• The Mathematical Education
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• v.63 no.2
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• pp.369-385
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• 2024

With the advancement of digital technology, a variety of digital materials are being utilized in education. For their appropriate use of digital resources, teachers need to be able to evaluate the quality of digital resource and determine the suitability for teaching. This study explored how preservice teachers evaluate TocToc-Math, an Artificial Intelligence (AI)-based math support system. Based on an evaluation framework developed through prior research, preservice teachers evaluated TocToc-Math with evidence-based criteria, including content quality, pedagogy, technology use, and mathematics curriculum alignment. The findings shows that preservice teachers positively evaluated TocToc-Math overall. The evaluation tendencies of preservice teachers were classified into three groups, and the specific characteristics of each factor differed depending on the group. Based on the research results, we suggest implications for improving preservice teachers' evaluation abilities regarding the use of digital technology and AI in mathematics education.

• Advances in concrete construction
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• v.11 no.1
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• pp.1-9
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• 2021

This article discusses the issue of optimizing controller design issues, in which the artificial intelligence (AI) evolutionary bat (EB) optimization algorithm is combined with the fuzzy controller in the practical application of the building. The controller of the system design includes different sub-parts such as system initial condition parameters, EB optimal algorithm, fuzzy controller, stability analysis and sensor actuator. The advantage of the design is that for continuous systems with polytypic uncertainties, the integrated H2/H∞ robust output strategy with modified criterion is derived by asymptotically adjusting design parameters. Numerical verification of the time domain and the frequency domain shows that the novel system design provides precise prediction and control of the structural displacement response, which is necessary for the active control structure in the fuzzy model. Due to genetic algorithm (GA), we use a hierarchical conditions of the Hurwitz matrix test technique and the limits of average performance, Hierarchical Fitness Function Structure (HFFS). The dynamic fuzzy controller proposed in this paper is used to find the optimal control force required for active nonlinear control of building structures. This method has achieved successful results in closed system design from the example.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.367-386
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• 2006

There are two strands for considering tile relationships between education and technology. One is the viewpoint of 'learning from computers' and the other is that of 'learning with computers'. In this paper, we call mathematics education with computers as 'computers and mathematics education' and this computer environments as microworlds. In this paper, we first suggest theoretical backgrounds ai constructionism, mathematization, and computer interaction. These theoretical backgrounds are related to students, school mathematics and computers, relatively As specific strategies to design a microworld, we consider a physical construction, fuctiionization, and internet interaction. Next we survey the different microworlds such as Logo and Dynamic Geometry System(DGS), and reform each microworlds for mathematical level-up of representation. First, we introduce the concept of action letters and its manipulation for representing turtle actions and recursive patterns in turtle microworld. Also we introduce another algebraic representation for representing DGS relation and consider educational moaning in dynamic geometry microworld. We design an integrating microworld between Logo and DGS. First, we design a same command system and we get together in a microworld. Second, these microworlds interact each other and collaborate to construct and manipulate new objects such as tiles and folding nets.

• The Mathematical Education
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• v.62 no.2
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• pp.289-302
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• 2023

In today's digital information society, student knowledge and skills to analyze big data and make informed decisions have become an important goal of school mathematics. Integrating big data statistical projects with digital technologies in high school <Artificial Intelligence> mathematics courses has the potential to provide students with a learning experience of high impact that can develop these essential skills. This paper proposes a set of guidelines for designing effective big data statistical project-based tasks and evaluates the tasks in the artificial intelligence mathematics textbook against these criteria. The proposed guidelines recommend that projects should: (1) align knowledge and skills with the national school mathematics curriculum; (2) use preprocessed massive datasets; (3) employ data scientists' problem-solving methods; (4) encourage decision-making; (5) leverage technological tools; and (6) promote collaborative learning. The findings indicate that few textbooks fully align with these guidelines, with most failing to incorporate elements corresponding to Guideline 2 in their project tasks. In addition, most tasks in the textbooks overlook or omit data preprocessing, either by using smaller datasets or by using big data without any form of preprocessing. This can potentially result in misconceptions among students regarding the nature of big data. Furthermore, this paper discusses the relevant mathematical knowledge and skills necessary for artificial intelligence, as well as the potential benefits and pedagogical considerations associated with integrating technology into big data tasks. This research sheds light on teaching mathematical concepts with machine learning algorithms and the effective use of technology tools in big data education.

• Communications for Statistical Applications and Methods
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• v.15 no.1
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• pp.117-124
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• 2008

The liquidity risk is defined as an additional risk in the market due to the timing and size of a trade. A recent work by Cetin et ai. (2003) proposes a rigorous mathematical model incorporating this liquidity risk into the arbitrage pricing theory. A practical problem arising in a real market application is an estimation problem of a liquidity cost. In this paper, we propose to estimate the liquidity cost function in the context of Cetin et al. (2003) using the constrained least square (LS) method, and illustrate it by analyzing the Kellogg company data.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.773-793
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• 2005

We consider interesting conditions, one of which will be called the disjoint $(A^2,\;D^2)-pair$ property, on genus $g{\geq}2$ Heegaard splittings of compact orient able 3-manifolds. Here a Heegaard splitting $(C_1,\;C_2;\;F)$ admits the disjoint $(A^2,\;D^2)-pair$ property if there are an essential annulus Ai normally embedded in $C_i$ and an essential disk $D_j\;in\;C_j((i,\;j)=(1,\;2)\;or\;(2,\;1))$ such that ${\partial}A_i$ is disjoint from ${\partial}D_j$. It is proved that all genus $g{\geq}2$ Heegaard splittings of toroidal manifolds and Seifert fibered spaces admit the disjoint $(A^2,\;D^2)-pair$ property.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1232-1239
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• 2006

In the present study, the unsteady Hartmann flow with heat transfer of a viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.

• Journal of Engineering Education Research
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• v.24 no.6
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• pp.79-85
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• 2021

In a future society where cutting-edge science technology such as artificial intelligence becomes commonplace, the demand for talented people with basic knowledge of mathematics and science is expected to increase continuously, and the educational infrastructure suitable for the characteristics of future generations is still insufficient. In particular, in the case of students taking convergence courses including practical training, there was a problem in communication with the instructor. In this study, we looked at the current status of distance learning at domestic universities that came suddenly due to the global pandemic of COVID-19. In addition, a case study of the use of technology was conducted to facilitate the interaction between instructors and learners through case analysis of distance classes in convergence subjects. Therefore, this study aims to introduce the case of developing lecture contents for smooth convergence education in a non-face-to-face educational environment targeting the developed AI convergence courses and applying them to the education of enrolled students.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.1-21
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• 2022

The purpose of this study is to analyze the current situation of EduTech, which is proposed as a way to build a flexible learning environment regardless of time and place according to the use of digital technology in mathematics subjects. The process of designing classes to use the EduTech platform, which is still in the development introduction stage, in public education is still difficult, and research to observe its effects and characteristics is also in its early stages. However, in the stage of preparing for future education, it is a meaningful process to grasp the current situation and point out the direction in preparation for the future in which EduTech will be actively applied to education. Accordingly, the current situation and utilization trends of EduTech at home and abroad were confirmed, and the functions and roles of EduTech platforms used in mathematics were analyzed. As a result of the analysis, the EduTech platform was pursuing learners' self-directed learning by constructing its functions so that they could be useful for individual learning of learners in hierarchical mathematics education. In addition, we have confirmed that the platform is evolving to be useful for teachers' work reduction, suitable activities, and evaluations learning management. Therefore, it is necessary to implement instructional design and individual customized learning support measures for students that can efficiently utilize these platforms in the future.