Search results for: Vocational Teaching Method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8531

Search results for: Vocational Teaching Method

8321 Creative Teaching of New Product Development to Operations Managers

Authors: Marco Leite, J. M. Vilas-Boas da Silva, Isabel Duarte de Almeida

Abstract:

New Product Development (NPD) has got its roots on an Engineering background. Thus, one might wonder about the interest, opportunity, contents and delivery process, if students from soft sciences were involved. This paper addressed «What to teach?» and «How to do it?», as the preliminary research questions that originated the introduced propositions. The curriculum-developer model that was purposefully chosen to adapt the coursebook by pursuing macro/micro strategies was found significant by an exploratory qualitative case study. Moreover, learning was developed and value created by implementing the institutional curriculum through a creative, hands-on, experiencing, problem-solving, problem-based but organized teamwork approach. Product design of an orange squeezer complying with ill-defined requirements, including drafts, sketches, prototypes, CAD simulations and a business plan, plus a website, written reports and presentations were the deliverables that confirmed an innovative contribution towards research and practice of teaching and learning of engineering subjects to non-specialist operations managers candidates.

Keywords: Teaching Engineering to Non-specialists, Operations Managers Education, Teamwork, Product Design and Development, Market- driven NPD, Curriculum development.

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8320 Calculation of Heating Load for an Apartment Complex with Unit Building Method

Authors: Ju-Seok Kim, Sun-Ae Moon, Tae-Gu Lee, Seung-Jae Moon, Jae-Heon Lee

Abstract:

As a simple to method estimate the plant heating energy capacity of an apartment complex, a new load calculation method has been proposed. The method which can be called as unit building method, predicts the heating load of the entire complex instead of summing up that of each apartment belonging to complex. Comparison of the unit heating load for various floor sizes between the present method and conventional approach shows a close agreement with dynamic load calculation code. Some additional calculations are performed to demonstrate it-s application examples.

Keywords: Unit Building Method, Unit Heating Load, TFMLoad.

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8319 Perceptions toward Adopting Virtual Reality as a Learning Aid in Information Technology

Authors: S. Alfalah, J. Falah, T. Alfalah, M. Elfalah, O. Falah

Abstract:

The field of education is an ever-evolving area constantly enriched by newly discovered techniques provided by active research in all areas of technologies. The recent years have witnessed the introduction of a number of promising technologies and applications to enhance the teaching and learning experience. Virtual Reality (VR) applications are considered one of the evolving methods that have contributed to enhancing education in many fields. VR creates an artificial environment, using computer hardware and software, which is similar to the real world. This simulation provides a solution to improve the delivery of materials, which facilitates the teaching process by providing a useful aid to instructors, and enhances the learning experience by providing a beneficial learning aid. In order to assure future utilization of such systems, students’ perceptions were examined toward utilizing VR as an educational tool in the Faculty of Information Technology (IT) in The University of Jordan. A questionnaire was administered to IT undergraduates investigating students’ opinions about the potential opportunities that VR technology could offer and its implications as learning and teaching aid. The results confirmed the end users’ willingness to adopt VR systems as a learning aid. The result of this research forms a solid base for investing in a VR system for IT education.

Keywords: Education, information, technology, virtual reality.

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8318 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

Abstract:

In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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8317 Convergence of ICT and Education

Authors: Raju Kumar

Abstract:

Information and communication technology (ICT) has become, within a very short time, one of the basic building blocks of modern society. Many countries now understanding the importance of ICT and mastering the basic skills and concepts of it as part of the core of education. Organizations, experts and practitioners in the education sector increasingly recognizing the importance of ICT in supporting educational improvement and reform. This paper addresses the convergence of ICT and education. When two technologies are converging to each other, together they will generate some great opportunities and challenges. This paper focuses on these issues. In introduction section, it explains the ICT, education, and ICT-enhanced education. In next section it describes need of ICT in education, relationship between ICT skills and education, and stages of teaching learning process. The next two sections describe opportunities and challenges in integrating ICT in education. Finally the concluding section summaries the idea and its usefulness.

Keywords: Education, Information and CommunicationTechnology, Learning, Teaching.

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8316 Promoting Mathematical Understanding Using ICT in Teaching and Learning

Authors: Kamel Hashem, Ibrahim Arman

Abstract:

Information and Communication Technologies (ICT) in mathematical education is a very active field of research and innovation, where learning is understood to be meaningful and grasping multiple linked representation rather than rote memorization, a great amount of literature offering a wide range of theories, learning approaches, methodologies and interpretations, are generally stressing the potentialities for teaching and learning using ICT. Despite the utilization of new learning approaches with ICT, students experience difficulties in learning concepts relevant to understanding mathematics, much remains unclear about the relationship between the computer environment, the activities it might support, and the knowledge that might emerge from such activities. Many questions that might arise in this regard: to what extent does the use of ICT help students in the process of understanding and solving tasks or problems? Is it possible to identify what aspects or features of students' mathematical learning can be enhanced by the use of technology? This paper will highlight the interest of the integration of information and communication technologies (ICT) into the teaching and learning of mathematics (quadratic functions), it aims to investigate the effect of four instructional methods on students- mathematical understanding and problem solving. Quantitative and qualitative methods are used to report about 43 students in middle school. Results showed that mathematical thinking and problem solving evolves as students engage with ICT activities and learn cooperatively.

Keywords: Dynamic Geometry Software, Information and Communication Technologies, Visualization, Mathematical Education.

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8315 Web Based Remote Access Microcontroller Laboratory

Authors: H. Çimen, İ. Yabanova, M. Nartkaya, S. M. Çinar

Abstract:

This paper presents a web based remote access microcontroller laboratory. Because of accelerated development in electronics and computer technologies, microcontroller-based devices and appliances are found in all aspects of our daily life. Before the implementation of remote access microcontroller laboratory an experiment set is developed by teaching staff for training microcontrollers. Requirement of technical teaching and industrial applications are considered when experiment set is designed. Students can make the experiments by connecting to the experiment set which is connected to the computer that set as the web server. The students can program the microcontroller, can control digital and analog inputs and can observe experiment. Laboratory experiment web page can be accessed via www.elab.aku.edu.tr address.

Keywords: Embedded systems education, distance learning, internet-based control, remote microcontroller laboratory.

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8314 Teacher Trainers’ Motivation in Transformation of Teaching and Learning: The Fun Way Approach

Authors: Malathi Balakrishnan, Gananthan M. Nadarajah, Noraini Abd Rahim, Amy Wong On Mei

Abstract:

The purpose of the study is to investigate the level of intrinsic motivation of trainers after attending a Continuous Professional Development Course (CPD) organized by Institute of Teacher Training Malaysia titled, “Transformation of Teaching and Learning the Fun Way”. This study employed a survey whereby 96 teacher trainers were given Situational Intrinsic Motivational Scale (SIMS) Instruments. Confirmatory factor analysis was carried out to get the validity of this instrument in local setting. Data were analyzed with SPSS for descriptive statistic. Semi- structured interviews were also administrated to collect qualitative data on participants’ experiences after participating in the two-day fun-filled program. The findings showed that the participants’ level of intrinsic motivation showed higher mean than the amotivation. The results revealed that the intrinsic motivation mean is 19.0 followed by Identified regulation with a mean of 17.4, external regulation 9.7 and amotivation 6.9. The interview data also revealed that the participants were motivated after attending this training program. It can be concluded that this program, which was organized by Institute of Teacher Training Malaysia, was able to enhance participants’ level of motivation. Self-Determination Theory (SDT) as a multidimensional approach to motivation was utilized. Therefore, teacher trainers may have more success using the “The fun way approach” in conducting training program in future.

Keywords: Teaching and Learning, Motivation, Teacher Trainer, SDT.

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8313 A New Preconditioned AOR Method for Z-matrices

Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.

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8312 A Family of Improved Secant-Like Method with Super-Linear Convergence

Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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8311 Advantages of Fuzzy Control Application in Fast and Sensitive Technological Processes

Authors: Radim Farana, Bogdan Walek, Michal Janosek, Jaroslav Zacek

Abstract:

This paper presents the advantages of fuzzy control use in technological processes control. The paper presents a real application of the Linguistic Fuzzy-Logic Control, developed at the University of Ostrava for the control of physical models in the Intelligent Systems Laboratory. The paper presents an example of a sensitive non-linear model, such as a magnetic levitation model and obtained results which show how modern information technologies can help to solve actual technical problems. A special method based on the LFLC controller with partial components is presented in this paper followed by the method of automatic context change, which is very helpful to achieve more accurate control results. The main advantage of the used system is its robustness in changing conditions demonstrated by comparing with conventional PID controller. This technology and real models are also used as a background for problem-oriented teaching, realized at the department for master students and their collaborative as well as individual final projects.

Keywords: Control, fuzzy logic, sensitive system, technological proves.

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8310 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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8309 Improved IDR(s) Method for Gaining Very Accurate Solutions

Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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8308 Denosing ECG using Translation Invariant Multiwavelet

Authors: Jeong Yup Han, Su Kyung Lee, Hong Bae Park

Abstract:

In this paper, we propose a method to reduce the various kinds of noise while gathering and recording the electrocardiogram (ECG) signal. Because of the defects of former method in the noise elimination of ECG signal, we use translation invariant (TI) multiwavelet denoising method to the noise elimination. The advantage of the proposed method is that it may not only remain the geometrical characteristics of the original ECG signal and keep the amplitudes of various ECG waveforms efficiently, but also suppress impulsive noise to some extent. The simulation results indicate that the proposed method are better than former removing noise method in aspects of remaining geometrical characteristics of ECG signal and the signal-to-noise ratio (SNR).

Keywords: ECG, TI multiwavelet, denoise.

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8307 Teaching Approach and Self-Confidence Effect Model Consistency between Taiwan and Singapore Multi-Group HLM

Authors: PeiWen Liao, Tsung Hau Jen

Abstract:

This study was conducted to explore the effects of two countries model comparison program in Taiwan and Singapore in TIMSS database. The researchers used Multi-Group Hierarchical Linear Modeling techniques to compare the effects of two different country models and we tested our hypotheses on 4,046 Taiwan students and 4,599 Singapore students in 2007 at two levels: the class level and student (individual) level. Design quality is a class level variable. Student level variables are achievement and self-confidence. The results challenge the widely held view that retention has a positive impact on self-confidence. Suggestions for future research are discussed.

Keywords: Teaching approach, self-confidence, achievement, multi-group HLM.

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8306 Direct Method for Converting FIR Filter with Low Nonzero Tap into IIR Filter

Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

Abstract:

In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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8305 Wavelet Based Identification of Second Order Linear System

Authors: Sudipta Majumdar, Harish Parthasarathy

Abstract:

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Keywords: Least squares method, linear system, system identification, wavelet transform.

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8304 Note to the Global GMRES for Solving the Matrix Equation AXB = F

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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8303 Direct Transient Stability Assessment of Stressed Power Systems

Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

Abstract:

This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: Power system, Transient stability, Critical trajectory method, Energy function method.

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8302 The Relevance of Sustainability Skills for International Students

Authors: Mary Panko, Rashika Sharma

Abstract:

Sustainability often appears to be an unfamiliar concept to many international students that enrol in a New Zealand technological degree. Lecturers’ experiences with classroom interactions and evaluation of assessments indicate that studying the concept enlightens and enhances international students understanding of sustainability. However, in most cases, even after studying sustainability in their degree programme, students are not given an opportunity to practice and apply this concept into their professions in their home countries. Therefore, using a qualitative approach, the academics conducted research to determine the change in international students understanding of sustainability before and after their enrolment in an Applied Technology degree. The research also aimed to evaluate if international students viewed sustainability of relevance to their professions and whether the students felt that they will be provided with an opportunity to apply their knowledge about sustainability in the industry. The findings of the research are presented in this paper.

Keywords: Education for sustainability, international students, vocational education.

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8301 A Descent-projection Method for Solving Monotone Structured Variational Inequalities

Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

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8300 The Practice of Teaching Chemistry by the Application of Online Tests

Authors: Nikolina Ribarić

Abstract:

E-learning is most commonly defined as a set of applications and processes, such as Web-based learning, computer-based learning, virtual classrooms and digital collaboration, that enable access to instructional content through a variety of electronic media. The main goal of an e-learning system is learning, and the way to evaluate the impact of an e-learning system is by examining whether students learn effectively with the help of that system. Testmoz is a program for online preparation of knowledge evaluation assignments. The program provides teachers with computer support during the design of assignments and evaluating them. Students can review and solve assignments and also check the correctness of their solutions. Research into the increase of motivation by the practice of providing teaching content by applying online tests prepared in the Testmoz program, was carried out with students of the 8th grade of Ljubo Babić Primary School in Jastrebarsko. The students took the tests in their free time, from home, for an unlimited number of times. SPSS was used to process the data obtained by the research instruments. The results of the research showed that students preferred to practice teaching content, and achieved better educational results in chemistry, when they had access to online tests for repetition and practicing in relation to subject content which was checked after repetition and practicing in "the classical way" – i.e., solving assignments in a workbook or writing assignments in worksheets.

Keywords: Chemistry class, e-learning, online test, Testmoz.

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8299 Error Propagation in the RK5GL3 Method

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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8298 Malaysia Folk Literature in Early Childhood Education

Authors: F. P. Chew, Z. Ishak

Abstract:

Malay Folk Literature in early childhood education served as an important agent in child development that involved emotional, thinking and language aspects. Up to this moment not much research has been carried out in Malaysia particularly in the teaching and learning aspects nor has there been an effort to publish “big books." Hence this article will discuss the stance taken by university undergraduate students, teachers and parents in evaluating Malay Folk Literature in early childhood education to be used as big books. The data collated and analyzed were taken from 646 respondents comprising 347 undergraduates and 299 teachers. Results of the study indicated that Malay Folk Literature can be absorbed into teaching and learning for early childhood with a mean of 4.25 while it can be in big books with a mean of 4.14. Meanwhile the highest mean value required for placing Malay Folk Literature genre as big books in early childhood education rests on exemplary stories for undergraduates with mean of 4.47; animal fables for teachers with a mean of 4.38. The lowest mean value of 3.57 is given to lipurlara stories. The most popular Malay Folk Literature found suitable for early children is Sang Kancil and the Crocodile, followed by Bawang Putih Bawang Merah. Pak Padir, Legends of Mahsuri, Origin of Malacca, and Origin of Rainbow are among the popular stories as well. Overall the undergraduates show a positive attitude toward all the items compared to teachers. The t-test analysis has revealed a non significant relationship between the undergraduate students and teachers with all the items for the teaching and learning of Malay Folk Literature.

Keywords: Big Book, Early Childhood Education, Malay FolkLiterature

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8297 Approximate Method of Calculation of Inviscid Hypersonic Flow

Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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8296 Convergence Analysis of the Generalized Alternating Two-Stage Method

Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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8295 Analysis of Distribution of Thrust, Torque and Efficiency of a Constant Chord, Constant Pitch C.R.P. Fan by H.E.S. Method

Authors: Morteza Abbaszadeh, Parvin Nikpoorparizi, Mina Shahrooz

Abstract:

For the first time since 1940 and presentation of theodorson-s theory, distribution of thrust, torque and efficiency along the blade of a counter rotating propeller axial fan was studied with a novel method in this research. A constant chord, constant pitch symmetric fan was investigated with Reynolds Stress Turbulence method in this project and H.E.S. method was utilized to obtain distribution profiles from C.F.D. tests outcome. C.F.D. test results were validated by estimation from Playlic-s analytical method. Final results proved ability of H.E.S. method to obtain distribution profiles from C.F.D test results and demonstrated interesting facts about effects of solidity and differences between distributions in front and rear section.

Keywords: C.F.D Test, Counter Rotating Propeller, H.E.S. Method, R.S.M. Method

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8294 Teacher Culture Inquiry of Classroom Observation at an Elementary School in Taiwan

Authors: Tsai-Hsiu Lin

Abstract:

Three dimensions of teacher culture hinder educational improvement: individualism, conservatism and presentism. To promote the professional development of teachers, these three aspects in teacher culture should be eliminated. Classroom observation may be a useful method of eliminating individualism. The Ministry of Education in Taiwan has attempted to reduce the isolation of teachers to promote their professional growth. Because classroom observation discourse varies, teachers are generally unwilling to allow their teaching to be observed. However, classroom observations take place in the country in the form of school evaluations. The main purpose of this study was to explore the differences in teachers’ conservatism, individualism and presentism after classroom observations had been conducted at an elementary school in Taiwan. The research method was a qualitative case study involving interviews with the school principal, the director of academic affairs, and two classroom teachers. The following conclusions were drawn: (1) Educators in different positions viewed classroom observations differently; (2) The classroom teachers did not highly value classroom observation; (3) There was little change in the teachers’ conservatism, individualism and presentism after classroom observation.

Keywords: Classroom observation, Lortie’s Trinity, teacher culture, teacher professional development

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8293 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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8292 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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