• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• 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.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.487-504
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• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.4
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• pp.576-582
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• 1996

This work studies qualitative thermal characteristics of PCM cold storage medium container and its surrounding streams. Experimental parameters are initial PCM temperature and cold water flow rate. A mathematical modeling was establised to estimate temperature distribution and the cooling process. We found that the phase-change temperatures of PCM varies from 6 to $8^{\circ}C$ which is constant for other materials and that the dominant heat transfer resistance is that on the container side taking about 3/4 of the total resistance. The one dimensional mathematical model predicts experimental data quit well.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.312-326
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• 2021

The prey-predator model is one of the most influential mathematical models in ecology and evolutionary biology. In this study, we considered a modified prey-predator model, which describes the rate of change for each species. The effects of modifications to the classical prey-predator model are investigated here. The conditions required for the existence of the first integral and the stability of the fixed points are studied. In particular, it is shown that the first integral exists only for a subset of the model parameters, and the phase portraits around the fixed points exhibit physically relevant phenomena over a wide range of the parameter space. The results show that adding coupling terms to the classical model widely expands the dynamics with great potential for applicability in real-world phenomena.

• East Asian mathematical journal
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• v.39 no.2
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• pp.183-198
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• 2023

Classroom observation instruments are often used to evaluate teachers' instructional practices and provide feedback to inform interventions or research studies, or professional development efforts. While designed as research tools, many classroom observation instruments can provide important information to support teachers' learning and instructional change by providing a focus for formative assessment or self-evaluation of practice. In this paper, we review two classroom observation tools and the protocols for their use with an implementation example for one of the tools. These tools are more foreign to the field compared to others but have features that might serve as affordances in relation to the purposes of a specific investigation.

• East Asian mathematical journal
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• v.39 no.4
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• pp.437-454
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• 2023

The core of the change in the era of the 4th industrial revolution is the change in the base of 'digital technology'. These changes are incomparably large and are expected to have a more important impact on our lives than ever before. One of the major inflection points in the transition to the digital era is the education field, and IT technology has become an essential element in the educational field. Accordingly, this study examines domestic research trends related to the educational environment based on digital technology. Then, we would like to provide implications for the establishment of a digital-based educational environment that will change in the future. To this end, Semantic network analysis has been conducted to quantitatively structure text data obtained from studies related to digital technology in the field of mathematics education over the past 10 years, and the discussion will continue based on the results.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.131-138
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• 1998

The aims of mathematical education are to improve uniformity and rigidity, and to apply to an information age which our society demands. One of the educational aims in the 6th educational curriculum emphasizes on the expansion of mathematical thought and utility, But, The change of contents in the text appears little. This means that mathematical teachers must actively develop the new types of problems. That the interests and concerns about mathematics lose the popularity and students recognize mathematics burdensome is the problems of not only teaching method, unrealistically given problems but abstractiveness and conceptions. Mathematical Modeling is classified exact model, almost exact theory based model and impressive model in accordance with the realistic situation and its equivalent degree of mathematical modeling. Mathematical Modeling is divided into normative model and descriptive model according to contributed roles of mathematics. The Modeling Applied Problems in the present text are exact model and stereotyped problems. That the expansion of mathematical thought in mathematics teaching fell into insignificance appears well in the result of evaluating students. For example, regardless of easy or hard problems, students tend to dislike the new types of mathematical problems which students can solve with simple thought and calculation. The ratings of the right answer tend to remarkably go down. If mathematical teachers entirely treat present situation, and social and scientific situation, students can expand the systematic thought and use the knowledge which is taught in the class. Through these abilities of solving problems, students can cultivate their general thought and systematic thought. So it is absolutely necessary for students to learn the Modeling Applied Problems.

• The Mathematical Education
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• v.54 no.4
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• pp.299-315
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• 2015

The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of 'derivative' as a tool to express the relationship with employing a concept of 'rate of change.' The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, $y=x^2$. In conclusion, we argue that covariational approach could not only facilitate students' construction of an initial function concept, but also support their understanding of the concept of 'derivative.'

• The Mathematical Education
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• v.47 no.1
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• pp.27-47
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• 2008

In this paper, we study the effect of writing activity as mathematical communication on the students's mathematics achievement, learning attitude, and mathematical tendency. For this purpose, we construct a experimental class and then analyze the students' change in those aspects after applying three-divided-note writing activity and colleague feedback on their works those students are in the experimental class. As a result of the experiment, we find that three-divided-note writing activity and colleague feedback made some significant changes on the students achievement in mathematics, learning attitude, but does not affect on mathematical tendency. We also offer some suggestions for further research. Firstly, the mathematical communication ability must be stressed in mathematics education. For this purpose, we need to develop the teaching and the evaluation method to use not only writing but also reading, speaking, and listening skills so that many teachers can apply this method easily to their classes. Second, we need to fix some realistic problems such as fair evaluation , the numbers of students per class, the numbers of lesson, and too much extra-work, and so on. Thirdly, we suggest to explore some methods for extending three- divided-note writing activity to evaluate mathematical essay and to study educational effects of colleague feedback on mathematics performance assessment.