• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.1-6
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• 1994

In this paper, some properties for a PI-ring satisfying the descending chain condition on essential left ideals are studied: Let R be a ring with a polynomial identity satisfying the descending chain condition on essential ideals. Then all minimal prime ideals in R are maximal ideals. Moreover, if R has only finitely many minimal prime ideals, then R is left and right Artinian. Consequently, if every primeideal of R is finitely generated as a left ideal, then R is left and right Artinian. A finitely generated PI-algebra over a commutative Noetherian ring satisfying the descending chain condition on essential left ideals is a finite module over its center.(omitted)

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.243-256
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• 2005

Abacus numerals were developed using the concept of the binary system to form decimal numerals. This would allow addition, subtraction, multiplication, and division to be performed based solely on the knowledge of the 14 forms of the numerals and three simple rules. These numerals were taught to 260 elementary school pupils of 3rd and 4th grade. After 90 minutes of instruction, they, nearly all, were able to understand principles to add, and to subtract, and partly to multiply using Abacus Numerals. Protected Abacus Numerals are proposed against forgery. An International Numeration System is proposed based on the form of Abacus Numerals to facilitate international communication. A new type of abacus is proposed.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.257-267
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• 2005

When notions of numbers are expanded from natural number to complex number, a similar mathematical phenomenon can be observed in each number. As a case study, to complex number, the phenomenon is investigated carefully and teaching materials are created. Then complex number is expressed with matrices and is geometrically treated, so a new number which is an extension of complex number is discovered. Thus, teaching material regarding to complex number and matrices is made for students of ordinary level. Moreover, for talented students, material about an extension of complex number can be added to the previous one.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.269-273
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• 2005

Nowadays application of modem achievements of information technologies in science, engineering and education is usual phenomenon. Application of these technologies allows easily creating new methods of learning of mathematics. More of new methods of creation of multimedia electronic manuals on high mathematics are founded to application of multimedia and communication opportunities of the computer. But application only multimedia and communication opportunities of the computer at creation of multimedia electronic manuals on high mathematics is insufficient to elimination of 'gap' between training and studying high mathematics. So, we offer a new way of the decision of this problem: creation of a multimedia electronic manual on high mathematics with built-in a mathematical environment MathCad in the national language.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.285-294
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• 2005

The author has been teaching with an instructional module consisting of many mathematical concepts, based on designs formed by personal names or words to arouse students' interesting in learning mathematics. This module has been growing since it was first used as a supplementary lesson for calculus students. Now it consists of concepts that connect with mathematical topics such as number sense, algebraic thinking, geometry, and statistical reasoning, as well as other subjects such as art and quilt design. With its content we can provide our students the basic mathematical knowledge needed for further study in their own fields. In this article, we will demonstrate the latest development of this instructional module, which makes connections between mathematical knowledge and the design of personal quilt patterns. We will exhibit a 'Quilt of Nations' which consists of the designed quilt blocks of different countries, such as USA, Japan, Taiwan, Korea and others, as well as a quilt design using the abbreviation of this seminar. Then we will talk about how the connections are built, and how to design these mathematically rich, uniquely created, beautifully designed, and personalized quilt block patterns.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.295-303
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• 2005

Students' mathematics application ability is a hot spot which mathematics education pays attention. So, I have carried on the test of mathematics application and the questionnaire survey to student of Senior One of the two middle schools. Through the test and the investigation, I discover that the level of the students' mathematics application ability is not high. To the simple application question, the difference of the male and the female is not big, but to the difficult application question, the male and the female has the remarkable difference. The students' lack of flexible and the original cognition monitoring ability in mathematics application process are afraid of studying mathematics application since childhood and lack of the training of this aspect. They thought mathematics foundation and reading understood ability is the key of mathematics application. Through analysis result of investigation, this paper proposed the way to raise mathematics application ability of students.

• The Mathematical Education
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• v.41 no.1
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• pp.109-126
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• 2002

In this thesis. we estimated the good reliability coefficient ${\beta}$$\sub$k/ that is unbiased, consistent and more efficient than Cronbach's ${\alpha}$$\sub$k/ in splitting of a test into several formats of subtests and several properties of ${\beta}$$\sub$k/ are also represented. The tables of coefficients of skewness and kurtosis are represented to test the significance of departures from normality. We got the cumulative normal plots of z'from the distribution which is departed from normality using the Bock's approximation procedure and we finally enumerated the transformed standardized scores z'and a new raw score X' which enable us to proceed further evaluation procedures depending on our assessment policy.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.43-51
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• 1995

In this paper, we introduce the almost linear spaces, a generalization of linear spaces. We prove that if the almost linear space X has a finite basis then, as in the case of a linear space, the cardinality of bases for the almost linear space X is unique. In the case X = Wx ＋ Vx, we prove that B'= {$\chi$'$_1,...,x'_n} is a basis for the algebraic dual X$^#$ of X if B = {$\chi$'$_1,...,x'_n} is a basis for the almost linear space X. And we have an example X($\neq$Wx ＋ Vx) which has no such a basis.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.53-59
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• 1995

Consider a solution y(t) of the nonlinear equation (E) y" ＋ f(t, y) = 0. A solution y(t) is said to be oscillatory if for every T ＞ 0 there exists $t_{0}$ ＞ T such that y($t_{0}$) = 0. Let F be the class of solutions of (E) which are indefinitely continuable to the right, i.e. y $\in$ F implies y(t) exists as a solution to (E) on some interval of the form [t$\sub$y/, $\infty$). Equation (E) is said to be oscillatory if each solution from F is oscillatory.(omitted)

• Research in Mathematical Education
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• v.3 no.1
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• pp.1-8
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• 1999

The present study extends previous research in this area by investigating perceptions of change and reactions to reform efforts by pre-service and practicing secondary school mathematics teachers in the People's Republic of China (PRC) and the United States of America. Interviews were used to gather data about school experiences, teaching practices, and planned changes in mathematics programs. Analysis of the interview data supported earlier findings with respect to the well-planned nature of lessons by PRC teachers and the influence of mathematics contents and examination systems in the PRC. Findings also indicated a general agreement among teachers from both countries favoring less lecturing and more discussion and interactive activities. There were contrasts by nationality in descriptions of future teaching, ideal lessons, sources of teaching ideas, and preferences about school mathematics programs.