• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.431-431
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• 2000

The modeling of 5-bar linkage robot manipulator dynamics by means of a mathematical and neural architecture is presented. Such a model is applicable to the design of a feedforward controller or adjustment of controller parameters. The inverse model consists of two parts: a mathematical part and a compensation part. In the mathematical part, the subsystems of a 5-bar linkage robot manipulator are constructed by applying Kawato's Feedback-Error-Learning method, and trained by given training data. In the compensation part, MLP backpropagation algorithm is used to compensate the unmodeled dynamics. The forward model is realized from the inverse model using the inverse of inertia matrix and the compensation torque is decoupled in the input torque of the forward model. This scheme can use tile mathematical knowledge of the robot manipulator and analogize the robot characteristics. It is shown that the model is reasonable to be used for design and initial gain tuning of a controller.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.187-210
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• 2017

The animated discussion about mathematical modeling that had studied consistently in Korea since 1990s has flourished, because mathematical modeling was involved in the teaching-learning method to improve problem solving competency on 2015 reformed mathematics curriculum. In an attempt to re-examine the educational value and necessity of application to school education field, this study was to review the literature of mathematical modeling in mathematical competencies perspective. As a result, mathematical modeling could not only be involved the components of problem solving competency, but also support other competencies; reasoning, creativity-amalgamation, data-processing, communication, and attitude -practice. In this regard, This paper suggested the necessity of the discussion about the position of mathematical modeling in mathematical competencies and the active use of mathematical modeling tasks in mathematics textbook or school classes.

• Journal of the Korean School Mathematics Society
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• v.24 no.3
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• pp.283-308
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• 2021

This study aims to analyze statistical tasks in Korean and Singaporean textbooks with the mathematical modeling perspective and compare the learning contents and experiences of students from both countries. I analyzed mathematical modeling tasks in the textbooks based on five aspects: (1) the mathematical modeling process, (2) the data type, (3) the expression type, (4) the context, and (5) the mathematical activity. The results of this study show that Korean and Singaporean textbooks provide the highest percentage of the "working-with-mathematics" task, the highest percentage of the "matching task," and the highest percentage of the "picture" task. The real-world context and mathematical activities used in Korean and Singaporean textbooks differed in percentage. This study provides implications for the development of textbook tasks to support future mathematical modeling activities. This includes providing a balanced experience in mathematical modeling processes and presenting tasks in various forms of expression to raise students' cognitive level and expand the opportunity to experience meaningful mathematizing. In addition, it is necessary to present a contextually realistic task for students' interest in mathematical modeling activities or motivation for learning.

• School Mathematics
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• v.6 no.3
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• pp.283-299
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• 2004

It is a very important objective of mathematical education to lead students to apply mathematics to the problem situations and to solve the problems. Assuming that mathematical modeling is appropriate for such mathematical education objectives, we must emphasize mathematical modeling learning. In this research, we focused what mathematical concepts are learned and what reasoning are applied and used through mathematical modeling. In the process of mathematical modeling, the students used several types of reasoning; deduction, induction and abduction. Although we cannot generalize a fact by a single case study, deduction has been used to confirm whether their model is correct to the real situation and to find solutions by leading mathematical conclusion and induction to experimentally verify whether their model is correct. And abduction has been used to abstract a mathematical model from a real model, to provide interpretation to existing a practical ground for mathematical results, and elicit new mathematical model by modifying a present model.

• The Korean Journal of Physiology and Pharmacology
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• v.23 no.5
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• pp.305-310
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• 2019

The physiomic approach is now widely used in the diagnosis of cardiovascular diseases. There are two possible methods for cardiovascular physiome: the traditional mathematical model and the machine learning (ML) algorithm. ML is used in almost every area of society for various tasks formerly performed by humans. Specifically, various ML techniques in cardiovascular medicine are being developed and improved at unprecedented speed. The benefits of using ML for various tasks is that the inner working mechanism of the system does not need to be known, which can prove convenient in situations where determining the inner workings of the system can be difficult. The computation speed is also often higher than that of the traditional mathematical models. The limitations with ML are that it inherently leads to an approximation, and special care must be taken in cases where a high accuracy is required. Traditional mathematical models are, however, constructed based on underlying laws either proven or assumed. The results from the mathematical models are accurate as long as the model is. Combining the advantages of both the mathematical models and ML would increase both the accuracy and efficiency of the simulation for many problems. In this review, examples of cardiovascular physiome where approaches of mathematical modeling and ML can be combined are introduced.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.45-65
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• 2020

This research is an analysis of communication that occurs during the quadratic function teaching and learning process of middle school students, which reflects mathematical modeling. For an in-depth analysis of the communication, Sfard(2008)'s discourse theory and language analysis framework were applied. A quadratic function mathematical modeling teaching and learning were conducted for the week second (1 hour) in June 2019 for students who studied the concept of a quadratic function and who passed a specified period (3 months). The results are as follows. First, The commo-gnitive conflict occurred because of differences in prior knowledge other than quadratic function among students. Second, in the course of communication, knowledge was expanded through problem-solving from different perspectives. These results can be interpreted as allowing students to clearly reveal problems in the communication process based on their understanding of the concept of quadratic functions and to facilitate cooperation among students. of the concept of quadratic functions and to facilitate cooperation among students.

• Research in Mathematical Education
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• v.8 no.1
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• pp.39-58
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• 2004

The School of Mathematical Sciences at University Sains Malaysia has offered a laboratory course on the integration of hand-held technology into the teaching and learning of mathematics since the beginning of the 2001/2002 academic year. This inquiry-based course highlights the explorations and application of mathematics in a data rich modeling environment. In addition, the course addresses several issues related to the effective integration of such technology into the mathematics curriculum. This paper discusses the appropriate use of graphing technology to present mathematical concepts and to support student's understanding in a student-centered learning environment, shares knowledge on the new mathematics that was made possible by hand-held technology, and summarizes student reactions to this innovative learning mode.

• Research in Mathematical Education
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• v.25 no.3
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• pp.201-225
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• 2022

This paper details case study vignettes that focus on enhancing the teaching and learning of geometry and measurement in the elementary grades with attention to pedagogical practices for teaching through problem solving with rigor and centering equitable teaching practices. Rigor is a matter of equity and opportunity (Dana Center, 2019). Rigor matters for each and every student and yet research indicates historically disadvantaged and underserved groups have more of an opportunity gap when it comes to rigorous mathematics instruction (NCTM, 2020). Along with providing a conceptual framework that focuses on the importance of equitable instruction, our study unpacks ways teachers can leverage their deep understanding of geometry and measurement learning trajectories to amplify the mathematics through rigorous problems using multiple approaches including learning by doing, challenged-based and mathematical modeling instruction. Through these vignettes, we provide examples of tasks taught through rigorous problem solving approaches that support conceptual teaching and learning of geometry and measurement. Specifically, each of the three vignettes presented includes a task that was implemented in an elementary classroom and a vertically articulated task that engaged teachers in a professional learning workshop. By beginning with elementary tasks to more sophisticated concepts in higher grades, we demonstrate how vertically articulating a deeper understanding of the learning trajectory in geometric thinking can add to the rigor of the mathematics.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.257-277
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• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• Korean Journal of Computational Design and Engineering
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• v.20 no.2
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• pp.93-103
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• 2015

In this study, we organize and explain various ways to construct 3D models in the 2D plane using Geogebra, mathematical education software that enables us to visualize dynamically the interaction between algebra and geometry. In these ways, we construct three unit vectors for 3 dimensions at a point on the Cartesian coordinates, on the basis of which we can build up the 3D models by putting together basic mathematical objects like points, lines or planes. We can apply the ways of constructing the 3 dimensions on the Cartesian coordinates to modeling of various structures in the real world, and have chances to translate, rotate, zoom, and even animate the structures by means of slider, one of the very important functions in Geogebra features. This study suggests that the visualizing and dynamic features of Geogebra help for sure to make understood and maximize learning effectiveness on mechanical modeling or the 3D CAD.