots,y_n] \otimes E[x_1, \cdots, x_n]$ with characteristic $k = p > 2$ (odd prime), where $$\mid$y_i$\mid$ = 2, $\mid$x_i$\mid$ = 1$ and $y_i = \betax_i, \beta$ is the Bockstein homomorphism. Topologically, $R = H^*(B(Z/p)^n,k)$. For a symmetric group $\sum_n, R^{\sum_n} = k[\sigma_1,\cdots,\sigma_n] \otimes E[d\sigma_1, \cdots, d\sigma_n]$ where d is the derivation satisfying $d(y_i) = x_i$ and $d(x_iy_i) = x_iy_i + x_jy_i, 1 \leq i, j \leq n$. We give a direct proof of this theorem by using induction.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.21-28
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• 2001

In this paper we show that the following results remain valid for arbitrary Jordan derivations as well: Let d be a derivation of a complex Banach algebra A. If $d^2(x){\in}rad(A)$ for all $x{\in}A$, then we have $d(A){\subseteq}rad(A)$ ([5, p. 243]), and in a case when A is unital, $d(A){\subseteq}rad(A)$ if and only if sup{$r(z^{-1}d(z)){\mid}z{\in}A$ invertible} < ${\infty}$([3]), where rad(A) stands for the Jacobson radical of A, and r(${\cdot}$) for the spectral radius.

• East Asian mathematical journal
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• v.5 no.2
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• pp.177-189
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• 1989