Search results for: mathematics anxiety

Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

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Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.

Keywords: learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.

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Authors: Elham Amini Boroujeni, Hamid Reza Momeni

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Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.

Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.

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Authors: Hans H. Diel

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A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Process, Modeling.

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Authors: Jingwen Shan

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In order to explore the key factors affecting the robot program learning intention of school students, this study takes the technology acceptance model as the theoretical basis and invites 167 students from Jiading District of Shanghai as the research subjects. In the robot course, the model of school students on their learning behavior is constructed. By verifying the causal path relationship between variables, it is concluded that teachers can enhance students’ perceptual usefulness to robotics courses by enhancing subjective norms, entertainment perception, and reducing technical anxiety, such as focusing on the gradual progress of programming and analyzing learner characteristics. Students can improve perceived ease of use by enhancing self-efficacy. At the same time, robot hardware designers can optimize in terms of entertainment and interactivity, which will directly or indirectly increase the learning intention of the robot course. By changing these factors, the learning behavior of primary and secondary school students can be more sustainable.

Keywords: TAM, learning behavior intentions, robot courses, primary and secondary school students.

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Authors: H. H. Goh, Q. S. Chua, S. W. Lee, B. C. Kok, K. C. Goh, K. T. K. Teo

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At present, the evaluation of voltage stability assessment experiences sizeable anxiety in the safe operation of power systems. This is due to the complications of a strain power system. With the snowballing of power demand by the consumers and also the restricted amount of power sources, therefore, the system has to perform at its maximum proficiency. Consequently, the noteworthy to discover the maximum ability boundary prior to voltage collapse should be undertaken. A preliminary warning can be perceived to evade the interruption of power system’s capacity. The effectiveness of line voltage stability indices (LVSI) is differentiated in this paper. The main purpose of the indices used is to predict the proximity of voltage instability of the electric power system. On the other hand, the indices are also able to decide the weakest load buses which are close to voltage collapse in the power system. The line stability indices are assessed using the IEEE 14 bus test system to validate its practicability. Results demonstrated that the implemented indices are practically relevant in predicting the manifestation of voltage collapse in the system. Therefore, essential actions can be taken to dodge the incident from arising.

Keywords: Critical line, line outage, line voltage stability indices (LVSI), maximum loadability, voltage collapse, voltage instability, voltage stability analysis.

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: Calculus functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.

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Authors: Ç. Erdoğan, T. Turan

Abstract:

Pediatric cancer patients experience multiple distressing, challenges, physical symptom such as fatigue, pain, sleep disturbance, and balance impairment that continue years after treatment completion. In recent years, yoga is often used in children with cancer to cope with these symptoms. Yoga practice is defined as a unique physical activity that combines physical practice, breath work and mindfulness/meditation. Yoga is an increasingly popular mind-body practice also characterized as a mindfulness mode of exercise. This study aimed to evaluate the impact of yoga intervention of children with cancer. This article planned searching the literature in this field. It has been determined that individualized yoga is feasible and provides benefits for inpatient children, improves health-related quality of life, physical activity levels, physical fitness. After yoga program, children anxiety score decreases significantly. Additionally, individualized yoga is feasible for inpatient children receiving intensive chemotherapy. As a result, yoga is an alternative and complementary medicine that can be safely used in children with cancer.

Keywords: Cancer treatment, children, nursing, yoga.

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Authors: Xu-xia Hu, Eric T. T. Wong

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The simulation of external aerodynamics is one of the most challenging and important automotive CFD applications. With the rapid developments of digital computers, CFD is used as a practical tool in modern fluid dynamics research. It integrates fluid mechanics disciplines, mathematics and computer science. In this study, two different types of simulations were made, one for the flow around a simplified high speed passenger car with a rear-spoiler and the other for the flow without a rear-spoiler. The standard k-ε model is selected to numerically simulate the external flow field of the simplified Camry model with or without a rear-spoiler. Through an analysis of the simulation results, a new rear spoiler is designed and it shows a mild reduction of the vehicle aerodynamics drag. This leads to less vehicle fuel consumption on the road.

Keywords: CFD, vehicle rear-spoiler design.

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Authors: Mairwen K. Jones, Lynne Harris, Lisa D. Vaccaro

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Obsessive-Compulsive Disorder (OCD) is a common and disabling condition. Therapist-delivered treatments that use exposure and response prevention have been found to be very effective in treating OCD, although they are costly and associated with high rates of attrition. Effective treatments that can be made widely available without the need for therapist contact are urgently needed. This case study represents the first published investigation of a self-administered cognitive treatment for OCD in a 50-year old female with a 20 year history of OCD. The treatment evaluation occurred over 27 weeks, including 12 weeks of self-administration of the Danger Ideation Reduction Therapy (DIRT) program. Decreases of between 23% to 33% on measures from pre-treatment to follow-up were observed. Bearing in mind the methodological limitations associated with a case study, we conclude that the results reported here are encouraging and indicate that further research effort evaluating the effectiveness of self-administered DIRT is warranted.

Keywords: Anxiety Treatment, Cognitive Therapy, Danger Ideation Reduction Therapy, Obsessive–Compulsive Disorder, Self- Administered Danger Ideation Reduction Therapy.

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Authors: Mohd Anuar Awang Idris, Muhammad Nubli Abdul Wahab, Nora Yusma Mohamed Yusoff

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Wudu’ (Ablution) and Zikr are amongst some of the spiritual tools which may help an individual control his mind, emotion and attitude. These tools are deemed to be able to deliver a positive impact on an individual’s psychophysiology. The main objective of this research is to determine the effects of Wudu’ (Ablution) and Zikr therapy using the biofeedback emWave application and technology. For this research, 13 students were selected as samples from the students’ representative body at the University Tenaga National, Malaysia. The DASS (Depression Anxiety Stress Scale) questionnaire was used to help with the assessment and measurement of each student’s ability in controlling his or her emotions before and after the therapies. The biofeedback emWave technology was utilized to monitor the student’s psychophysiology level. In addition, the data obtained from the Heart rate variability (HRV) test have also been used to affirm that Wudu’ and Zikr had had significant impacts on the student’s success in controlling his or her emotional pressure.

Keywords: Biofeedback emWave, emotion, psychophysiology, wudu’, zikr.

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Authors: Phang Chang, Phang Piau

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Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

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Authors: Perpetua O. Ezeji, Kelechi E. Ezeji

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There has been considerable anxiety in society that social media distracts from education and reduces the social skills of young people. Following this, educators have sought ways to mitigate its negative effects on educational attainment while incorporating its positive aspects into the learning process. This study sought to examine the impact of social media on the study habits of students of Alvan Ikoku Federal College of Education, Owerri. The research design involved survey technique where questionnaires were used to collect data from a sample of the student population. Statistical package for social sciences (SPSS) was used to analyse the data. Spearman’s Rho was the specific tool used for analysis. It was presented in frequency tables and bar charts. Findings from variables investigated showed that at p<0.5, social media usage had a significant impact on the study habits of students of Alvan Ikoku Federal College of Education, Owerri. This indicated the need for stakeholders in the community to employ counselling and other proactive measures to ensure that students maintained proper focus on their primary assignment for schooling.

Keywords: Education, social media, study habits, technology.

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Authors: Nurettin Simsek, Özlem Cakır

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The aim of this study is to point out whether personalization of mathematical word problems could affect student achievement or not. The research was applied on two-grades students at spring semester 2008-2009. Before the treatment, students personal data were taken and given to the computer. During the treatment, paper-based personalized problems and paper-based non personalized problems were prepared by computer as the same problems and then these problems were given to students. At the end of the treatment, students- opinion was taken. As a result of this research, it was found out that there were no significant differences between learners through personalized or non-personalized materials, and also there were no significant differences between gender through personalized and non-personalized problems. However, opinion of students was highly positive through the personalized problems.

Keywords: Personalization, word problem, computer aided personalization.

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Authors: Mona Taheri

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For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

Keywords: Multiple algebra, mathematics, universal algebra.

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Authors: Pei Wen Liao, Tsung Hau Jen

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the data of Taiwanese 8th grader in the 4th cycle of Trends in International Mathematics and Science Study (TIMSS) are analyzed to examine the influence of the science teachers- preference in experimental teaching on the relationships between the affective variables ( the perceived usefulness of science, ease of using science and science learning interest) and the academic achievement in science. After dealing with the missing data, 3711 students and 145 science teacher-s data were analyzed through a Hierarchical Linear Modeling technique. The major objective of this study was to determine the role of the experimental teaching moderates the relationship between perceived usefulness and achievement.

Keywords: TIMSS database, Science achievement, Experimental teaching, Perceived Usefulness, Perceived Ease of Use

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

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As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: Yaşar Baykul, Musa Gürsel, Hacı Sulak, Erhan Ertekin, Ersen Yazıcı, Osman Dülger, Yasin Aslan, Kağan Büyükkarcı

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The reliability of the tools developed to learn the learning styles is essential to find out students- learning styles trustworthily. For this purpose, the psychometric features of Grasha- Riechman Student Learning Style Inventory developed by Grasha was studied to contribute to this field. The study was carried out on 6th, 7th, and 8th graders of 10 primary education schools in Konya. The inventory was applied twice with an interval of one month, and according to the data of this application, the reliability coefficient numbers of the 6 sub-dimensions pointed in the theory of the inventory was found to be medium. Besides, it was found that the inventory does not have a structure with 6 factors for both Mathematics and English courses as represented in the theory.

Keywords: Learning styles, Grasha-Riechmann, reliability, validity.

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Authors: Subramaniam Chandran

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This paper explains how mobile learning assures sustainable e-education for multicultural group of students. This paper reports the impact of mobile learning on distance education in multicultural environment. The emergence of learning technologies through CD, internet, and mobile is increasingly adopted by distance institutes for quick delivery and cost-effective purposes. Their sustainability is conditioned by the structure of learners as well as the teaching community. The experimental study was conducted among the distant learners of Vinayaka Missions University located at Salem in India. Students were drawn from multicultural environment based on different languages, religions, class and communities. During the mobile learning sessions, the students, who are divided on language, religion, class and community, were dominated by play impulse rather than study anxiety or cultural inhibitions. This study confirmed that mobile learning improved the performance of the students despite their division based on region, language or culture. In other words, technology was able to transcend the relative deprivation in the multicultural groups. It also confirms sustainable e-education through mobile learning and cost-effective system of instruction. Mobile learning appropriates the self-motivation and play impulse of the young learners in providing sustainable e-education to multicultural social groups of students.

Keywords: E-Education, mobile learning, multiculturalism.

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Authors: Simon B. N. Thompson

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Cortisol is essential to the regulation of the immune system and yawning is a pathological symptom of multiple sclerosis (MS). Electromyography activity (EMG) in the jaw muscles typically rises when the muscles are moved and with yawning is highly correlated with cortisol levels in healthy people. Saliva samples from 59 participants were collected at the start and after yawning, or at the end of the presentation of yawning-provoking stimuli, in the absence of a yawn, together with EMG data and questionnaire data: Hospital Anxiety and Depression Scale, Yawning Susceptibility Scale, General Health Questionnaire, demographic, health details. Exclusion criteria: chronic fatigue, diabetes, fibromyalgia, heart condition, high blood pressure, hormone replacement therapy, multiple sclerosis, stroke. Significant differences were found between the saliva cortisol samples for the yawners, t (23) = -4.263, p = 0.000, as compared with the non-yawners between rest and post-stimuli, which was nonsignificant. Significant evidence was found to support the Thompson Cortisol Hypothesis suggesting that rises in cortisol levels are associated with yawning. Further research is exploring the use of cortisol as an early diagnostic tool for MS. Ethics approval granted and professional code of conduct, confidentiality, and safety issues are approved therein.

Keywords: Cortisol, Multiple Sclerosis, Yawning, Thompson’s Cortisol Hypothesis.

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Authors: C. Barreto Carvalho, C. da Motta, M. Sousa, J. Cabral, A. L. Carvalho, E. B. Peixoto

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The aim of the current study was to develop and validate a Response to Stressful Situations Scale (RSSS) for the Portuguese population. This scale assesses the degree of stress experienced in scenarios that can constitute positive, negative and more neutral stressors, and also describes the physiological, emotional and behavioral reactions to those events according to their intensity. These scenarios include typical stressor scenarios relevant to patients with schizophrenia, which are currently absent from most scales, assessing specific risks that these stressors may bring on subjects, which may prove useful in non-clinical and clinical populations (i.e. Patients with mood or anxiety disorders, schizophrenia). Results from Principal Components Analysis and Confirmatory Factor Analysis of two adult samples from general population allowed to confirm a three-factor model with good fit indices: χ2 (144)= 370.211, p = 0.000; GFI = 0.928; CFI = 0.927; TLI = 0.914, RMSEA = 0.055, P(rmsea ≤0.005) = .096; PCFI = .781. Further data analysis of the scale revealed that RSSS is an adequate assessment tool of stress response in adults to be used in further research and clinical settings, with good psychometric characteristics, adequate divergent and convergent validity, good temporal stability and high internal consistency.

Keywords: Assessment, stress events, stress response, stress vulnerability.

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Authors: Feng Cheng Chang

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A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000.

Keywords: Polynomial roots, greatest common divisor, Longhand polynomial division, Euclidean GCD Algorithm.

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: Covariation reasoning, exponential function, modeling, representations.

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Authors: Jiming Yang

Abstract:

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.

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Authors: Nicoletta Adamo-Villani

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The object of this research is the design and evaluation of an immersive Virtual Learning Environment (VLE) for deaf children. Recently we have developed a prototype immersive VR game to teach sign language mathematics to deaf students age K- 4 [1] [2]. In this paper we describe a significant extension of the prototype application. The extension includes: (1) user-centered design and implementation of two additional interactive environments (a clock store and a bakery), and (2) user-centered evaluation including development of user tasks, expert panel-based evaluation, and formative evaluation. This paper is one of the few to focus on the importance of user-centered, iterative design in VR application development, and to describe a structured evaluation method.

Keywords: 3D Animation, Virtual Reality, Virtual Learning Environments, User-Centered Design, User-centered Evaluation.

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Authors: Saipunidzam Mahamad, Mohammad Noor Ibrahim, Mohamad Izzriq Ab Malek Foad, ShakirahMohd Taib

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With the proliferation of the mobile device technologies, mobile learning can be used to complement and improve traditional learning problems. Both students and teachers need a proper and handy system to monitor and keep track the performance of the students. This paper presents an implementation of M-learning for primary school in Malaysia by using an open source technology. It focuses on learning mathematics using handheld devices for primary schools- students aged 11 and 12 years old. Main users for this system include students, teachers and the administrator. This application suggests a new mobile learning environment with mobile graph for tracking the students- progress and performance. The purpose of this system is not to replace traditional classroom but to complement the learning process. In a testing conducted, students who used this system performed better in their examination.

Keywords: M-Learning, Automated Mobile Graph.

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Authors: Christopher C. Anyadubalu

Abstract:

Biological, psychological and social experiences and perceptions of healthcare services in patients medically diagnosed of coronary heart disease were investigated using a sample of 10 participants whose responses to the in-depth interview questions were analyzed based on inter-and-intra-case analyses. The results obtained revealed that advancing age, single status, divorce and/or death of spouse and the issue of single parenting negatively impacted patients- biopsychosocial experiences. The patients- experiences of physical signs and symptoms, anxiety and depression, past serious medical conditions, use of self-prescribed medications, family history of poor mental/medical or physical health, nutritional problems and insufficient physical activities heightened their risk of coronary attack. Collectivist culture served as a big source of relieve to the patients. Patients- temperament, experience of different chronic life stresses/challenges, mood alteration, regular drinking, smoking/gambling, and family/social impairments compounded their health situation. Patients were satisfied with the biomedical services rendered by the healthcare personnel, whereas their psychological and social needs were not attended to. Effective procedural treatment model, a holistic and multidimensional approach to the treatment of heart disease patients was proposed.

Keywords: Biopsychosocial, Coronary Heart Disease, Experience, Patients, Perception, Perspective.

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Authors: Tai-Hwa Emily Lu

Abstract:

This study was a part of the three-year longitudinal research on setting up an math learning model for the disadvantaged students in Taiwan. A target 2nd grade class with 10 regular students and 6 disadvantaged students at a disadvantaged area in Taipei participated in this study. Two units of a market basal math textbook concerning fractions, three-dimensional figures, weight and capacity were adapted to enhance their math learning motivations, confidences and effects. The findings were (1) curriculum adaptation was effective on enhancing students- learning motivations, confidences and effects; (2) story-type problems and illustrations decreased difficulties on understanding math language for students from new immigrant families and students with special needs; (3) “concrete – semiconcrete – abstract" teaching strategies and hands-on activities were essential to raise students learning interests and effects; and (4) curriculum adaptation knowledge and skills needed to be included in the pre- and in-service teacher training programs.

Keywords: curriculum adaptations, mathematics, disadvantaged students, inclusive classroom

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Authors: Rudy Agustriyanto, Akbarningrum Fatmawati

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The utilization of cheese whey as a fermentation substrate to produce bio-ethanol is an effort to supply bio-ethanol demand as a renewable energy. Like other process systems, modeling is also required for fermentation process design, optimization and plant operation. This research aims to study the fermentation process of cheese whey by applying mathematics and fundamental concept in chemical engineering, and to investigate the characteristic of the cheese whey fermentation process. Steady state simulation results for inlet substrate concentration of 50, 100 and 150 g/l, and various values of hydraulic retention time, showed that the ethanol productivity maximum values were 0.1091, 0.3163 and 0.5639 g/l.h respectively. Those values were achieved at hydraulic retention time of 20 hours, which was the minimum value used in this modeling. This showed that operating reactor at low hydraulic retention time was favorable. Model of bio-ethanol production from cheese whey will enhance the understanding of what really happen in the fermentation process.

Keywords: Cheese whey, ethanol, fermentation, modeling.

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Authors: Harpreet Singh Dhillon, Abhijit Mitra

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A reduced-bit multiplication algorithm based on the ancient Vedic multiplication formulae is proposed in this paper. Both the Vedic multiplication formulae, Urdhva tiryakbhyam and Nikhilam, are first discussed in detail. Urdhva tiryakbhyam, being a general multiplication formula, is equally applicable to all cases of multiplication. It is applied to the digital arithmetic and is shown to yield a multiplier architecture which is very similar to the popular array multiplier. Due to its structure, it leads to a high carry propagation delay in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in the multiplication of large numbers as it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and is further optimized by use of some general arithmetic operations such as expansion and bit-shifting to take advantage of bit-reduction in multiplication. We illustrate the proposed algorithm by reducing a general 4x4-bit multiplication to a single 2 x 2-bit multiplication operation.

Keywords: Multiplication, algorithm, Vedic mathematics, digital arithmetic, reduced-bit.

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