Search results for: mathematical literacy

Authors: Amira Abdelrasoul, Huu Doan, Ali Lohi

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An efficient and well-planned ultrafiltration process is becoming a necessity for monetary returns in the industrial settings. The aim of the present study was to develop a mathematical model for an accurate prediction of ultrafiltration membrane fouling of latex effluent applied to homogeneous and heterogeneous membranes with uniform and non-uniform pore sizes, respectively. The models were also developed for an accurate prediction of power consumption that can handle the large-scale purposes. The model incorporated the fouling attachments as well as chemical and physical factors in membrane fouling for accurate prediction and scale-up application. Both Polycarbonate and Polysulfone flat membranes, with pore sizes of 0.05 µm and a molecular weight cut-off of 60,000, respectively, were used under a constant feed flow rate and a cross-flow mode in ultrafiltration of the simulated paint effluent. Furthermore, hydrophilic ultrafilic and hydrophobic PVDF membranes with MWCO of 100,000 were used to test the reliability of the models. Monodisperse particles of 50 nm and 100 nm in diameter, and a latex effluent with a wide range of particle size distributions were utilized to validate the models. The aggregation and the sphericity of the particles indicated a significant effect on membrane fouling.

Keywords: membrane fouling, mathematical modeling, power consumption, attachments, ultrafiltration

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Authors: Deborah L. Smith

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To review our program and determine the best redesign options, department members gathered feedback and input through focus groups, analysis of data, and a review of the current research to ensure that the changes proposed were not based solely on the state’s new professional standards. In designing course assignments and assessments, we listened to a variety of constituents, including students, other institutions of higher learning, MDE webinars, host teachers, literacy clinic personnel, and other disciplinary experts. As a result, we are designing a program that is more inclusive of a variety of field experiences for growth. We have determined ways to improve our program by connecting academic disciplinary knowledge, educational psychology, and community building both inside and outside the classroom for professional learning communities. The state’s release of new professional standards led my department members to question what is working and what needs improvement in our program. One aspect of our program that continues to be supported by research and data analysis is the function of supervised field experiences with meaningful feedback. We seek to expand in this area. Other data indicate that we have strengths in modeling a variety of approaches such as cooperative learning, discussions, literacy strategies, and workshops. In the new program, field assignments will be connected to multiple courses, and efforts to scaffold student learning to guide them toward best evidence-based practices will be continuous. Despite running a program that meets multiple sets of standards, there are areas of need that we directly address in our redesign proposal. Technology is ever-changing, so it’s inevitable that improving digital skills is a focus. In addition, scaffolding procedures for English Language Learners (ELL) or other students who struggle is imperative. Diversity, equity, and inclusion (DEI) has been an integral part of our curriculum, but the research indicates that more self-reflection and a deeper understanding of culturally relevant practices would help the program improve. Connections with professional learning communities will be expanded, as will leadership components, so that teacher candidates understand their role in changing the face of education. A pilot program will run in academic year 22/23, and additional data will be collected each semester through evaluations and continued program review.

Keywords: DEI, field experiences, program redesign, teacher preparation

Procedia PDF Downloads 147

Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

Procedia PDF Downloads 282

Authors: Kyung Hwa Shin

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Primary school music education plays a crucial role in nurturing students' musical abilities and fostering a lifelong appreciation for music. As we embark on the 21st century, it becomes imperative to explore advanced approaches that can effectively engage and empower students in the realm of music. This study aims to shed light on the aspects of primary school music education in South Korea, with a specific focus on the incorporation of the Zoltán Kodály Concept. The Zoltán Kodály Concept, developed by Hungarian composer and educator Zoltán Kodály (Kodály, 1974) advocates for a holistic music education that integrates singing, movement, and music literacy. This concept has gained recognition worldwide for its effectiveness in developing musicianship and enhancing music learning experiences. This study will delve into the ways in which the Zoltán Kodály Concept has been adapted and implemented in the context of South Korean primary school music education. It will highlight the benefits of this approach in nurturing students' musical skills, fostering creativity, and promoting cultural understanding through music. Furthermore, it will enhance the delivery of the Kodály-based curriculum challenges posed by the 21st-century digital age. Drawing on this research, pedagogical practices, and case studies, this study will provide valuable insights into the practical applications of the Zoltán Kodály Concept in South Korean primary school music education. It will discuss the impact of this approach on student engagement, motivation, and achievement, as well as the role of teachers in facilitating effective implementation. Additionally, it will address the professional development opportunities available to music educators to enhance their pedagogical skills in line with the Kodály philosophy. Ultimately, it aims to inspire and empower educators, policymakers, and researchers to embrace the Zoltán Kodály Concept as a transformative and forward-thinking approach to primary school music education in the 21st century. By embracing current aspects and progressive methodologies, South Korea can continue to strengthen its music education system and cultivate a generation of musically literate and culturally enriched individuals.

Keywords: primary school music education, Zoltán Kodály concept, 21st century, South Korea, music literacy, pedagogy, curriculum

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Authors: Rahimah Saimin

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Previous research has shown that young children can learn from educational television programmes, videos or other technological media. However, the blending of any of these with traditional printed-based text appears to be omitted. Repeated viewing is an important factor in children's ability to comprehend the content or plot. The present study combined videos with traditional printed-based text and required repeated viewing and is original and distinctive. The first study was a pilot study to explore whether the intervention is implementable in ordinary classrooms. The second study explored whether the curricular embedding is important or whether the video with curricular embedding is effective. The third study explored the effect of “dosage”, i.e. whether a longer/ more intense intervention has a proportionately greater effect on outcomes. Both measured outcomes (comprehension, word sounds, and early word recognition) and unmeasured outcomes (engagement to reading traditional printed-based texts or/and multimodal texts) were obtained from this study. Observation indicated degree of engagement in reading. The theoretical framework was multimodality theory combined with Piaget’s and Vygotsky’s learning theories. An experimental design was used with 4-5-year-old children in nursery schools and primary schools. Six links to video clips exploring non-fiction science content were provided to teachers. The first session is whole-class and subsequent sessions small-group. The teacher then engaged the children in dialogue using supplementary materials. About half of each class was selected randomly for pre-post assessments. Two assessments were used the British Picture Vocabulary Scale (BPVSIII) and the York Assessment of Reading for Comprehension (YARC): Early Reading. Different programme fidelity means were deployed- observations, teacher self-reports attendance logs and post-delivery interviews. Data collection is in progress and results will be available shortly. If this multiphase study show effectiveness in one or other application, then teachers will have other tools which they can use to enhance vocabulary, letter knowledge and word reading. This would be a valuable addition to their repertoire.

Keywords: language skills, literacy skills, multimodality, video

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Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

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Authors: Javad Khaligh, Aghileh Heydari, Ali Akbar Heydari

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Mathematical epidemiological models for the spread of disease through a population are used to predict the prevalence of a disease or to study the impacts of treatment or prevention measures. Initial conditions for these models are measured from statistical data collected from a population since these initial conditions can never be exact, the presence of chaos in mathematical models has serious implications for the accuracy of the models as well as how epidemiologists interpret their findings. This paper confirms the chaotic behavior of a model for dengue fever and SI by investigating sensitive dependence, bifurcation, and 0-1 test under a variety of initial conditions.

Keywords: epidemiological models, SEIR disease model, bifurcation, chaotic behavior, 0-1 test

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Ana Maria Reis D'Azevedo Breda, Catarina Maria Neto da Cruz

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The Japanese art of origami provides a rich context for designing exploratory mathematical activities for children and young people. By folding a simple sheet of paper, fascinating and surprising planar and spatial configurations emerge. Equally surprising is the unfolding process, which also produces striking patterns. The procedure of folding, unfolding, and folding again allows the exploration of interesting geometric patterns. When adequately and systematically done, we may deduce some of the mathematical rules ruling origami. As the child/youth folds the sheet of paper repeatedly, he can physically observe how the forms he obtains are transformed and how they relate to the pattern of the corresponding unfolding, creating space for the understanding/discovery of mathematical principles regulating the folding-unfolding process. As part of a 2023 Summer Academy organized by a Portuguese university, a session entitled “Folding, Thinking and Generalizing” took place. Twenty-three students attended the session, all enrolled in the 2nd cycle of Portuguese Basic Education and aged between 10 and 12 years old. The main focus of this session was to foster the development of critical cognitive and socio-emotional skills among these young learners using origami. These skills included creativity, critical analysis, mathematical reasoning, collaboration, and communication. Employing a qualitative, descriptive, and interpretative analysis of data collected during the session through field notes and students’ written productions, our findings reveal that structured origami-based activities not only promote student engagement with mathematical concepts in a playful and interactive but also facilitate the development of socio-emotional skills, which include collaboration and effective communication between participants. This research highlights the value of integrating origami into educational practices, highlighting its role in supporting comprehensive cognitive and emotional learning experiences.

Keywords: skills, origami rules, active learning, hands-on activities

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Authors: Abdullahi Mohammed Auwal

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Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: adsorption, mathematical modeling, nanocarbons, numerical analysis

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Nicolás Clavijo Buriticá, Laura Viviana Triana Sanchez

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This research develops a productive context associated with the aquaculture industry in northern Tolima-Colombia, specifically in the town of Lerida. Strategic aspects of chain of fish Production-Distribution, especially those related to supply network design of an association devoted to cultivating, farming, processing and marketing of fish are addressed. This research is addressed from a special approach of Supply Chain Management (SCM) which guides management objectives to the system sustainability; this approach is called Sustainable Supply Chain Management (SSCM). The network design of fish production-distribution system is obtained for the case study by two mathematical programming models that aims to maximize the economic benefits of the chain and minimize total supply chain costs, taking into account restrictions to protect the environment and its implications on system productivity. The results of the mathematical models validated in the productive situation of the partnership under study, called Asopiscinorte shows the variation in the number of open or closed locations in the supply network that determines the final network configuration. This proposed result generates for the case study an increase of 31.5% in the partial productivity of storage and processing, in addition to possible favorable long-term implications, such as attending an agile or not a consumer area, increase or not the level of sales in several areas, to meet in quantity, time and cost of work in progress and finished goods to various actors in the chain.

Keywords: Sustainable Supply Chain, mathematical programming, aquaculture industry, Supply Chain Design, Supply Chain Configuration

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Authors: Gak-Gyu Kim, Won Il Jung

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According to a remarkable development of science and technology, function and role of the system of engineering fields has recently been diversified. The system has become increasingly more complex and precise, and thus, system designers intended to maximize reliability concentrate more effort at the design stage. This study deals with the reliability redundancy optimization problem (RROP) for k-out-of-n: G system configuration with cold standby and warm standby components. This paper further intends to present the optimal mathematical model through which the following three elements of (i) multiple components choices, (ii) redundant components quantity and (iii) the choice of redundancy strategies may be combined in order to maximize the reliability of the system. Therefore, we focus on the following three issues. First, we consider RROP that there exists warm standby state as well as cold standby state of the component. Second, as eliminating an approximation approach of the previous RROP studies, we construct a precise model for system reliability. Third, given transition time when the state of components changes, we present not simply a workable solution but the advanced method. For the wide applicability of RROPs, moreover, we use absorbing continuous time Markov chain and matrix analytic methods in the suggested mathematical model.

Keywords: RROP, matrix analytic methods, k-out-of-n: G system, MTTF, absorbing continuous time Markov Chain

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

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The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.

Keywords: closed-loop design, closed-loop supply chain, design evaluation, supply chain management, sustainable design model

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

Procedia PDF Downloads 275

Authors: Jayanta Bora, Sukhvinder Kaur, Ashok Agarwal, Sangeeta Kaul

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Background: It is important for targeted interventions to consider vulnerabilities of female sex workers (FSWs) such as poverty, work-related mobility and literacy for effective human immunodeficiency virus (HIV) prevention. This paper examines the association between vulnerability and behavioural outcomes among FSWs in Thane district, Maharashtra under USAID PHFI-PIPPSE project. Methods: Data were used from the Behavioural Tracking Survey, a cross-sectional behavioural study conducted in 2015 with 503 FSWs randomly selected from 12 TI-NGOs which were functioning and providing services to FSWs in Thane district prior to April 2014 in Thane district of Maharashtra. We have created the “vulnerability index”, a composite index of literacy, factors of dependence (alternative livelihood options, current debt), and aspects of sex work (mobility and duration in sex work) as a dependent variable. The key independent measures used were program exposure to intervention, service uptake, self-confidence, and self-identity. Bi-variate and multivariate logistic regressions were used to examine the study objectives. Results: A higher proportion of FSWs who were in the age-group 18–25 years from brothel/street /home/ lodge-based were categorized as highly vulnerable to HIV risk as compared to bar-based sex worker (74.1% versus 59.8%, P,0.002); regression analysis highlighted lower odds of vulnerability among FSWs who were aware of services and visited NGO clinic for medical check-up and counselling for STI [AOR= 0.092, 95% CI 0.018-0.460; P,0.004], However, lower odds of vulnerability on confident in supporting fellow sex worker in crisis [AOR= 0.601, 95% CI 0.476-0.758; P, 0.000] and were able to turn away clients when they refused to use a condom during sex [AOR= 0.524, 95% CI 0.342-0.802; P, 0.003]. Conclusion: The results highlight that FSWs associated with TIs and getting services are less vulnerable and highly empowered. As a result of behavioural change communication and other services provided by TIs, FSWs were able to successfully negotiate about condom use with their clients and manage solidarity in the crisis situation for fellow FSWs. Therefore, it is evident from study paper that TI prevention programs may transform the lives of masses considerably and may open a window of opportunity to infuse the information and awareness about HIV risk.

Keywords: female sex worker, HIV prevention, HIV service uptake, vulnerability

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Authors: Gurmeet Singh Cheema, Gurjinder Singh, Amardeep Singh Kang

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Aluminium alloy 6061 is a medium to high strength heat-treatable alloy which has very good corrosion resistance and very good weldability. Friction Stir Welding was developed and this technique has attracted considerable interest from the aerospace and automotive industries since it is able to produce defect free joints particularly for light metals i.e aluminum alloy and magnesium alloy. In the friction stir welding process, welding parameters such as tool rotational speed, welding speed and tool shoulder diameter play a major role in deciding the weld quality. In this research work, an attempt has been made to understand the effect of tool rotational speed, welding speed and tool shoulder diameter on friction stir welded AA6061 aluminium alloy joints. Statistical tool such as central composite design is used to develop the mathematical relationships. The mathematical model was developed to predict mechanical properties of friction stir welded aluminium alloy joints at the 95% confidence level.

Keywords: aluminium alloy, friction stir welding, central composite design, mathematical relationship

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Authors: Jacob A. Braun

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This paper uses mathematical modeling to show the spread of Herpes Simplex type-2 with and without the usage of condoms in a college population. The model uses four differential equations to calculate the data for the simulation. The dt increment used is one week. It also runs based on a fixated period. The period chosen was five years to represent time spent in college. The average age of the individual is 21, once again to represent the age of someone in college. In the total population, there are almost two times as many women who have Herpes Simplex Type-2 as men. Additionally, Herpes Simplex Type-2 does not have a known cure. The goal of the model is to show how condom usage affects women’s chances of receiving the virus in the hope of being able to reduce the number of women infected. In the end, the model demonstrates that condoms offer significant protection to women from the virus. Since fewer women are infected with the virus when condoms are used, in turn, fewer males are infected. Since Herpes Simplex Type-2 affects the carrier for their whole life, a small decrease of infections could lead to large ramifications over time. Specifically, a small decrease of infections at a young age, such as college, could have a very big effect on the long-term number of people infected with the virus.

Keywords: college, condom, Herpes, mathematical modelling

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Authors: Marlone D. Severo

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A pre- and post-test quasi-experimental design was used to test the intervention of Trachtenberg Speed Math on the mathematical competency of sixty (60) matched-paired students with a poor performing grade in Mathematics from one of the biggest public national high school at the South of Metro Manila. Both control and experimental group were administered with the Attitude Towards Mathematics Inventory (ATMI) before the pretest were given and both group showed high dislike for Mathematics. Pretest showed a 53 percent accuracy for the control group and 51 percent for the experimental group using a 15-item long multiplication test without any aid of a computing device. The experimental group were taught how to use the Trachtenberg number-keys and techniques in multiplication between October 2014 to March 2015. Post-test showed an improvement in the experimental group with 96 percent accuracy for the control group and a dismal 57 percent for the control group in long-multiplication. Post-test ATMI were administered. The control group showed a great dislike towards Mathematics, while the experimental group showed a positive attitude towards the subject.

Keywords: attitude towards mathematics, mathematical competency, number-keys, trachtenberg speed math

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: mathematical modeling, ordinary differential equations, endocrine system, delay differential equation

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

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Authors: Aydin Azizi, Aburrahman Tanira

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The main source of energy used in this modern age is fossil fuels. There is a myriad of problems that come with the use of fossil fuels, out of which the issues with the greatest impact are its scarcity and the cost it imposes on the planet. Fossil fuels are the only plausible option for many vital functions and processes; the most important of these is transportation. Thus, using this source of energy wisely and as efficiently as possible is a must. The aim of this work was to explore utilising mathematical modelling and artificial intelligence techniques to enhance fuel consumption in passenger cars by focusing on the speed at which cars are driven. An artificial neural network with an error less than 0.05 was developed to be applied practically as to predict the rate of fuel consumption in vehicles.

Keywords: mathematical modeling, neural networks, fuel consumption, fossil fuel

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Authors: Artem Sedov, Aigerim Uyzbayeva, Valeriya Tyo

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The presented article is showing results of dynamic modeling with Mathlab software of optimal automatic room climate control system for two experimental houses in Astana, one of which has circle plan and the other one has square plan. These results are showing that building geometry doesn't influence on climate system PID-controls configuring. This confirms theoretical implication that optimal automatic climate control system parameters configuring should depend on building's internal space volume, envelope heat transfer, number of people inside, supply ventilation air flow and outdoor temperature.

Keywords: climate control system, climate physics, dome-like building, mathematical modeling

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Authors: M. Rodionov, Z. Dedovets

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This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: mathematics, motivation, secondary school, student, practical problem

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Authors: Sergey M. Karabanov, Dmitry V. Suvorov, Dmitry Yu. Tarabrin

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The operating principle of magnetically controlled microelectromechanical system (MEMS) switches is based on controlling the beam movement under the influence of a magnetic field. Currently, there is a MEMS switch design with a flexible ferromagnetic electrode in the form of a fixed-terminal beam, with an electrode fastened on a straight or cranked anchor. The basic performance characteristics of magnetically controlled MEMS switches (service life, sensitivity, contact resistance, fast response) are largely determined by the flexible electrode design. To ensure the stable and controlled motion of the flexible electrode, it is necessary to provide the optimal design of a flexible electrode.

Keywords: flexible electrode, magnetically controlled MEMS, mathematical modeling, mechanical stress

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Authors: Michael Lousis

Abstract:

The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic throughout the development of the Kassel Project in England and Greece was accomplished. How much retentive these errors were over three-years in the officially provided school instruction of Arithmetic in these countries has also been shown. The learners’ errors in Arithmetic stemmed from a sample, which was comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. The sample was purposefully selected according to the students’ participation in each testing session in the development of the three-year project, in both domains simultaneously in Arithmetic and Algebra. Specific teaching practices have been invented and are presented in this study for subverting these learners’ errors, which were found out to be retentive to the level of the nationally provided mathematical education of each country. The invention and the development of these proposed teaching practices were founded on the rationality of the theoretical accounts concerning the explanation, prediction and control of the errors, on the conceptual metaphor and on an analysis, which tried to identify the required cognitive components and skills of the specific tasks, in terms of Psychology and Cognitive Science as applied to information-processing. The aim of the implementation of these instructional practices is not only the subversion of these errors but the achievement of the mathematical competence, as this was defined to be constituted of three elements: appropriate representations - appropriate meaning - appropriately developed schemata. However, praxis is of paramount importance, because there is no independent of science ‘real-truth’ and because praxis serves as quality control when it takes the form of a cognitive method.

Keywords: arithmetic, cognitive science, cognitive psychology, information-processing paradigm, Kassel project, level of the nationally provided mathematical education, praxis, remedial mathematical teaching practices, retentiveness of errors

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