• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.9-17
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• 2002

In this Paper, we will show that every basically disconnected space is a projective object in the category $Tych_{\sigma}$ of Tychonoff spaces and $_{\sigma}Z^{#}$ -irreducible maps and that if X is a space such that ${\Beta} {\Lambda} X={\Lambda} {\Beta} X$, then X has a projective cover in $Tych_{\sigma}$. Moreover, observing that for any weakly Linde1of space, ${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$ is $_{\sigma}Z^{#}$-irreducible, we will show that the projective objects in $wLind_{\sigma}$/ of weakly Lindelof spaces and $_{\sigma}Z^{#}$-irreducible maps are precisely the basically disconnected spaces.

• Research in Mathematical Education
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• v.8 no.4
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• pp.293-307
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• 2004

Psychological and social theories have influenced on making sense of teaching and learning of mathematics. This paper analyzes major influences of such theories - behaviorism cognitivism, and situativity - on mathematics education. Instead of reviewing the theories perse, it intends to explicate how different perspectives have shaped our understanding of mathematics education both in theory and in practice. Given that the current mathematics education reform ideas are theoretically based on the constructivist and the sociocultural perspectives, the main focus is given on cognitivism, situativity, and various coordinations between the two. Exploring about psychological and social theories in the context of mathematics education is expected to enrich our understanding of where we have come from and where we are going.

• Research in Mathematical Education
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• v.8 no.4
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• pp.261-277
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• 2004

Julia sets, their variants and generalizations have been studied extensively by using the Picard iterations. The purpose of this paper is to introduce Mann iterative procedure in the study of Julia sets. Escape criterions with respect to this process are obtained for polynomials in the complex plane. New escape criterions are significantly much superior to their corresponding cousins. Further, new algorithms are devised to compute filled Julia sets. Some beautiful and exciting figures of new filled Julia sets are included to show the power and fascination of our new venture.

• Research in Mathematical Education
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• v.8 no.4
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• pp.227-260
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• 2004

This article represents a survey on the Romanian mathematics education. we emphasize not only some of recent, specific and significant Romanian methods concerning the teaching and learning of mathematics, starting from the pre-school and primary level to the university mathematics education, but also the role of the national and international mathematical competitions, the education of mathematics teacher, the formation of the researchers in mathematics, their contributions and perspectives, the mathematics education in society and culture, the technology in mathematics education, links between research and practice, topical developments and for the future and other related topics.

• The Mathematical Education
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• v.23 no.2
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• pp.5-11
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• 1985

There arc numerous techniques available to appraise pupil achievement in elementary school mathematics. The teacher must utilize a variety of approaches to assess pupil growth in the mathematics curriculum. Each evaluation technique has its strengths as well as weaknesses. Thus, a specific evaluation technique may be utilized as a check on other approaches to appraisal. Pupil achievement must be assessed in terms of stated relevant understandings. skills, and attitudinal objectives. It is not adequate to appraise pupil growth in terms of understandings objectives only. Pupils must also be assessed in terms of skills objectives. The understandings acquired by learners must be utilized; thus, skills objectives need to be stressed adequately in ongoing units of study in elementary school mathematics. Adequate emphasis also needs to be placed upon pupils achieving attitudinal goals. Desireable attitudes on the part of learners aid in achieving understandings and skills objectives. A defensible program of evaluation would then stress that pupil achievement be adequately appraised in terms of understandings, skills, and attitudinal objectives.

• The Mathematical Education
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• v.37 no.1
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• pp.101-114
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• 1998

In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.37-49
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• 2004

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.51-61
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• 2004

We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.29-36
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• 2004

Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and ｙ be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.55-69
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• 2003

It is clear that students attending at technical high schools, which are commonly believed to have low mathematical learning standard, are able to improve their mathematical learning abilities through concrete operational activities. One thing that teachers should remember is that the subject in learning is the student not the teacher any more, so that teachers are able to become assistants by letting students study independently rather than passively.