• Research in Mathematical Education
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• v.6 no.2
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• pp.123-133
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• 2002

The authors examined a college mathematics professor's change process in teaching practice by analyzing the teacher's reflective journal. Her change engaged cooperative learning method in a college Algebra course and was geared toward the reform-oriented methods. The change processes were revealed as a bumpy road that was full of struggles and challenges to both the teacher and students. The analysis also showed that a reflective journey needed a proper means and support system from a teacher's environment such as institution. This research clearly showed that brining a genuine change in teaching practice toward a broad educational goal was a combined effort among the participants of education.

• The Mathematical Education
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• v.46 no.4
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• pp.465-482
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• 2007

The purpose of this study was to explore how pre-service elementary school teachers participate in a course specifically designed to help them learn how to analyze instruction in terms of the levels of cognitive demand of mathematical tasks. This paper describes what prospective teachers learned while reading the cases of "implementing standards-based mathematics instruction", analyzing all tasks of one unit in one elementary mathematics textbook, observing master teachers' mathematics instruction as well as their colleagues during the practicum period, and developing their own cases on the basis of the design and implementation of instruction focused on mathematical tasks. This paper includes various reflections of the prospective teachers.

• Coupled systems mechanics
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• v.12 no.1
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• pp.21-40
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• 2023

In thisstudy, the vibration problem ofthermo elastic carbon nanotubes conveying pulsating viscous nano fluid subjected to a longitudinal magnetic field is investigated via Euler-Bernoulli beam model. The controlling partial differential equation of motion is arrived by adopting Eringen's non local theory. The instability domain and pulsation frequency of the CNT is obtained through the Galerkin's method. The numerical evaluation of thisstudy is devised by Haar wavelet method (HWM). Then, the proposed model is validated by analyzing the critical buckling load computed in presentstudy with the literature. Finally, the numerical calculation ofsystem parameters are shown as dispersion graphs and tables over non local parameter, magnetic flux, temperature difference, Knudsen number and viscous parameter.

• East Asian mathematical journal
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• v.19 no.1
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• pp.17-26
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• 2003

This paper demonstrates the CAS technique of analyzing the nature and the structure of the numerical error for education and research purposes. This also illustrates the CAS approach in experimenting with the numerical operations in an arbitrary computer number system and also in doing error analysis in a visual manner.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.53-60
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• 2000

We evaluate some interesting families of infinite series expressed in terms of the Psi (or Digamma) and Zeta functions by analyzing the well-known identity associated with $_3F_2$ due to Watson. Some special cases are also considered.

• East Asian mathematical journal
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• v.16 no.2
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• pp.233-237
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• 2000

Since the time of Euler, there have been many proofs giving the value of $\zeta(2n)$. We also give an evaluation of $\zeta(2n)$ by analyzing the generating function of Bernoulli numbers.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.81-100
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• 2022

The purpose of this study is to develop a framework for analyzing the solution spaces of open-ended task and to explore their usefulness and applicability based on the analysis of solution spaces constructed by students. Based on literature reviews and previous studies, researchers developed a framework for analyzing solution spaces (OMR-framework) organized into subspaces of outcome spaces, method spaces, representation spaces which could be used in structurally analyzing students' solutions of open-ended tasks. In our research, we developed open-ended tasks which had various outcomes and methods that could be solved by using the concepts of factors and multiples and assigned the tasks to 181 elementary school fifth and sixth graders. As a result of analyzing the student's solution spaces by applying the OMR-framework, it was possible to systematically analyze the characteristics of students' understanding of the concept of factors and multiples and their approach to reversible and constructive thinking. In addition to formal mathematical representations, various informal representations constructed by students were also analyzed. It was revealed that each space(outcome, method, and representation) had a unique set of characteristics, but were closely interconnected to each other in the process. In conclusion, it can be said that method of analyzing solution spaces of open-ended tasks of this study are useful for systemizing and analyzing the solution spaces and are applicable to the analysis of the solutions of open-ended tasks.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.73-88
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• 2022

Mathematics is a way of thinking. To do mathematics means to think mathematically. In other words, mathematics education and mathematics literacy are related. In elementary and secondary school mathematics education in many countries, teaching of mathematics using textbooks is conducted mostly in their native language. So mathematics education takes place while reading, writing, listening, and speaking mathematics. Analysis of mathematics textbooks for the lower grades of undergraduate mathematics shows that most advanced countries in mathematics use excellent undergraduate mathematics textbooks written in their native language. However, the ratio of using imported textbooks from foreign countries is particularly high in the case of textbooks for mathematics majors at Korean universities. In this article, the effect of language used in university mathematics education is analized. In particular, the importance of high-quality leading-edge university mathematics textbooks in native language is introduced by analyzing the case of Bourbaki in France and 'War of language' at the Israel Institute of Technology. The innovation of French university mathematics education in the 20th century began with Bourbaki's 'Fundamentals of Mathematics', a French textbook written in his native language. Israel's Technion and the Hebrew University of Jerusalem continue to teach all subjects in their mother tongue. This has led to produce many Nobel Prize and Fields medal winners in these two countries. This study shows that textbooks and languages used in university mathematics education has affected mathematical literacy.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.333-357
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• 2007

One of the most important issues in mathematics education is to restore the educational foundation of school mathematics, which requires fundamental discussions about 'What are the reasons for teaching mathematics?'. This study begins with the problematic that mathematics education is generally pursued as an instrumental know-ledge, which is useful to solve everyday problems or develop scientific technology. This common notion cannot be overcome as long as the mathematics education is viewed as bringing up the learners' ability to work out practical problems. In this paper we discuss the value of mathematics education reflecting on the theory of 'two fold structure of mind'. And we examine the ideas pursued by mathematics educators analyzing the educational theory of Plato and Froebel. Furthermore, we review the mathematics educational theory of F. Klein, an educator who led the reformation of mathematics education in the early 20th century and established the basic modern philosophy and curriculum of mathematics education. In particular, reflecting on the 'two fold structure of mind,' we reexamine his mathematics educational theory in the aspect of the mind cultivation so as to elucidate his ideas more clearly. Moreover, for the more deep discussion about Klein's thoughts on the mathematics education, his viewpoint on tile teaching of 'functional thinking' for the mind cultivation is reexamined based on the research results found in the developments of mathematics education after Klein. As the result we show that under the current mathematics education, which regards mathematics as a practical tools for solving everyday problems and an essential device for developing science and technology, there is a more important value for cultivating the human mind, and argue that mathematics education should contribute to the mind cultivation by emphasizing such an educational value.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.603-623
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• 2013

This paper proposes analyzing monthly rainfall patterns using copula and pricing related rainfall insurance using it. We analyze 30-year monthly precipitation data for 9 Korean cities between June and September using copula showing so that it can effectively generate realistic monthly rainfall patterns. In addition, we show that our copula rainfall models can be used in pricing various kinds of rainfall insurances effectively.