Earticle

오늘날 수학교육에서는 단순한 지식 습득보다 맥락화된 과제 속에서 수학적 지식 을 추출 또는 적용하는 방식이 선호된다. 이러한 목적을 위해 출발점이 현실 맥락 이라는 특성을 지닌 수학적 모델링은 유용하고, 이때 과제 맥락에 대한 개인의 처 리 방식 및 과제 수행에 대한 영향은 다양한 것으로 알려져 있다. 특히 미래 사회 인재로서의 영재에게 사회적 특성의 역량이 요구되지만, 영재의 인지적 발달이 정 의적 발달을 보장하지 않는다는 사실을 고려할 때, 영재교육에서 사회적 맥락으로 부터 출발하는 수학적 모델링 활동은 유의미한 성과를 낳을 것으로 기대된다. 이에 본 연구에서는 초등수학영재의 사회적 맥락 과제에 대한 수학적 모델링 과정에서 나타나는 과제 맥락 처리 유형을 개별(수학적>통합적>양면적>현실적), 모둠별(통합 적>수학적)로 분석하여 유형의 특징과 변화를 통해 사회적 맥락이 과제 수행에 미 치는 영향을 파악하고 교수학적 시사점을 도출하였다.

In contemporary mathematics education, an emphasis is placed on extracting and applying mathematical knowledge within contextualized tasks, rather than mere acquisition of simple knowledge. Mathematical modelling, which starts from real-world contexts, is a useful approach to achieving this goal. It is well-known that individual task performance is influenced in various ways by the context of the tasks. In particular, although gifted students as future social leaders are expected to possess social competence, it is important to note that cognitive development alone in gifted individuals does not guarantee their ability to meet social demands. Therefore, the application of mathematical modeling activities rooted in social contexts is anticipated to yield substantive outcomes in the domain of gifted education. To address this, this study analyzed types of dealing with the context, both on an individual basis (mathematics bound > integrating > ambivalent > reality bound) and within collaborative settings (integrating > mathematics bound), within the realm of mathematical modeling of social context tasks for elementary school gifted students. This analysis leads us to understand the impact of the social context on task performance and derive didactical implications.

연구의 목적은 ICME(2008,Mexico) 모델링 TSG21에서 논의한 모델링의 두 과제 설정 MMa, MeA이 학교수학에 효율적으로 적용이 될 수 있는지를 알아보는데 있다. 이 실험에서 수학과 교육과정에 적용할 수 있는 몇 가지 중요한 점을 발견했는데, 첫째는 MMa 집단이 통제집단 IPS에 모델링 문항에서 성취도에 유의미한 차이를 보였고, 정보처리 문항에서도 좋은 성취수준을 보였다. 다시 말하면 모델링 MMa, MeA 교육이 가능하게 현행 학교 문제해결 또는 개념 학습에 포함이 되고 더욱 발전 되는 시스템을 가질 수 있다. 둘째는 실험집단의 학생들이 생성한 모델링 처음 3단계 상황분석, 수학질문 구성, 모델설정에서 독특한 발견전략을 사용하였고 후반 2단계에서도 전통적 IPS 문제해결과 좋은 연결성을 보였다. 또, 실험집단 MMa, MeA 학생들이 개념적 시스템의 구성과정을 잘 이해했으며 Lesh & Sriraman(2005a, 2005b)의 개념적 시스템의 구성을 뒷받침 해 주었다. 셋째는 과제설정 MEA, MMa 간에 모델링의 사고행동인 수학적 상황 센스를 만들기(S), 창조하기(C), 확장하기(E), 재 정의하기(RF)가 교실에서 활발하게 일어났다는 점이다. 따라서 Pollak등이 제언한 모델링 활동은 현행 IPS 활동과 의미 있게 교류 될 수 있다.

The purpose of this study was to examine the effects of tasks setting for mathematical modelling in the complex real situations. The tasks setting( MMa,MeA) in mathematical modelling was so important that we can't ignore its effects to develop meaning and integrate mathematical ideas. The experimental setting were two groups (N=103, N=103) at public high school and non-experimental setting was one group(N=103). In mathematical achievement, we found meaningful improvement for MeA group on modelling tasks, but no meaningful effect on information processing tasks. The statistical method used was ACONOVA analysis. Beside their achievement, we were much concerned about their modelling approach that TSG21 had suggested in Category " Educational & Cognitive Modelling". Subjects who involved in experimental works showed very interesting approach as Exploration, analysis in some situation ⇒ Math. questions ⇒ Setting models ⇒ Problem solution ⇒ Extension, generalization, but MeA group spent a lot of time on step: Exploration, analysis and MMa group on step, Setting models. Both groups integrated actively many heuristics that schoenfeld defined. Specially, Drawing and Modified Simple Strategy were the most powerful on approach step 1,2,3. It was very encouraging that those experimental setting was improved positively more than the non-experimental setting on mathematical belief and interest. In our school system, teaching math. modelling could be a answer about what kind of educational action or environment we should provide for them. That is, mathematical modelling could be the most important source of motivation on the future mathematical learning.

본 연구에서는 삼각함수의 모델링을 통한 그래픽 과정의 효과를 알아보기 위한 실험연구로 실험과정의 분석을 질적연구 방법으로 처리했다. 이를 위해 수학적 모델링의 절차를 세분하여 기존의 모델에 두 단계, 즉, 질문의 생성과 아이디어 교환을 강조하는 놀이실험단계와 컴퓨터 그래픽 과정의 단계를 추가했다. 실험은 고등학교 2학년을 대상으로 실험반(TMG) 26명이 참여했고, 데이터의 질적 분석을 위해 활동지, 면담 및 실험과정의 관찰자료를 분석하였다. 국내외 대부분의 연구가 통계적 방법을 이용한 양적 분석 방법이기 때문에 교사들에게는 모델링 수업에 큰 도움을 주지 못한다. 연구결과로 (1) 기존의 수학적 모델링의 절차에 두 개의 단계를 추가하여 보다 세분화한 모델링의 과정은 질문생성, 아이디어교환, 동료들과 소통 등에서 긍정적인 결과를 볼 수 있었다. (2) 실험학교의 수학과 수업에 컴퓨터 그래픽을 포함한 테크놀로지의 도입은 양과 수(Quantity) 교육에 매우 적절함을 보여주었다.

The purpose of this study is to qualitatively examine the effects of graphics representation of trigonometry modelling concerning question generating and idea sharing. The experimental setting(Experiment Group) was one class (N=26) at a public high school. The modelling process was designed as a process-oriented conceptualization divided into three steps i.e., (1) game with idea sharing and question generating, (2) graphic representation, and (3) symbolization in the mathematical applied tasks related to trigonometry function. The result indicates that Graphic Representation with Game Activity increases the opportunity of question generating and idea sharing during experimental work. Also, the results show that the introduction of computer graphics enhances the teaching of mathematical quantity in highschool classrooms.

In this paper, we research on the modern Internet of things system structure optimization methodology based on the information theory and the communication signal transmission model. We analyze the current IOT system from the following aspects. (1) Reliable delivery, that is, through some of the Internet and telecommunication network integration, it will send some information about the object accurately in real time; For the Internet of things, it is an integrated which is by a variety of network and the access and application technology of an integrated, at the same time it is also a can make the objects and people, nature and people as well as a platform for communication between objects and the objects. (2) The comprehensive perception which is to use some of the perception, capture and real-time measurement technology to information acquisition and access to an object with the sensing device can achieve data readout and data sent and no contact some automated to realize long-distance induction. (3) Intelligent processing, is one of the core content of the Internet of things, is to use some intelligent computing some analysis was carried out on large amount of information and data disposal, the Internet of things is able to intelligently control object by the computer network technology, micro processing technology, wireless communication technology and sensor technology product of development of fusion, therefore the Internet of things can be representative even instead of rational analysis. Through combining the information theory and the efficient signal transmission models, we optimize the current IOT architecture and the final experiment result indicates the feasibility of the proposed methodology.

With the arrival of global economic integration, the enterprise gradually realized the joint and downstream enterprises form a complementary advantage on its importance to enhance the overall competitiveness of the supply chain. To deal with the corresponding challenges, in this paper, we conduct research on pricing and the advertising coordination of multi retailer supply chain from the general perspectives of common interest maximization. For the two stage supply chain consisting of a single manufacturer and single retailer as the background, study retailers to establish online channel and manufacturers to establish the online channel and applicable condition, the difference between two kinds of the channel model and double channel of supply chain coordination mechanism. The core idea of supply chain management is focus on supply chain node enterprise specializing in their core business, and outsources non-core business to other enterprises, so as to achieve supply chain of all enterprises focus on their good at business. Our research optimizes the traditional game theory framework to achieve the better model for the issues. The experimental analysis verifies the feasibility and the effectiveness of our approach compared with the others.

The short-range inertial aircraft has a short flight time, and its flight accuracy is influenced by various disturbance factors, and it is highly difficult to control the guidance. In this paper, various disturbance influences on the flight accuracy of ignoring after launching” aircraft is researched, through the mathematical modeling of such kind of aircraft and the mathematical modeling of various disturbance factors, the corresponding disturbance flight disturbance trajectory is analyzed under the influence of many disturbance factors like crosswind, initial disturbance and thrust eccentric, and it is concluded that the position control inertial guidance is a good plan, which can effectively eliminate the crosswind disturbance influence, then the engine thrust curve is relatively curve, the axial accelerometer can be omitted. For the above inertial guidance plan, the accuracy of angular position gyroscope on the aircraft is an important factor to decide the inertial guidance accuracy of the aircraft, thus providing key technical basis for the comprehensive evaluation of overall aircraft plan and the deep research of aircraft.

At present, the 3D object model technique is being applied in the simulation, virtual reality, 3D film industry and culture protection, and many other fields which can be widely applied. However, the existing 3D reconstruction technology is based on the complex and often expensive sensors. Therefore, we conduct research on computer graphics theory and mathematical modelling based 3D reconstruction methodology with Kinect. We firstly introduce the basic concepts and application of Kinect system which serves as the preliminary of our research. Then, we conduct mathematical modelling for our proposed system with theoretical analysis. Later, experiment and numerical simulation is conducted for verifying the robustness and effectiveness of our proposed approach. The visualized and numerical simulation result indicates that our method outperforms and holds better accuracy compared with other popular adopted algorithms. In the future, we plan to combine more optimization techniques to polish and modify our approach.

There have been many research efforts on biofilter modeling including Ottengraf et al. who derived a model equation for the concentration profile of pollutants(e.g., VOCs) in the biolayer and solved their outlet concentration of the waste gas stream through biofilter. However, for most of research works done so far, the effects to explain the effect of adsorption of organic particles to medium(i.e., adsorbent) have been ignored. In this work biofilter modeling accompanying process lumping has been proposed and the theoretical effect of adsorption property of the medium, on the biofilter performance of eliminating organic components in waste gas stream, is intensively discussed.

본 연구는 수학적 모델링의 과제공간을 설정하고 이를 기반으로 모델링 과제의 복잡성을 나타내는 평가척도(rating scheme)를 설계하여 그것의 타당도를 확인하였다. 예비 수학교사를 대상으로 두 단계의 과정을 거쳐 실험을 진행하였고 다음과 같은 결과를 얻을 수 있었다. 첫째는 종전의 문제구조를 표현한 문제공간을 발전시켜 모델링 과제에 맞는 과제공간을 설정하고, 모델링 과제의 복잡성을 수치로 나타내는 계량적인 평가척도를 설계하여 의미 있는 타당도를 확인하였다. 둘째로는 모델링 과제 복잡성의 평가척도, 학생 성취수준, 과제 특수 발견 전략의 개수 사이에는 일관된 패턴이 있음을 발견하였다.

The purpose of this study was to decide the task space and Rating Scheme of task difficulty in complicated mathematical modelling situations. One of main objective was also to conform the validation of Rating Scheme to determine the degree of difficulty by comparing the student performance with the statement of the theoretical model. In spring 2014, the experimental setting was in Modelling Cource for 38 in-service teachers in mathematics education. In conclusions, we developed the Model of Task Space based on their solution paths in mathematical modelling tasks and Rating Scheme for task difficulty. The Validity of Rating Scheme to determine the degree of task difficulty based on comparing the student performance gave us the meaningful results. Within a modelling task the student performance verifies the degree of difficulty in terms of scoring higher using solution approaches determined as easier and vice versa. Another finding was some relations among three research topics, that is, degree of task difficulty on rating scheme, levels of students performance and numbers of specific heuristic. Those three topics showed the impressive consistence pattern.

The paper describes some principles how we design the mathematics curriculum through mathematical Modelling. since the motivation for modelling is that it give us a cheap and rapid method of answering illposed problem concerning the real world situations. The experiment was focussed on the possibility that they can involved in modelling problem sets and carry modelling process. The main principles could be described as follows. principle 1. we as a teacher should introduce the modelling problems which have many constraints at the begining situation, but later eliminate those constraints possibly. principle 2. we should avoid the modelling real situations which contain the huge data collection in the classroom, but those could be involved in the mathematics club and job oriented problem solving. principle 3. Analysis of modelling situations should be much emphasized in those process of mathematics curriculum principle 4. As a matter of decision, the teachers should have their own activities that do mathematics curriculum free. principle 5. New strategies appropriate in solving modelling problem could be developed, so that these could contain those of polya's heusistics

Gas separation via hollow fibre membrane modules (HFMM) is deemed to be a promising technology for natural gas sweetening, particularly for lowering the level of carbon dioxide (CO₂) in natural gas, which can cause various problems during transportation and process operation. Separation performance via HFMM is affected by membrane properties, module specifications and operating conditions. In this study, a mathematical model for HFMM is developed, which can be used to assess the effects of the aforementioned variables on separation performance. Appropriate boundary conditions are imposed to resolve steady-state values of permeate variables and incorporated in the model equations via an iterative numerical procedure. The developed model is proven to be reliable via model validation against experimental data in the literature. Also, the model is capable of capturing axial variations of process variables as well as predicting key performance indicators. It can be extended to simulate a large-scale plant and identify an optimal process design and operating conditions for improved separation efficiency and reduced cost.

In [1, 2], we studied the string-like system with time-varying delay. Unlike the string system, the plate system must consider both longitudinal and transverse strains. First, we consider the physical phenomenon of an axially moving plate concerning kinetic energy, potential energy, and work dones. By the energy conservation law in physics, we have a nonlinear plate-like system with internal time delay.

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t > 0 heat is generated within the circular disk at a rate of g(r, z, t) $Btu/hr.ft^3$. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature $Q_3(r,t)$ and the upper surface ($Z={\infty}$) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.

Some of the initial steps necessary for the application of Kalman filter will be discussed in general. The application of filtering for tracking system will then be illustrated by simple examples. Practical implementation problems as well as hardware synthesis difficulties, are discussed.

Cellular kinetics formulate the basis of tumor immune system dynamics which may be synthesized mathematically as cascades of bilinear systems which are connected by nonlinear dynamical terms. In this manner, a foundation for the control of syngeneic tumors is presented. We have analyzed the mechanisms of controlling the infiltration of lymphocytes into tumor tissues. Simulated anneal ins, a general-purpose method of multivariate optimization, is applied to combinatorial optimization, which is to find the minimum of a given function depending on many parameters. We compare the results of the different methods including the global optimization algorithm, known as simutated annealing.

OBJECTIVES Although the role of specific holidays in modifying transmission dynamics of infectious diseases has received some research attention, the epidemiological impact of public holidays on the transmission of coronavirus disease 2019 (COVID-19) remains unclear. METHODS To assess the extent of increased transmission frequency during public holidays, we collected COVID-19 incidence and mobility data in Hokkaido, Tokyo, Aichi, and Osaka from February 15, 2020 to September 30, 2021. Models linking the estimated effective reproduction number (Rt) with raw or adjusted mobility, public holidays, and the state of emergency declaration were developed. The best-fit model included public holidays as an essential input variable, and was used to calculate counterfactuals of Rt in the absence of holidays. RESULTS During public holidays, on average, Rt increased by 5.71%, 3.19%, 4.84%, and 24.82% in Hokkaido, Tokyo, Aichi, and Osaka, respectively, resulting in a total increase of 580 (95% confidence interval [CI], 213 to 954), 2,209 (95% CI, 1,230 to 3,201), 1,086 (95% CI, 478 to 1,686), and 5,211 (95% CI, 4,554 to 5,867) cases that were attributable to the impact of public holidays. CONCLUSIONS Public holidays intensified the transmission of COVID-19, highlighting the importance of considering public holidays in designing appropriate public health and social measures in the future.