Search results for: demystifying mathematics

Authors: A. Kulandai Therese

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The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs.

Keywords: corona graph, degree, eccentricity, eccentric connectivity index, first zagreb index, second zagreb index, subdivision graphs

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Authors: Valencia P. L. Rodrigo, Morita A. Adelina, Vargas V. Martin

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This proposal consists of an analysis of macro concepts involved within an organization growth using educational technologies, which will relate each concept, in a mathematical way with a vision of harmonic work. Working collaboratively, competitively and cooperatively so that this growth is harmonious and homogenous, coining a new term, Harmonic Work. The Harmonic Work ensures that the organization grows in all business directions, allowing managers to project a much more accurate growth, making clear the contribution of each department, resulting in an algorithm that analyzes each of the variables both endogenous and exogenous, establishing different performance indicators in its process of growth.

Keywords: business projection, collaboration, competitiveness, educational technology, harmonious growth

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Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

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We study the molecular evolution of insulin from the metric geometry point of view. In mathematics, and particularly in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from the geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: metric geometry, evolution, insulin, C. elegans

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Authors: Karam Chand Gupta

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When steel reinforcement is placed in mesh form in circular concrete slab at base or domes at top in case of over head service reservoir or any other structure, it is difficult to estimate/measure the total quantity of steel that would be needed or placed. For the purpose of calculating the total length of the steel bars, at present, the practice is – the length of each bar is measured and then added up. This is tiresome and time consuming process. I have derived a mathematics formula with the help of which we can calculate in one line the quantity of total steel that will be needed. This will not only make it easy and time saving but also avoids any error in making entries and calculations.

Keywords: dome, mesh, slab, steel

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Anne Marie Morrin

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This paper will focus on the design, delivery and assessment of a transdisciplinary STEAM (Science, Technology, Engineering, Arts, and Mathematics) education initiative in a college of education in Ireland. The project explores a transdisciplinary approach to supporting STEAM education where the concepts, methodologies and assessments employed derive from visual art sessions within initial teacher education. The research will demonstrate that the STEAM Education approach is effective when visual art concepts and methods are placed at the core of the teaching and learning experience. Within this study, emphasis is placed on authentic collaboration and transdisciplinary pedagogical approaches with the STEAM subjects. The partners included a combination of teaching expertise in STEM and Visual Arts education, artists, in-service and pre-service teachers and children. The inclusion of all stakeholders mentioned moves towards a more authentic approach where transdisciplinary practice is at the core of the teaching and learning. Qualitative data was collected using a combination of questionnaires (focused and open-ended questions) and focus groups. In addition, the data was collected through video diaries where students reflected on their visual journals and transdisciplinary practice, which gave rich insight into participants' experiences and opinions on their learning. It was found that an effective program of STEAM education integration was informed by co-teaching (continuous professional development), which involved a commitment to adaptable and flexible approaches to teaching, learning, and assessment, as well as the importance of continuous reflection-in-action by all participants. The delivery of a transdisciplinary model of STEAM education was devised to reconceptualizatise how individual subject areas can develop essential skills and tackle critical issues (such as self-care and climate change) through data visualisation and technology. The success of the project can be attributed to the collaboration, which was inclusive, flexible and a willingness between various stakeholders to be involved in the design and implementation of the project from conception to completion. The case study approach taken is particularistic (focusing on the STEAM-ED project), descriptive (providing in-depth descriptions from varied and multiple perspectives), and heuristic (interpreting the participants’ experiences and what meaning they attributed to their experiences).

Keywords: collaboration, transdisciplinary, STEAM, visual arts education

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Authors: Vinai K. Singh

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For reducing impulsive noise without degrading image contours, median filtering is a powerful tool. In multiband images as for example colour images or vector fields obtained by optic flow computation, a vector median filter can be used. Vector median filters are defined on the basis of a suitable distance, the best performing distance being the Euclidean. Euclidean distance is evaluated by using the Euclidean norms which is quite demanding from the point of view of computation given that a square root is required. In this paper an optimal piece-wise linear approximation of the Euclidean norm is presented which is applied to vector median filtering.

Keywords: euclidean norm, quasi euclidean norm, vector median filtering, applied mathematics

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: A. Schuchter, M. Promegger

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The outbreak of the COVID-19 pandemic has shown us that online education is so much more than just a cool feature for teachers – it is an essential part of modern teaching. In online math teaching, it is common to use tools to share screens, compute and calculate mathematical examples, while the students can watch the process. On the other hand, flipped classroom models are on the rise, with their focus on how students can gather knowledge by watching videos and on the teacher’s use of technological tools for information transfer. This paper proposes a co-educational teaching approach for coding and engineering subjects with the help of drone-building to spark interest in technology and create a platform for knowledge transfer. The project combines aspects from mathematics (matrices, vectors, shaders, trigonometry), physics (force, pressure and rotation) and coding (computational thinking, block-based programming, JavaScript and Python) and makes use of collaborative-shared 3D Modeling with clara.io, where students create mathematics knowhow. The instructor follows a problem-based learning approach and encourages their students to find solutions in their own time and in their own way, which will help them develop new skills intuitively and boost logically structured thinking. The collaborative aspect of working in groups will help the students develop communication skills as well as structural and computational thinking. Students are not just listeners as in traditional classroom settings, but play an active part in creating content together by compiling a Handbook of Knowledge (called “open book”) with examples and solutions. Before students start calculating, they have to write down all their ideas and working steps in full sentences so other students can easily follow their train of thought. Therefore, students will learn to formulate goals, solve problems, and create a ready-to use product with the help of “reverse engineering”, cross-referencing and creative thinking. The work on drones gives the students the opportunity to create a real-life application with a practical purpose, while going through all stages of product development.

Keywords: flipped classroom, co-creational education, coding, making, drones, co-education, ARCS-model, problem-based learning

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Authors: Giorgia Zotti

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This research comprehensively investigates the multifaceted interplay determining school performance, individual backgrounds, and regional disparities within the landscape of Italian secondary education. Leveraging data gleaned from the INVALSI 2021-2022 database, the analysis meticulously scrutinizes two fundamental distributions of educational achievements: the standardized Invalsi test scores and official grades in Italian and Mathematics, focusing specifically on final-year secondary school students in Italy. Applying a comprehensive methodology, the study initially employs Data Envelopment Analysis (DEA) to assess school performances. This methodology involves constructing a production function encompassing inputs (hours spent at school) and outputs (Invalsi scores in Italian and Mathematics, along with official grades in Italian and Math). The DEA approach is applied in both of its versions: traditional and conditional. The latter incorporates environmental variables such as school type, size, demographics, technological resources, and socio-economic indicators. Additionally, the analysis delves into regional disparities by leveraging the Theil Index, providing insights into disparities within and between regions. Moreover, in the frame of the inequality of opportunity theory, the study quantifies the inequality of opportunity in students' educational achievements. The methodology applied is the Parametric Approach in the ex-ante version, considering diverse circumstances like parental education and occupation, gender, school region, birthplace, and language spoken at home. Consequently, a Shapley decomposition is applied to understand how much each circumstance affects the outcomes. The outcomes of this comprehensive investigation unveil pivotal determinants of school performance, notably highlighting the influence of school type (Liceo) and socioeconomic status. The research unveils regional disparities, elucidating instances where specific schools outperform others in official grades compared to Invalsi scores, shedding light on the intricate nature of regional educational inequalities. Furthermore, it emphasizes a heightened inequality of opportunity within the distribution of Invalsi test scores in contrast to official grades, underscoring pronounced disparities at the student level. This analysis provides insights for policymakers, educators, and stakeholders, fostering a nuanced understanding of the complexities within Italian secondary education.

Keywords: inequality, education, efficiency, DEA approach

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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, differential algebraic equations, solvers, spreadsheet

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Authors: Prasita Sooksamran, Wareerat Kaewurai

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STEM is an integrated teaching approach promoted by the Ministry of Education in Thailand. STEM Education is an integrated approach to teaching Science, Technology, Engineering, and Mathematics. It has been questioned by Thai teachers on the grounds of how to integrate STEM into the classroom. Therefore, the main objective of this study is to develop a science instructional model based on the STEM approach to enhance scientific mind and problem-solving skills for primary students. This study is participatory action research, and follows the following steps: 1) develop a model 2) seek the advice of experts regarding the teaching model. Developing the instructional model began with the collection and synthesis of information from relevant documents, related research and other sources in order to create prototype instructional model. 2) The examination of the validity and relevance of instructional model by a panel of nine experts. The findings were as follows: 1. The developed instructional model comprised of principles, objective, content, operational procedures and learning evaluation. There were 4 principles: 1) Learning based on the natural curiosity of primary school level children leading to knowledge inquiry, understanding and knowledge construction, 2) Learning based on the interrelation between people and environment, 3) Learning that is based on concrete learning experiences, exploration and the seeking of knowledge, 4) Learning based on the self-construction of knowledge, creativity, innovation and 5) relating their findings to real life and the solving of real-life problems. The objective of this construction model is to enhance scientific mind and problem-solving skills. Children will be evaluated according to their achievements. Lesson content is based on science as a core subject which is integrated with technology and mathematics at grade 6 level according to The Basic Education Core Curriculum 2008 guidelines. The operational procedures consisted of 6 steps: 1) Curiosity 2) Collection of data 3) Collaborative planning 4) Creativity and Innovation 5) Criticism and 6) Communication and Service. The learning evaluation is an authentic assessment based on continuous evaluation of all the material taught. 2. The experts agreed that the Science Instructional Model based on the STEM Education Approach had an excellent level of validity and relevance (4.67 S.D. 0.50).

Keywords: instructional model, STEM education, scientific mind, problem solving

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Authors: Kazuhisa Takagi

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This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: dynamic mathematical object, javascript, google drive, transfer jet

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Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

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In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

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Authors: Rupali Bhardwaj

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Cryptography is the science of using mathematics to encrypt and decrypt data; the data are converted into some other gibberish form, and then the encrypted data are transmitted. The primary purpose of this paper is to provide two levels of security through a two-step process, rather than transmitted the message bits directly, first encrypted it using 2D cellular automata and then scrambled with Arnold Cat Map transformation; it provides an additional layer of protection and reduces the chance of the transmitted message being detected. A comparative analysis on effectiveness of scrambling technique is provided by scrambling degree measurement parameters i.e. Gray Difference Degree (GDD) and Correlation Coefficient.

Keywords: scrambling, cellular automata, Arnold cat map, game of life, gray difference degree, correlation coefficient

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Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

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This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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Authors: Gabriela Steffen

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Learning in a bilingual classroom not only implies learning in two languages or in an L2, it also means learning content subjects through the means of bilingual or plurilingual resources, which is of a qualitatively different nature than ‘monolingual’ learning. These resources form elements of a didactics of plurilingualism, aiming not only at the development of a plurilingual competence, but also at drawing on plurilingual resources for nonlinguistic subject learning. Applying a didactics of plurilingualism allows for taking account of the specificities of bilingual content subject learning in bilingual education classrooms. Bilingual education is used here as an umbrella term for different programs, such as bilingual education, immersion, CLIL, bilingual modules in which one or several non-linguistic subjects are taught partly or completely in an L2. This paper aims at discussing first results of a study on pupil group work in bilingual classrooms in several Swiss primary schools. For instance, it analyses two bilingual classes in two primary schools in a French-speaking region of Switzerland that follows a part of their school program through German in addition to French, the language of instruction in this region. More precisely, it analyses videotaped classroom interaction and in situ classroom practices of pupil group work in a mathematics lessons. The ethnographic observation of pupils’ group work and the analysis of their interaction (analytical tools of conversational analysis, discourse analysis and plurilingual interaction) enhance the description of whole-class interaction done in the same (and several other) classes. While the latter are teacher-student interactions, the former are student-student interactions giving more space to and insight into pupils’ talk. This study aims at the description of the linguistic and multimodal resources (in German L2 and/or French L1) pupils mobilize while carrying out a mathematical task. The analysis shows that the accomplishment of the mathematical task takes place in a bilingual mode, whether the whole-class interactions are conducted rather in a bilingual (German L2-French L1) or a monolingual mode in L2 (German). The pupils make plenty of use of German L2 in a setting that lends itself to use French L1 (peer groups with French as a dominant language, in absence of the teacher and a task with a mathematical aim). They switch from French to German and back ‘naturally’, which is regular for bilingual speakers. Their linguistic resources in German L2 are not sufficient to allow them to (inter-)act well enough to accomplish the task entirely in German L2, despite their efforts to do so. However, this does not stop them from carrying out the task in mathematics adequately, which is the main objective, by drawing on the bilingual resources at hand.

Keywords: bilingual content subject learning, bilingual primary education, bilingual pupil group work, bilingual teaching/learning resources, didactics of plurilingualism

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Authors: Osk Dagsdottir

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Background—Gait classifying allows clinicians to differentiate gait patterns into clinically important categories that help in clinical decision making. Reliable comparison of gait data between normal and patients requires knowledge of the gait parameters of normal children's specific age group. However, there is still a lack of the gait database for normal children of different ages. Objectives—This study aims to investigate the kinematics of the lower limb joints during gait for normal children in different age groups. Methods—Fifty-three normal children (34 boys, 19 girls) were recruited in this study. All the children were aged between 5 to 16 years old. Age groups were defined as three types: young child aged (5-7), child (8-11), and adolescent (12-16). When a participant agreed to take part in the project, their parents signed a consent form. Vicon® motion capture system was used to collect gait data. Participants were asked to walk at their comfortable speed along a 10-meter walkway. Each participant walked up to 20 trials. Three good trials were analyzed using the Vicon Plug-in-Gait model to obtain parameters of the gait, e.g., walking speed, cadence, stride length, and joint parameters, e.g., joint angle, force, moments, etc. Moreover, each gait cycle was divided into 8 phases. The range of motion (ROM) angle of pelvis, hip, knee, and ankle joints in three planes of both limbs were calculated using an in-house program. Results—The temporal-spatial variables of three age groups of normal children were compared between each other; it was found that there was a significant difference (p < 0.05) between the groups. The step length and walking speed were gradually increasing from young child to adolescent, while cadence was gradually decreasing from young child to adolescent group. The mean and standard deviation (SD) of the step length of young child, child and adolescent groups were 0.502 ± 0.067 m, 0.566 ± 0.061 m and 0.672 ± 0.053 m, respectively. The mean and SD of the cadence of the young child, child and adolescent groups were 140.11±15.79 step/min, 129±11.84 step/min, and a 115.96±6.47 step/min, respectively. Moreover, it was observed that there were significant differences in kinematic parameters, either whole gait cycle or each phase. For example, RoM of knee angle in the sagittal plane in the whole cycle of young child group is (65.03±0.52 deg) larger than child group (63.47±0.47 deg). Conclusion—Our result showed that there are significant differences between each age group in the gait phases and thus children walking performance changes with ages. Therefore, it is important for the clinician to consider the age group when analyzing the patients with lower limb disorders before any clinical treatment.

Keywords: action research, creative learning, mathematics education, professional development

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Authors: Satoshi Kusaka

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The term ‘competency’ is attracting considerable scholarly attention worldwide with the advance of globalization in the 21st century and with the arrival of a knowledge-based society. In the current world environment, familiarity with varied disciplines is regarded to be vital for personal success. The idea of a competency-based educational system was mooted by the ‘Definition and Selection of Competencies (DeSeCo)’ project that was conducted by the Organization for Economic Cooperation and Development (OECD). Further, attention to this topic is not limited to developed countries; it can also be observed in developing countries. For instance, the importance of a competency-based curriculum was mentioned in the ‘2013 Harmonized Curriculum Framework for the East African Community’, which recommends key competencies that should be developed in primary schools. The introduction of such curricula and the reviews of programs are actively being executed, primarily in the East African Community but also in neighboring nations. Taking Mozambique as a case in point, the present paper examines the conception of ‘competency’ as a target of frontline education in developing countries. It also aims to discover the manner in which the syllabus, textbooks and lessons, among other things, in primary-level math education are developed and to determine the challenges faced in the process. This study employs the perspective of competency-based education design to analyze how the term ‘competency’ is defined in the primary-level math syllabus, how it is reflected in the textbooks, and how the lessons are actually developed. ‘Practical competency’ is mentioned in the syllabus, and the description of the term lays emphasis on learners' ability to interactively apply socio-cultural and technical tools, which is one of the key competencies that are advocated in OECD's ‘Definition and Selection of Competencies’ project. However, most of the content of the textbooks pertains to ‘basic academic ability’, and in actual classroom practice, teachers often impart lessons straight from the textbooks. It is clear that the aptitude of teachers and their classroom routines are greatly dependent on the cultivation of their own ‘practical competency’ as it is defined in the syllabus. In other words, there is great divergence between the ‘syllabus’, which is the intended curriculum, and the content of the ‘textbooks’. In fact, the material in the textbooks should serve as the bridge between the syllabus, which forms the guideline, and the lessons, which represent the ‘implemented curriculum’. Moreover, the results obtained from this investigation reveal that the problem can only be resolved through the cultivation of ‘practical competency’ in teachers, which is currently not sufficient.

Keywords: competency, curriculum, mathematics education, Mozambique

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Authors: Selma Bouasria, Mahi Abdelkader, Abbès Azzi, Herouz Keltoum

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This paper reports concept was used into the computational fluid dynamics (CFD) code cfx through user-defined functions to assess ventilation efficiency inside (forced-ventilation local). CFX is a simulation tool which uses powerful computer and applied mathematics, to model fluid flow situations for the prediction of heat, mass and momentum transfer and optimal design in various heat transfer and fluid flow processes to evaluate thermal comfort in a room ventilated (highly-glazed). The quality of the solutions obtained from CFD simulations is an effective tool for predicting the behavior and performance indoor thermo-aéraulique comfort.

Keywords: ventilation, thermal comfort, CFD, indoor environment, solar air heater

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Authors: Ogbeta I. Joseph, Habiba B. A. Awwalu, Otokiti Jimoh

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This paper entitled science education in Nigeria issues and challenges highlighted the role of science education to the development of science and technology in Nigeria. Science embraces every attempt of human to explore and manage the natural world, the contribution of science education to the technological development of the nation, the role of science education in ICT development, the importance of mathematics in the development of science education, the paper also analyzed the challenges facing the development of science education to include corruption, insecurity, and political instability, the paper concluded by encouraging the government and other stakeholders in educational sector to pay more attention to the teaching and learning of science in our schools. Therefore recommended the development that emphasizes should be on the teaching and learning of science base subjects in the school.

Keywords: education, science, technology and national development, challenges

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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: M. Tiachachat, M. Mihoubi

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The Bell polynomials are special polynomials in combinatorial analysis that have a wide range of applications in mathematics. They have interested many authors. The exponential partial Bell polynomials have been well reduced to some special combinatorial sequences. Numerous researchers had already been interested in the above polynomials, as evidenced by many articles in the literature. Inspired by this work, in this work, we propose a family of special polynomials named after the 2-successive partial Bell polynomials. Using the combinatorial approach, we prove the properties of these numbers, derive several identities, and discuss some special cases. This family includes well-known numbers and polynomials such as Stirling numbers, Bell numbers and polynomials, and so on. We investigate their properties by employing generating functions

Keywords: 2-associated r-Stirling numbers, the exponential partial Bell polynomials, generating function, combinatorial interpretation

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Authors: Jialin Wu, Zhiwei Lian, Jieyu Tang, Jingyun Shen

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Tornado is a serious and unpredictable natural disaster, which has an important impact on people's production and life. The probability of being hit by tornadoes in China was analyzed considering the principles of tornado formation. Then some suggestions on layout and shapes for newly-built buildings were provided combined with the characteristics of tornado wind fields. Fuzzy clustering and inverse closeness methods were used to evaluate the probability levels of tornado risks in various provinces based on classification and ranking. GIS was adopted to display the results. Finally, wind field single-vortex tornado was studied to discuss the optimized design of rural low-rise houses in Yancheng, Jiangsu as an example. This paper may provide enough data to support building and urban design in some specific regions.

Keywords: tornado probability, computational fluid dynamics, fuzzy mathematics, optimal design

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Authors: Bijan Gillani, Roya Gillani

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The purpose of this paper is to propose a pedagogical model where engineering provides the interconnection to integrate the other topics of science, technology, engineering, and mathematics. The author(s) will first present a brief discussion of cognitive theory and then derive an integrated pedagogy to use engineering and technology, such as drones, sensors, camera, iPhone, radio waves as the nexus to an integrated curriculum development for the other topics of STEM. Based on this pedagogy, one example developed by the author(s) called “Drones and Environmental Science,” will be presented that uses a drone and related technology as an appropriate instructional delivery medium to apply Piaget’s cognitive theory to create environments that promote the integration of different STEM subjects that relate to environmental science.

Keywords: cogntive theories, drone, environmental science, pedagogy

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Authors: Vicario Marina, Bustos Freddy, Olivares Jesús, Gómez Pilar

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This paper presents a didactic model and a tool as educational resources to support the learning of geometry; they focus on topics difficult to understand. The target population is elementary school students. The tool is based on a collaborative educational approach using multi-touch devices. The proposal is based on the challenges found in the instructional design and prototype implementation. Traditionally, elementary students have had many problems assimilating mathematical topics; this new Educatronic prototype facilitates the learning experience using exercises and they were tested with different children demonstrating the benefits of the prototype by improving their mathematical skills.

Keywords: educatronic prototype, geometry, multitouch surface, educational computing, primary school, mathematics, educational informatics

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Authors: Lola Rosalia Saavedra Guzman, Plamen Neytchev Netchev

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In general, agnosticism is perceived as an uncertainty between a well-structured (religious) belief (in some Christian or pagan deity) and its absolute and total absence, often causing the suspicion that an agnostic is an atheist, which is "reinsured" in case if their personal belief is wrong. All of this, along with the prevailing view among the naturalists that science has already demonstrated the inexistence of God, has compelled us to seek the foundation of agnosticism and faith in the contemporary formal human logic, advanced mathematics, and the natural sciences. Along the way, we will find that no natural science can demonstrate the existence of God, nor could it discard it for rational considerations, which show that there is something beyond. After all, it seems that the human intellect is insufficient to respond surely with yes or no to the existence of higher intelligences leaving unconditional faith as the only path to God for Christians and transcendent techniques, for pagan religious beliefs.

Keywords: agnosticism, formal logic, axioms and postulates, Gödel theorems, and logical faults

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Authors: Ana Breda, Catarina Cruz

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Daily, we face unpredictable events, often attributed to chance, as there is no justification for such an occurrence. Chance, understood as a source of uncertainty, is present in several aspects of human life, such as weather forecasts, dice rolling, and lottery. Surprisingly, humans and some animals can quickly adjust their behavior to handle efficiently doubly stochastic processes (random events with two layers of randomness, like unpredictable weather affecting dice rolling). This adjustment ability suggests that the human brain has built-in mechanisms for perceiving, understanding, and responding to simple probabilities. It also explains why current trends in mathematics education include probability concepts in official curriculum programs, starting from the third year of primary education onwards. In the first years of schooling, children learn to use a certain type of (specific) vocabulary, such as never, always, rarely, perhaps, likely, and unlikely, to help them to perceive and understand the probability of some events. These are keywords of crucial importance for their perception and understanding of probabilities. The development of the probabilistic concepts comes from facts and cause-effect sequences resulting from the subject's actions, as well as the notion of chance and intuitive estimates based on everyday experiences. As part of a junior summer school program, which took place at a Portuguese university, a non-formal learning experiment was carried out with 18 children in the 5th and 6th grades. This experience was designed to be implemented in a dynamic of a serious ice-breaking game, to assess their levels of probabilistic, critical, and creative thinking in understanding impossible, certain, equally probable, likely, and unlikely events, and also to gain insight into how the non-formal learning context influenced their achievements. The criteria used to evaluate probabilistic thinking included the creative ability to conceive events classified in the specified categories, the ability to properly justify the categorization, the ability to critically assess the events classified by other children, and the ability to make predictions based on a given probability. The data analysis employs a qualitative, descriptive, and interpretative-methods approach based on students' written productions, audio recordings, and researchers' field notes. This methodology allowed us to conclude that such an approach is an appropriate and helpful formative assessment tool. The promising results of this initial exploratory study require a future research study with children from these levels of education, from different regions, attending public or private schools, to validate and expand our findings.

Keywords: critical and creative thinking, non-formal mathematics learning, probabilistic thinking, serious game

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Authors: Thanh Nga Thai

Abstract:

A major issue in air transportation is in flight safety. Recent developments in control engineering have an attractive potential for resolving new issues related to guidance, navigation, and control of flying vehicles. Many future atmospheric missions will require increased on board autonomy including fault diagnosis and the subsequent control and guidance recovery actions. To improve designing system diagnostic, an efficient FDI- fault detection and identification- methodology is necessary to achieve. Contribute to characteristic of different faults in sensor and actuator in the view of mathematics brings a lot of profit in some condition changes in the system. This research finds some profit to reduce a trade-off to achieve between fault detection and performance of the closed loop system and cost and calculated in simulation.

Keywords: fault detection and identification, sensor faults, actuator faults, flight control system

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