• School Mathematics
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• v.9 no.1
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• pp.119-139
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• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• Korean Journal of Agricultural and Forest Meteorology
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• v.12 no.2
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• pp.122-131
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• 2010

This paper introduces the concept of a virtual ecosystem and reports the following three mathematical approaches that could be widely used to construct such an ecosystem, along with examples: (1) a molecular dynamics simulation approach for animal flocking behavior, (2) a stochastic lattice model approach for termite colony behavior, and (3) a rule-based cellular automata approach for biofilm growth. The ecosystem considered in this study consists of artificial organisms and their environment. Each organism in the ecosystem is an agent that interacts autonomously with the dynamic environment, including the other organisms within it. The three types of model were successful to account for each corresponding ecosystem. In order to accurately mimic a natural ecosystem, a virtual ecosystem needs to take many ecological variables into account. However, doing so is likely to introduce excess complexity and nonlinearity in the analysis of the virtual ecosystem's dynamics. Nonetheless, the development of a virtual ecosystem is important, because it can provide possible explanations for various phenomena such as environmental disturbances and disasters, and can also give insights into ecological functions from an individual to a community level from a synthetic viewpoint. As an example of how lower and higher levels in an ecosystem can be connected, this paper also briefly discusses the application of the second model to the simulation of a termite ecosystem and the influence of climate change on the termite ecosystem.

• Journal of The Korean Association For Science Education
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• v.34 no.4
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• pp.335-347
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• 2014

Size/scale is a central idea in the science curriculum, providing explanations for various phenomena. However, few studies have been conducted to explore student understanding of this concept and to suggest instructional approaches in scientific contexts. In contrast, there have been more studies in mathematics, regarding the use of number lines to relate the nature of numbers to operation and representation of magnitude. In order to better understand variations in student conceptions of size/scale in scientific contexts and explain learning difficulties including alternative conceptions, this study suggests an approach that links mathematics with the analysis of student conceptions of size/scale, i.e. the analysis of mathematical structure and reasoning for a number line. In addition, data ranging from high school to college students facilitate the interpretation of conceptual complexity in terms of mathematical development of a number line. In this sense, findings from this study better explain the following by mathematical reasoning: (1) varied student conceptions, (2) key aspects of each conception, and (3) potential cognitive dimensions interpreting the size/scale concepts. Results of this study help us to understand the troublesomeness of learning size/scale and provide a direction for developing curriculum and instruction for better understanding.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Korean Journal of Remote Sensing
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• v.26 no.5
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• pp.593-603
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• 2010

Most spatial data acquisition systems employing a set of frame cameras may have suffered from their small fields of view and poor base-distance ratio. These limitations can be significantly reduced by employing an omni-directional camera that is capable of acquiring images in every direction. Bundle Block Adjustment (BBA) is one of the existing georeferencing methods to determine the exterior orientation parameters of two or more images. In this study, by extending the concept of the traditional BBA method, we attempt to develop a mathematical model of BBA for omni-directional images. The proposed mathematical model includes three main parts; observation equations based on the collinearity equations newly derived for omni-directional images, stochastic constraints imposed from GPS/INS data and GCPs. We also report the experimental results from the application of our proposed BBA to the real data obtained mainly in urban areas. With the different combinations of the constraints, we applied four different types of mathematical models. With the type where only GCPs are used as the constraints, the proposed BBA can provide the most accurate results, ${\pm}5cm$ of RMSE in the estimated ground point coordinates. In future, we plan to perform more sophisticated lens calibration for the omni-directional camera to improve the georeferencing accuracy of omni-directional images. These georeferenced omni-directional images can be effectively utilized for city modelling, particularly autonomous texture mapping for realistic street view.

• The Mathematical Education
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• v.60 no.4
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• pp.467-491
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• 2021

This study is a study on the coding mathematics curriculum that converges elementary and middle school mathematics and information subjects and a minimum coding game-based education method for this. For the past 3 years, the coding mathematics curriculum and educational methods to effectively operate the curriculum were studied by applying them to 6th graders of elementary school and 1st graders of middle school. As a result of the first year of research, the coding mathematics curriculum was modified to a coding environment including the mathematical concept of a three-dimensional coordinate space, and the three-dimensional object was improved to be output as a real 3D print. As a result of the 2nd year study, it was improved so that even low-level students can build buildings by introducing different level commands for each component of the building so that self-directed learning is possible. As a result of the 3rd year study, a teaching-learning strategy based on a minimal coding game was designed to induce an increase in the level of computational thinking, and evaluation and feedback for diagnosing computational thinking were developed. Educational methods to promote self-directed learning and computing thinking ability, and researched coding mathematics curriculum are meaningful for the research and practice of the convergence education of school mathematics and informatics.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.19-38
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• 2008

This study aims to investigate the evolution of calculating the volume of a sphere in eastern and western mathematical history. In western case, Archimedes', Cavalieri's and Kepler's approaches, and in eastern case, Nine Chapters';, Liu Hui's and Zus' approaches are worthy of noting. The common idea of most of these approaches is the infinitesimal concept corresponding to Cavalieri's or Liu-Zu's principle which would developed to the basic idea of Calculus. So this study proposes an alternative to organization of math-textbooks or instructional procedures for teaching the volume of a sphere based on the principle.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.251-568
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• 1998

It is the purpose of this study that is to examine the practice and awareness on the use of calculator and to find the method to utilize the calculator as the tool in elementary school mathematics. Recently, it is recommendes strongly to use technical tools such as calculator and computer for the quiltative development on mathematics education. But we prohibite the usage of calculator and do not have the policy to use the calculator in our country because we have little understanding about it. The following direction for educational development is focused not on the repeat learning through the written computation, but on the ability for students to choose an operator and to perform the task with their own objects and strategies. By using the calculator, We can do the followings : 1)to help the mathematical concept develop, 2)to expand the computational ability from written computation to both mental computation and computational estimation, 3)to use the practical value in the problem situation, 4)to reinforce the problem solving, 5)to obtain the interest and the confedence on mathematics. Therefore, we must endevor actively for the broad usage of calculator in the mathematics class.

• Journal of Korean Society of Water and Wastewater
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• v.26 no.2
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• pp.257-264
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• 2012

The concept of a non-contact type of UV disinfection system was introduced in this study. UV lamps and their quartz sleeves hang over the water surface and there is no interface between the sleeve and water. Obviously, there is no fouling. Based on optical laws and other UV distribution models, a detail mathematical model for a non-contact type UV disinfection system was developed in this study. Pathway length of UV light in a non-contact type photoreactor is longer than that in a submerged type photoreactor because the light is more refractive while passing through 3 interfaces of medium. But the pathway length passing through the water media is not significantly longer than that in a submerged type photoreactor so, the absorption of UV light by water is not significantly different from the other system. Due to the reflection effect, UV intensity is rapidly decreased as the horizontal distance from the light source is increased. The reflective attenuation in a non-contact type photoreactor is higher than that in a submerged type photoreactor. These mean that the short photoreactor is advantageous than the narrow-long photoreactor for the non-contact type photoreactor in an optical point of view.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.12
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• pp.1155-1163
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• 2004

Extracellular signal-regulated kinase (ERK) signaling pathway is one of the mitogen-activated protein kinase (MAPK) signal transduction pathways. This pathway is known as pivotal in many signaling networks that govern proliferation, differentiation and cell survival. The ERK signaling pathway comprises positive and negative feedback loops, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. In this paper, we attempt to model the ERK pathway by considering both of the positive and negative feedback mechanisms based on Michaelis-Menten kinetics. In addition, we propose a fraction ratio model based on the mass action law. We first develop a mathematical model of the ERK pathway with fraction ratios. Secondly, we analyze the dynamical properties of the fraction ratio model based on simulation studies. Furthermore, we propose a concept of an inhibitor, catalyst, and substrate (ICS) controller which regulates the inhibitor, catalyst, and substrate concentrations of the ERK signal transduction pathway. The ICS controller can be designed through dynamical analysis of the ERK signaling transduction pathway within limited concentration ranges.