• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.895-906
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• 2015

Recently, Li [12] gave an asymptotic formula for the ultimate ruin probability in a delayed-claim risk model with constant force of interest and pairwise quasi-asymptotically independent and extended-regularly-varying-tailed claims. This paper extends Li's result to the case in which the risk model is perturbed by diffusion, the claims are consistently-varying-tailed and the main-claim interarrival times are widely lower orthant dependent.

• Research in Mathematical Education
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• v.13 no.1
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• pp.23-30
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• 2009

How to promote creativity for all students in mathematics education is always a hot topic for mathematics educators. Based on the theory study and practice in the project "Open-ended Questions in Mathematics" granted by Ministry of Basic Education Curriculum Study Center in China, the paper reported the effect of "Open-ended Questions in Mathematics" on the way to change the development of thinking ability, to inspire students to develop thinking flexibility, to expand their imagination, to stimulate their interest in learning, and to foster students' creativity.

• The Mathematical Education
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• v.23 no.1
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• pp.53-65
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• 1984

Teachers need to provide a variety of learning experiences for pupils in elementary school mathematics. This is necessary due to pupils (a) achieving at diverse levels of accomplishment in the mathematics curriculum. (b) individually possessing different learning styles. The following, among others, can be relevant learning activities to present to pupils: 1. using a selected series of elementary school mathematics textbooks. 2. utilizing the flannel board to guide individual pupil achievement in mathematics. 3. helping pupils attach meaning to learning through the use of markers. 1. guiding pupils in learning by using place value charts. 5. aiding learner achievement through the use of transparencies and the overhead projector. 6. stimulating learner interest in mathematics with the use of selected filmstrips. 7. using graphs in functional situations. 8. helping young pupils to develop interest in numbers by singing songs directly related to ongoing units of study in elementary school mathematics. 9. using the geoboard to help pupils experience the world of geometry. 10. providing drill and practice for pupils so that previous developed learnings will not be forgotten.

• The Mathematical Education
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• v.24 no.2
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• pp.27-34
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• 1986

At present, Japanese textbooks of mathematics for elementary and secondary schools are thorized by the Ministry of Education. In former days, this system was also in effect for mentary schools until 1905 and for secondary schools until 1944. this article we discuss the start and the change of this system until 1905 and its influences the textbooks of mathematics. The main interest of the system was originally to prevent the textbooks from having the pressions which have the fear of breaking laws, disturbing the public morals or mistaking real facts. The interest changed to assure that the textbooks might comply with the ional standards of teaching syllabuses. And the standards such as the ones of the sizes of ers in the textbooks were made public one after another. The comments attached to the textbooks which applied for the authorization often pointed out use of unsuitable concrete numbers. The comments were often concerned with the difficulty words or sentenses for elementary schools and with the incorrectness of mathematical contents secondary schools. We conclude that the system encouraged the rapid modernization and regularization of Japanese tbooks during this period. We may note that there was a tendency not to adopt an extremely usual trial into the textbooks.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.41-55
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• 2006

Although gifted students are well ready in the perspective of intelligence, in order to make their learning highly effective, it is necessary to revitalize their intellectual abilities and progress it into proactive learning behaviour It is requisite to stress on the affective variables for achieving this. This study examined and analyzed affective variables for the subject mathematics on self-concept toward mathematics, attitude, interest, mathematical anxiety, and learning habits.

• Research in Mathematical Education
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• v.17 no.1
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• pp.15-27
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• 2013

Division of fractions is always a difficult topic for primary school students. Most of the presentations in teaching the topic in textbooks are procedural, asking students to invert the second fraction and multiply it with the first one, that is, $$\frac{a}{b}{\div}\frac{c}{d}=\frac{a}{b}{\times}\frac{d}{c}$$. Such procedural approach in teaching diminishes both the understanding of structure in mathematics and the interest in learning the subject. This paper discussed the formulation of teaching the division of fractions, which based on research lessons in some primary five classrooms. The formulated lessons started with an analogy to division of integers and working with division of fractions with equal denominators and then extended to division of fractions in general. It is found that the using of analogy helps students to invent their procedure in working the division problem. Some procedures found by students are discussed, with the focus on the development of their invention and mathematical thinking.

• Research in Mathematical Education
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• v.8 no.1
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• pp.1-18
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• 2004

Current interest in mathematics learning that focuses on understanding, mathematical reasoning and meaning making underscores the need to develop ways of analyzing classrooms that foster these types of learning. In this paper, the author show that the constructs of social and socio-mathematical norms, which grew out of taking a symbolic interactionist perspective, and Toulmins scheme for argumentation, as elaborated for mathematics education by Krummheuer [The ethnology of argumentation. In: The emergence of mathematical meaning: Interaction in classroom cultures (1995, pp. 229-269). Hillsdale, NJ: Erlbaum], provide us with means to analyze aspects of explanation, justification and argumentation in mathematics classrooms, including means through which they can be fostered. Examples from a variety of classrooms are used to clarify how these notions can inform instruction at all levels, from the elementary grades through university-level mathematics.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.301-320
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• 2013

Although many people have recognized the importance of history of mathematics in mathematics education, there are few studies that history and mathematics educations are connected. In this paper, we present and discuss the ways of introducing the instruction with mathematics machines. This instruction use the history of mathematics as part of a class not as a tool to stimulate students' interest but as a goal that it can be targeted mathematical itself. To do this, we first analyze the characteristics of applying history of mathematics in mathematical education, second, describe the meaning and the educational value of mathematical machines, and finally explained the way of applying history of mathematics with mathematics machines. The Instruction of history of mathematics with mathematics machines has advantages that practice (manipulation and experiment) and theory (elaboration of definition, production of conjectures and constructions of proofs) are interlaced within a historic-cultural perspective.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.831-839
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• 1996

In the last years there has been growing interest in concepts of positive (negative) dependence of stochastic processes such that concepts are considerable us in deriving inequalities in probability and statistics. Lehmann [7] introduced various concepts of positive(negative) dependence in the bivariate case. Stronger notions of bivariate positive(negative) dependence were later developed by Esary and Proschan [6]. Ahmed et al.[2], and Ebrahimi and Ghosh[5] obtained multivariate versions of various positive(negative) dependence as described by Lehmann[7] and Esary and Proschan[6]. Concepts of positive(negative) dependence for random variables have subsequently been extended to stochastic processes in different directions by many authors.

• The Mathematical Education
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• v.53 no.1
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• pp.41-55
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• 2014

In recent years, there has been increasing interest in the pedagogical importance of counter-examples that contradict statements about mathematics education research and the curriculum revision process for high school mathematics courses. Using a literature research method, this study analyzed views about counter-examples according to a method of approach to statements and the classification of counter-examples and their criteria. The study also described the learnability of the content of counter-examples presented in Korean secondary school mathematics textbooks. The results showed that generating many counter-examples enables learners to understand mathematical concepts exactly, construct links between mathematical contents, and have flexible thoughts about mathematical objects. Considering the learnability of counter-examples, the contents of counter-examples in school mathematics textbooks are needed for mathematics teachers and students to generate numerous counter-examples and verify the justification of generating counter-examples in various manners.