• The Korean Journal of Community Living Science
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• v.22 no.4
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• pp.519-533
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• 2011

The objective of this study was to follow up changes in knowledge related to the mathematics education field work of preliminary early childhood teachers. The subjects of this research were 28 students who were taking mathematics education courses in early childhood education departments at various universities. This research ran for 15 weeks and was conducted through field work relating to mathematics education. The study collected data from pre-service teachers' knowledge, the diagram of concept, writing journals, interviews, and materials from the internet. Through this procedure, pre-service teachers' knowledge for mathematics education could later be expanded, ordered, and integrated. In addition, pre-service teachers not only understood the importance of contents and levels of lesson plans, but also learned how to utilize educational media to make effective lessons. Furthermore, pre-service teachers realized that the mathematical concepts of students could be expanded depending on the contents and methods of pre-service teachers' lesson plans and students could then apply these concepts into daily situations.

• Research in Mathematical Education
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• v.25 no.4
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• pp.285-309
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• 2022

A large body of previous studies investigated mathematical tasks by analyzing the design process prior to lessons or textbooks. While researchers have revealed the significant roles of mathematical tasks within written curricular, there has been a call for studies about how mathematical tasks are implemented or what is experienced and learned by students as enacted curriculum. This article proposes a mathematical task analytic framework based on a holistic definition of tasks encompassing both written tasks and the process of task enactment. We synthesized the features of the mathematical tasks and developed a task analytic framework with multiple dimensions: breadth, depth, bridging, openness, and interaction. We also applied the scoring rubric to analyze three multiplication tasks to illustrate the framework by its five dimensions. We illustrate how a series of tasks are analyzed through the framework when students are engaged in multiplicative thinking. The framework can provide important information about the qualities of planned tasks for mathematics instruction (proactive) and the qualities of implemented tasks during instruction (reactive). This framework will be beneficial for curriculum designers to design rich tasks with more careful consideration of how each feature of the tasks would be attained and for teachers to transform mathematical tasks with the provision of meaningful learning activities into implementation.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.977-998
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• 2009

In this article, we give a comparative study on the last 300 years of USA and Korean tertiary mathematics. The first mathematics classes in United States were offered before July, 1638, but the real founding of tertiary mathematics courses was in 1640 when Henry Dunster assumed the duties of the presidency at Harvard. President Dunster read arithmetics and geometry on Mondays and Tuesdays to the third year students during the first three quarters, and astronomy in the last quarter. So tertiary mathematics education in United States began at Harvard which is the oldest college in USA. After 230 years since then, Benjamin Peirce in 1870 made a major and first American contribution to mathematics and got an attention from European mathematicians. Major change on the role of Harvard mathematics from teaching to research made by G.D. Birkhoff when he joined as an assistant professor in 1912. Tertiary mathematics education in Korea started long before Chosun Dynasty. But it was given to only small number of government actuarial officers. Modern mathematics education of tertiary level in Korea was given at Sungkyunkwan, Ewha, Paichai, and Soongsil. But all college level education opportunity, particularly in mathematics, was taken over by colonial government after 1920. And some technical and normal schools offered some tertiary mathematics courses. There was no college mathematics department in Korea until 1945. After the World War II, the first college mathematics department was established, and Rimhak Ree in 1949 made a major and first Korean contribution to modern mathematics, and later found Ree group. He got an attention from western mathematicians for the first time as a Korean. It can be compared with Benjamin Peirce's contribution for USA.

• 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.

• East Asian mathematical journal
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• v.38 no.4
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• pp.379-396
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• 2022

In this paper, we investigate distribution strategies in the Egyptian fraction, and through this, we examine the distribution strategies of (fraction)÷(fraction) and then provide some educational implications. The (natural number)÷(natural number) of the sharing situation has the meaning of 'share' per unit, which can be seen as a situation where the unit ratio is determined. These concepts can also naturally be extended to the case of (fraction)÷(fraction) by some problem posing situations. That is to say, the case of (fraction)÷(fraction) can be deduced the case (natural number)÷(natural number) by the re-statement of the problem.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.557-564
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• 2010

By using an idea of C$\u{a}$dariu and Radu [4], we prove the generalized Hyers-Ulam stability of the functional equation f(x + y,z - w) + f(x - y,z + w) = 2f(x, z) + 2f(y, w). The quadratic form $f\;:\;\mathbb{R}\;{\times}\;\mathbb{R}{\rightarrow}\mathbb{R}$ given by f(x, y) = $ax^2\;+\;by^2$ is a solution of the above functional equation.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.269-278
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• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.675-678
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• 2006

We show that every real polynomial of degree n can be represented by the sum of two real polynomials of degree n, each having only real zeros. As an example of this, we consider a real polynomial with even degree whose all zeros lie on the imaginary axes except the origin.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.1-6
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• 1998

The paper refers to ordered semigroups in which $x^2 (x \in S)$ are left ideal elements. We mainly show that this $po$-semigroup is left regular if and only if S is a union of left simple subsemigroups of S.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.331-340
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• 2023

In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the n-maximal ideal, the maximal dimension of a ring S (M. dim(S)), the maximal depth of an ideal K of S (M.d(K)) and maximal height of an ideal K(M.d(K)).