Search results for: demystifying mathematics

Authors: Yeonjune Kang

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A triangulation of a planar region is a partition of that region into triangles. In the finite element method, triangulations are often used as the grid underlying a computation. In order to be suitable as a finite element mesh, a triangulation must have well-shaped triangles, according to criteria that depend on the details of the particular problem. For instance, most methods require that all triangles be small and as close to the equilateral shape as possible. Stated differently, one wants to avoid having either thin or flat triangles in the triangulation. There are many triangulation procedures, a particular one being the one known as the longest edge bisection algorithm described below. Starting with a given triangle, locate the midpoint of the longest edge and join it to the opposite vertex of the triangle. Two smaller triangles are formed; apply the same bisection procedure to each of these triangles. Continuing in this manner after n steps one obtains a triangulation of the initial triangle into 2n smaller triangles. The longest edge algorithm was first considered in the late 70’s. It was shown by various authors that this triangulation has the desirable properties for the finite element method: independently of the number of iterations the angles of these triangles cannot get too small; moreover, the size of the triangles decays exponentially. In the present paper we consider a related triangulation algorithm we refer to as the largest angle bisection procedure. As the name suggests, rather than bisecting the longest edge, at each step we bisect the largest angle. We study the properties of the resulting triangulation and prove that, while the general behavior resembles the one in the longest edge bisection algorithm, there are several notable differences as well.

Keywords: angle bisectors, geometry, triangulation, applied mathematics

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Authors: Penn P. Wu, Jeannie Jo

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Blockchain technology has rapidly gained popularity in industry. This paper attempts to assist academia to answer four questions. First, should community colleges begin offering education to nurture blockchain-literate students for the job market? Second, what are the appropriate topical areas to cover? Third, should it be an individual course? And forth, should it be a technical or management course? This paper starts with identifying the knowledge domains of blockchain technology and the topical areas each domain has, and continues with placing them in appropriate academic territories (Computer Sciences vs. Business) and subjects (programming, management, marketing, and laws), and then develops an evaluation model to determine the appropriate topical area for community colleges to teach. The evaluation is based on seven factors: maturity of technology, impacts on management, real-world applications, subject classification, knowledge prerequisites, textbook readiness, and recommended pedagogies. The evaluation results point to an interesting direction that offering an introductory course is an ideal option to guide students through the learning journey of what blockchain is and how it applies to business. Such an introductory course does not need to engage students in the discussions of mathematics and sciences that make blockchain technologies possible. While it is inevitable to brief technical topics to help students build a solid knowledge foundation of blockchain technologies, community colleges should avoid offering students a course centered on the discussion of developing blockchain applications.

Keywords: blockchain, pedagogies, blockchain technologies, blockchain course, blockchain pedagogies

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Authors: Abigail Gragg

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The goal of this research study was to adjudicate if implementing Howard Gardner’s multiple levels of intelligence would enhance student achievement levels in an Algebra 1 College Preparatory class. This was conducted within every class by incorporating one level of the eight levels of intelligence into small group work in stations. Every class was conducted utilizing small-group instruction. Achievement levels were measured through various forms of collected data that expressed student understandings in class through formative assessments versus student understandings on summative assessments. The data samples included: assessments (i.e. summative and formative assessments), observable data, video recordings, a daily log book, student surveys, and checklists kept during the observation periods. Formative assessments were analyzed during each class period to measure in-class understanding. Summative assessments were dissected per question per accuracy to review the effects of each intelligence implemented. The data was collated into a coding workbook for further analysis to conclude the resulting themes of the research. These themes include 1) there was no correlation to multiple levels of intelligence enhancing student achievement, 2) bodily-kinesthetic intelligence showed to be the intelligence that had the most improvement on test questions and 3) out of all of the bits of intelligence, interpersonal intelligence enhanced student understanding in class.

Keywords: stations, small group instruction, multiple levels of intelligence, Mathematics, Algebra 1, student achievement, secondary school, instructional Pedagogies

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Authors: Guizella Rocabado, Cassidy Wilkes

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It is well known that chemistry is one of the most feared courses in college. Although many students enjoy learning about science, most of them perceive that chemistry is “too difficult”. These perceptions of chemistry result in many students not considering Science, Technology, Engineering, and Mathematics (STEM) majors because they require chemistry courses. Ultimately, these perceptions are also thought to be related to high attrition rates of students who begin STEM majors but do not persist. Students perceived costs of a chemistry class can be many, such as task effort, loss of valued alternatives, emotional, and others. These costs might be overcome by students’ interests and goals, yet the level of perceived costs might have a lasting impact on the students’ overall perception of chemistry and their desire to pursue chemistry and other STEM careers in the future. In this mixed methods study, we investigated task effort and emotional cost, as well as a mastery or performance goal orientation, and the impact these constructs may have on achievement in general chemistry classrooms. Utilizing cluster analysis as well as student interviews, we investigated students’ profiles of perceived cost and goal orientation as it relates to their final grades. Our results show that students who are well prepared for general chemistry, such as those who have taken chemistry in high school, display less negative perceived costs and thus believe they can master the material more fully. Other interesting results have also emerged from this research, which has the potential to have an impact on future instruction of these courses.

Keywords: chemistry education, motivation, affect, perceived costs, goal orientations

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Authors: M. Khazam, M. Altawil, A. Eljabri

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Fluid properties in states near a vapor-liquid critical region are the most difficult to measure and to predict with EoS models. The principal model difficulty is that near-critical property variations do not follow the same mathematics as at conditions far away from the critical region. Libyan NC98 field in Sirte basin is a typical example of near critical fluid characterized by high initial condensate gas ratio (CGR) greater than 160 bbl/MMscf and maximum liquid drop-out of 25%. The objective of this paper is to model NC98 phase behavior with the proper selection of EoS parameters and also to model reservoir depletion versus gas cycling option using measured PVT data and EoS Models. The outcomes of our study revealed that, for accurate gas and condensate recovery forecast during depletion, the most important PVT data to match are the gas phase Z-factor and C7+ fraction as functions of pressure. Reasonable match, within -3% error, was achieved for ultimate condensate recovery at abandonment pressure of 1500 psia. The smooth transition from gas-condensate to volatile oil was fairly simulated by the tuned PR-EoS. The predicted GOC was approximately at 14,380 ftss. The optimum gas cycling scheme, in order to maximize condensate recovery, should not be performed at pressures less than 5700 psia. The contribution of condensate vaporization for such field is marginal, within 8% to 14%, compared to gas-gas miscible displacement. Therefore, it is always recommended, if gas recycle scheme to be considered for this field, to start it at the early stage of field development.

Keywords: EoS models, gas-condensate, gas cycling, near critical fluid

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Authors: Sarvada Nand

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Teacher quality is directly proportional to the achievement level of students. Recent researches reveal that the teacher learning communities enhance the quality of teacher. It is a proven fact that community does help in enhancing teachers’ self-esteem as professionals, their teaching skills and enhancing classroom transaction that results in the higher achievement of students. The purpose of this study is to develop TLC and provide them platform where they share their views and ideas on various academic issues. The study examines how teachers conceptualize TLCs, up to what extent TLC help in developing professionalism among teachers and how they prepare themselves for the days to come. In this study, pre-test in five subjects, Hindi, English, Mathematics, Science and Social Studies was conducted and a questionnaire was designed to judge the teachers' attitude towards teaching practice. After completion of the project duration of three and a half-month, an exercise of post-test was conducted in all the above subjects. The post tests show tremendous improvements in achievement level of those students who were regular in their classes and were attended through this new method. A visible shift in teacher’s attitude is seen for the better. They were able to realize their own potentials. There was a group of Facilitators formed to perform continuously supervision and monitor in regular intervals so that they could easily handle the challenges, and factors much important for the attainment towards the fulfillment of the objectives.

Keywords: teacher learning communities, best practice, teacher professionalism, student achievement

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Authors: Xiaoming Yang, Abby Folberg, Carey Ryan, Lwetzel, Tgoering

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We examined gender differences in entrepreneurial career interests drawing on goal congruity theory, which posits that people adopt gender-stereotypic goal orientations in response to social pressures to conform to traditional gender roles. Aspiring entrepreneurs (N = 351) first wrote three to five sentences about what they believed made an entrepreneur successful. They then completed measures of agentic and communal goal orientations (i.e., male and female stereotypic orientations, respectively) and indicated their interests in starting ventures in stereotypically feminine (e.g., salon), masculine (e.g., auto-repair) and science, technology, engineering, and mathematics (STEM; e.g., software developer) ventures. Qualitative analyses demonstrated that participants ascribed agentic and, more specifically, dominance, attributes to entrepreneurs; few participants ascribed communal attributes (e.g., warmth). Bifactor structural equation modeling indicated that, as expected, agentic goal orientations included dimensions of competence, self-direction, and dominance orientations and communal goal orientations were unidimensional. Further, as expected, dominance and communal orientations partially accounted for gender differences in all three career types. We discuss implications for entrepreneurial education and practice from a goal congruity perspective and the use of bifactor modeling to improve the measurement of goal orientations.

Keywords: gender, entrepreneurship, gender stereotypes, agentic and communal goal orientations, entrepreneurship education

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Nodelman V.

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Despite serious difficulties in the assimilation of the conceptual system of Calculus, software in the educational process is used only occasionally, and even then, mainly for illustration purposes. The following are a few reasons: The non-trivial nature of the studied material, Lack of skills in working with software, Fear of losing time working with software, The variety of the software itself, the corresponding interface, syntax, and the methods of working with the software, The need to find suitable models, and familiarize yourself with working with them, Incomplete compatibility of the found models with the content and teaching methods of the studied material. This paper proposes an active use of the developed non-commercial software VusuMatica, which allows removing these restrictions through Broad support for the studied mathematical material (and not only Calculus). As a result - no need to select the right software, Emphasizing the unity of mathematics, its intrasubject and interdisciplinary relations, User-friendly interface, Absence of special syntax in defining mathematical objects, Ease of building models of the studied material and manipulating them, Unlimited flexibility of models thanks to the ability to redefine objects, which allows exploring objects characteristics, and considering examples and counterexamples of the concepts under study. The construction of models is based on an original approach to the analysis of the structure of the studied concepts. Thanks to the ease of construction, students are able not only to use ready-made models but also to create them on their own and explore the material studied with their help. The presentation includes examples of using VusuMatica in studying the concepts of limit and continuity of a function, its derivative, and integral.

Keywords: counterexamples, limitations and requirements, software, teaching and learning calculus, user-friendly interface and syntax

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Authors: Angelina A. Tzacheva, Jaishree Ranganathan

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Interest in (STEM) Science Technology Engineering Mathematics education especially Computer Science education has seen a drastic increase across the country. This fuels effort towards recruiting and admitting a diverse population of students. Thus the changing conditions in terms of the student population, diversity and the expected teaching and learning outcomes give the platform for use of Innovative Teaching models and technologies. It is necessary that these methods adapted should also concentrate on raising quality of such innovations and have positive impact on student learning. Light-Weight Team is an Active Learning Pedagogy, which is considered to be low-stake activity and has very little or no direct impact on student grades. Emotion plays a major role in student’s motivation to learning. In this work we use the student feedback data with emotion classification using surveys at a public research institution in the United States. We use Actionable Pattern Discovery method for this purpose. Actionable patterns are patterns that provide suggestions in the form of rules to help the user achieve better outcomes. The proposed method provides meaningful insight in terms of changes that can be incorporated in the Light-Weight team activities, resources utilized in the course. The results suggest how to enhance student emotions to a more positive state, in particular focuses on the emotions ‘Trust’ and ‘Joy’.

Keywords: actionable pattern discovery, education, emotion, data mining

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Authors: Jelena Slugan, Ivica Ružić

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We are witnessing the rapid development of technologies that change the world around us. However, curriculums and teaching processes are often slow to adapt to the change; it takes time, money and expertise to implement technology in the classroom. Therefore, the University of Split, Croatia, partnered with local school Marko Marulić High School and created the project "Modern competence in modern high schools" as part of which five different curriculums for STEM areas were developed. One of the curriculums involves combining information technology with physics. The main idea was to teach students how to use different circuits and microcomputers to explore nature and physical phenomena. As a result, using electrical circuits, students are able to recreate in the classroom the phenomena that they observe every day in their environment. So far, high school students had very little opportunity to perform experiments independently, and especially, those physics experiment did not involve ICT. Therefore, this project has a great importance, because the students will finally get a chance to develop themselves in accordance to modern technologies. This paper presents some new methods of teaching physics that will help students to develop experimental skills through the study of deterministic nature of physical laws. Students will learn how to formulate hypotheses, model physical problems using the electronic circuits and evaluate their results. While doing that, they will also acquire useful problem solving skills.

Keywords: ICT in physics, curriculum, laboratory activities, STEM (science, technology, engineering, mathematics)

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Authors: Araceli Martínez Ortiz

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An educational research effort is analyzed using systems theory to document the power of collective impact when addressing multiple factors contributing towards the retention of students majoring in science, technology, engineering and mathematics (STEM) academic programs. This research promotes understanding on how networked communities may work effectively toward a shared vision and mutually aligned activities that result in sustained, large scale change. The actions of a team of researchers in their third year of collaboration are presented to describe a model that positively aligns work efforts resulting in greater total gains. The goals of the multiple programs managed by the funded program team are to: 1) expand the number of students who choose to study a STEM field of study; 2) promote student collaborative learning; 3) support faculty understanding of the funds of knowledge of diverse students and 4) establish innovative and robust STEM education research that will lead to the development of nationally replicable, scalable models for broadening participation in STEM. The impacts of this research effort are measured through quantitative statistical analysis of the changes in second-year STEM undergraduate student retention rates and representation rates of women, Hispanics and African American STEM majors.

Keywords: collaborative impact, diversity, student retention, systems theory, STEM education

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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Differential equations are of fundamental importance in engineering and applied mathematics, since many physical laws and relations appear mathematically in the form of such equations. The equilibrium state of structures consisting of one-dimensional elements can be described by an ordinary differential equation. The response of these kinds of structures under the loading, namely relationship between the displacement field and loading field, can be predicted by the solution of these differential equations and on satisfying the given boundary conditions. When the effect of change of geometry under loading is taken into account in modeling of equilibrium state, then these differential equations are partially integrable in quartered. They also exhibit instability characteristics when the structures are loaded compressively. The purpose of this paper is to represent the ability of the Modified Newmark Method in analyzing flexural-torsional instability of struts for both bifurcation and non-bifurcation structural systems. The results are shown to be very accurate with only a small number of iterations. The method is easily programmed, and has the advantages of simplicity and speeds of convergence and easily is extended to treat material and geometric nonlinearity including no prismatic members and linear and nonlinear spring restraints that would be encountered in frames. In this paper, these abilities of the method will be extended to the system of linear differential equations that govern strut flexural torsional stability.

Keywords: instability, torsion, flexural, buckling, modified newmark method stability

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Authors: Shielilo R. Amihan, Ederliza De Jesus

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The study determined the predictors of college performance of 2nd Yr students of UPHSD-Calamba. This quantitative study conducted a survey using the Scholastic Abilities Test for Adults (SATA), and the retrieval of entrance examinations results and current General Weighted Average (GWA) of the 242 randomly selected respondents. The mean, Pearson r and multiple regression analyses through SPSS revealed that students are capable of verbal, non-verbal and quantitative reasoning, reading vocabulary, comprehension, math calculation, and writing mechanics but have difficulty in math application and writing composition. The study found out the Scholastic Ability and Achievement, except in mathematics, are significantly related to college performance. It concludes that students with high ability and achievement may perform better in college. However, only English subset results in the entrance exam predicts the academic success of students in college while SATA and Math entrance exam results do not. The study recommends providing pre-college Math and Writing courses as requisites in college. It also suggests implementing formative curriculum-based enhancement programs on specific priority areas, profiling programs towards informed individual academic decision-making, revising the Entrance Examinations, monitoring the development of the students, and exploring other predictors of college academic performance such as non-cognitive factors.

Keywords: scholastic ability, scholastic achievement, entrance exam, college performance

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Authors: Solly M. Seeletse, Joel L. Thabane

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Students enrolling at the Sefako Makgatho Health Sciences University (SMU) come mostly from the previously disadvantaged communities of South Africa. Their backgrounds are deprived in resources and modern technologies of education. Most of those admitted in the basic sciences were rejected in medicine and health related study programmes in SMU. Mathematics (maths) is the main subject for admission into SMU study programmes. However, maths results are usually low. In an attempt to help to prepare the students in the neighbourhood schools of SMU, some Maths educators partnered with local schools to communicate the needs and investigate the causes of poor maths results. They embarked on an action research to determine the level of educators’ maths education. The general aim of the research was to investigate the causes of deficiencies in maths teaching and results in the local secondary schools, focusing on teachers and learners. Asking the teachers about their education and learners about maths concepts of most difficulty, these were identified. The researchers assisted in teaching the difficult concepts. The study highlighted the most difficult concepts and the teachers’ lack of training in some content. Intervention of the researchers showed to be effective only for the very poor performing schools. Those with descent pass rates of over 50% did not benefit from it. This was the sign of lack of optimality in the methods used. The research recommendations suggested that intervention methods should be improved to be effective in all schools, and extension of the endeavours to more schools.

Keywords: action research, intervention, social responsibility, support

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Authors: Abdul Halim Abdullah, Nur Liyana Zainal Abidin, Mahani Mokhtar

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Problem-solving is an activity which can encourage students to use Higher Order Thinking Skills (HOTS). Learning fractions can be challenging for students since empirical evidence shows that students experience difficulties in solving the fraction problems. However, visual methods can help students to overcome the difficulties since the methods help students to make meaningful visual representations and link abstract concepts in Mathematics. Therefore, the purpose of this study was to investigate whether there were any changes in students’ HOTS at the four highest levels when learning the fractions by using Thinking Blocks. 54 students participated in a quasi-experiment using pre-tests and post-tests. Students were divided into two groups. The experimental group (n=32) received a treatment to improve the students’ HOTS and the other group acted as the control group (n=22) which used a traditional method. Data were analysed by using Mann-Whitney test. The results indicated that during post-test, students who used Thinking Blocks showed significant improvement in their HOTS level (p=0.000). In addition, the results of post-test also showed that the students’ performance improved significantly at the four highest levels of HOTS; namely, application (p=0.001), analyse (p=0.000), evaluate (p=0.000), and create (p=0.000). Therefore, it can be concluded that Thinking Blocks can effectively encourage students to use the four highest levels of HOTS which consequently enable them to solve fractions problems successfully.

Keywords: Thinking Blocks, Higher Order Thinking Skills (HOTS), fractions, problem solving

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Authors: Chaiyawat Musikapan, Ratchatin Chancharoen, Saknan Bongsebandhu-Phubhakdi

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For many recent years, soft robotic fingers were used for supporting the patients who had survived the neurological diseases that resulted in muscular disorders and neural network damages, such as stroke and Parkinson’s disease, and inflammatory symptoms such as De Quervain and trigger finger. Generally, the major hand function is significant to manipulate objects in activities of daily living (ADL). In this work, we proposed the model of soft actuator that manufactured by full 3D printing without the molding process and one material for use. Furthermore, we designed the model with a technique of multi cavitation cells (MC-Cells). Then, we demonstrated the curvature bending, fluidic pressure and force that generated to the model for assistive finger flexor and hand grasping. Also, the soft actuators were characterized in mathematics solving by the length of chord and arc length. In addition, we used an adaptive push-button switch machine to measure the force in our experiment. Consequently, we evaluated biomechanics efficiency by the range of motion (ROM) that affected to metacarpophalangeal joint (MCP), proximal interphalangeal joint (PIP) and distal interphalangeal joint (DIP). Finally, the model achieved to exhibit the corresponding fluidic pressure with force and ROM to assist the finger flexor and hand grasping.

Keywords: biomechanics efficiency, curvature bending, hand functional assistance, multi cavitation cells (MC-Cells), range of motion (ROM)

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Authors: Indhumathi Gopal

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Undergraduate research is well documented in Science, Technology, Engineering, and Mathematics (STEM), neurosciences, and microbiology disciplines, though it is hardly part of a physical fitness & wellness discipline. However, students need experiential learning opportunities, like internships and research assistantships, to get ahead with graduate schools and be gainfully employed. The first step towards this goal is to have students do a simple research project in a semester-long course. The value of research experiences and how to integrate research activity in a physical fitness & wellness course are discussed. The investigator looks into a mini research project, “Awareness of Obesity among College Students” and explains how to guide students through the research process, including journal search, data collection, and basic statistics. Besides, students will be introduced to the statistical package program SPSS 22.0 to assist with data evaluation. The lab component of the combined lecture-physical activity course could include the measurement of student’s weight with respect to their height to obtain body mass index (BMI). Students could categorize themselves in accordance with the World Health Organization’s guidelines. Results obtained after completing the data analysis help students be aware of their own potential health risks associated with overweight and obesity. Overweight and obesity are risk factors for hypertension, hypercholesterolemia, heart disease, stroke, diabetes, and certain types of cancer. It is hoped that this experience will get students interested in scientific studies, gain confidence, think critically, and develop problem-solving and good communication skills.

Keywords: physical fitness, undergraduate research experience, obesity, BMI

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Authors: Blair D. Macdonald

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After nearly one hundred years of its origin, foundational quantum mechanics remains one of the greatest unexplained mysteries in physicists today. Within this time, chaos theory and its geometry, the fractal, has developed. In this paper, the propagation behaviour with an iteration of a simple fractal, the Koch Snowflake, was described and analysed. From an arbitrary observation point within the fractal set, the fractal propagates forward by oscillation—the focus of this study and retrospectively behind by exponential growth from a point beginning. It propagates a potentially infinite exponential oscillating sinusoidal wave of discrete triangle bits sharing many characteristics of light and quantum entities. The model's wave speed is potentially constant, offering insights into the perception and a direction of time where, to an observer, when travelling at the frontier of propagation, time may slow to a stop. In isolation, the fractal is a superposition of component bits where position and scale present a problem of location. In reality, this problem is experienced within fractal landscapes or fields where 'position' is only 'known' by the addition of information or markers. The quantum' measurement problem', 'uncertainty principle,' 'entanglement,' and the classical-quantum interface are addressed; these are a problem of scale invariance associated with isolated fractality. Dual forward and retrospective perspectives of the fractal model offer the opportunity for unification between quantum mechanics and cosmological mathematics, observations, and conjectures. Quantum and cosmological problems may be different aspects of the one fractal geometry.

Keywords: measurement problem, observer, entanglement, unification

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Authors: Ramin Rostamkhani, Thurasamy Ramayah

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One of the most important topics of today’s industrial organizations is the challenging issue of supply chain management. In this field, scientists and researchers have published numerous practical articles and models, especially in the last decade. In this research, to our best knowledge, the discussion of data modeling of supply chain management components using well-known statistical distribution functions has been considered. The world of science owns mathematics, and showing the behavior of supply chain data based on the characteristics of statistical distribution functions is innovative research that has not been published anywhere until the moment of doing this research. In an analytical process, describing different aspects of functions including probability density, cumulative distribution, reliability, and failure function can reach the suitable statistical distribution function for each of the components of the supply chain management. It can be applied to predict the behavior data of the relevant component in the future. Providing a model to adapt the best statistical distribution function in the supply chain management components will be a big revolution in the field of the behavior of the supply chain management elements in today's industrial organizations. Demonstrating the final results of the proposed model by introducing the process capability indices before and after implementing it alongside verifying the approach through the relevant assessment as an acceptable verification is a final step. The introduced approach can save the required time and cost to achieve the organizational goals. Moreover, it can increase added value in the organization.

Keywords: analyzing, process capability indices, statistical distribution functions, supply chain management components

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Authors: Ledeza Jordan Babiano

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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.

Keywords: mathematical structure, algebra word problems, translation, errors

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Authors: Sedat Simsek, Tugay Arat

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Today's communication concept, which has a great revolution with the printing press which has been found by Gutenberg, has no boundary thanks to advanced communication devices and the internet. It is possible to take advantage in many areas, such as from medicine to social sciences or from mathematics to education, from the computers that was first produced for the purpose of military services. The use of these developing technologies in the field of education has created a great vision changes in both training and having education. Materials, which can be considered as basic communication resources and used in traditional education has begun to lose its significance, and some technologies have begun to replace them such as internet, computers, smart boards, projection devices and mobile phone. On the other hand, the programs and applications used in these technologies have also been developed. University students use virtual books instead of the traditional printed book, use cell phones instead of note books, use the internet and virtual databases instead of the library to research. They even submit their homework with interactive methods rather than printed materials. The traditional education system, these technologies, which increase productivity, have brought a new dimension to education. The aim of this study is to determine the influence of technologies in the learning process of students and to find whether is there any similarities and differences that arise from the their faculty that they have been educated and and their learning process. In addition to this, it is aimed to determine the level of ICT usage of students studying at the university level. In this context, the advantages and conveniences of the technology used by students are also scrutinized. In this study, we used surveys to collect data. The data were analyzed by using SPSS 16 statistical program with the appropriate testing.

Keywords: education, communication technologies, role of technology, teaching

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Authors: Youssef A. Yakoub, Ramy M. Shaaban

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Covid-19 has changed and affected the whole world dramatically in a new way that the entire world, even scientists, have not imagined before. The educational institutions around the world have been fighting since Covid-19 hit the world last December to keep the educational process unchanged for all students. E-learning was a must for almost all US universities during the pandemic. It was specifically more challenging to use eLearning instead of regular classes among students who take practical education. The aim of this study is to examine the perception of STEM students towards using eLearning instead of traditional methods during their practical study. Focus groups of STEM students studying at a western Pennsylavian, mid-size university were interviewed. Semi-structured interviews were designed to get an insight on students’ perception towards the alternative educational methods they used in the past seven months. Using convenient sampling, four students were chosen from different STEM fields: science of physics, technology, electrical engineering, and mathematics. The interview was primarily about the extent to which these students were satisfied, and their educational needs were met through distance education during the pandemic. The interviewed students were generally able to do a satisfactory performance during their virtual classes, but they were not satisfied enough with the learning methods. The main challenges they faced included the inability to have real practical experience, insufficient materials posted by the faculty, and some technical problems associated with their study. However, they reported they were satisfied with the simulation programs they had. They reported these simulations provided them with a good alternative to their traditional practical education. In conclusion, this study highlighted the challenges students face during the pandemic. It also highlighted the various learning tools students see as good alternatives to their traditional education.

Keywords: eLearning, STEM education, COVID-19 crisis, online practical training

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Authors: Sanaz Ahmadzadeh Siyahrood, Arghavan Ebrahimi, Mohammadjavad Mahdavinejad

Abstract:

Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.

Keywords: angle, equal triangle, square, structural hierarchy

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Authors: Maria Gonzalez Alriols, Itziar Egues, Maria A. Andres, Mirari Antxustegi

Abstract:

Peer to peer learning is an educational tool very useful to enhance teamwork and reinforce cooperation between mates. It is particularly successful to work with students of different level of previous knowledge, as it often happens among pupils of subjects in the first course of science and engineering studies. Depending on the performed pre-university academic itinerary, the acquired knowledge in disciplines as mathematics, physics, or chemistry may be quite different. This fact is an added difficulty to the tuition of first-course basic science subjects of engineering degrees, with inexperienced students that do not know each other. In this context, peer to peer learning applied in small groups facilitates the communication between mates and makes it easier for the students with low level to be helped by the ones with better prior knowledge. In this work, several collaborative learning strategies were designed to be applied in the tuition of the subject 'chemistry', which is imparted in the first course of an engineering degree. Students were organized in groups combining mates with different level of prior knowledge. The teaching role was offered to the more experienced students who were responsible for designing learning pills to help the other mates in their group. This workload was rewarded with an extra mark, and more extra points were offered to all the group mates if every student in the group reached a determined level at the end of the semester. It was very important to start these activities from the beginning of the semester in order to avoid absenteeism. The obtained results were positive as a higher percentage of mates signed up and passed the final exam, the obtained final marks were higher, and a much better atmosphere was observed in the class.

Keywords: peer to peer tuition, collaborative learning, engineering instruction, chemistry

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Authors: S. Vijayakumar, S. B. Rathna Kumar, Navnath D Jagadale

Abstract:

Learning and teaching are the challenges ahead in the education of the students with hearing impairment using sign language (SHISL). Either the students or teachers face difficulties in the process of learning/teaching. Communication is one of the main barriers while teaching SHISL. Further, the courses of study or the subjects are limited to SHISL at least in countries like India. Students with hearing impairment mainly opt for sign language as a communication mode. Subjects like physics, chemistry, advanced mathematics etc. are not available in the curriculum for the SHISL since their content and ideas are complex. In India, exemption for language papers is being given for the students with hearing impairment. It may give opportunity to them to secure secondary/ higher secondary qualifications. It is a known fact that students with hearing impairment are facing difficulty in their future carrier. They secure neither a higher study nor a good employment opportunity. Vocational training in various trades will land them in few jobs with few bucks in pocket. However, not all of them are blessed with higher positions in government or private sectors in competitive fields or where the technical knowledge is required. E learning with sign language instructions can be used for teaching languages and science subjects. Computer Based Instruction (CBI), Computer Based Training (CBT), and Computer Assisted Instruction (CAI) are now part-and-parcel of Modern Education. It will also include signed video clip corresponding to the topic. Learning language subjects will improve the understanding of concepts in different subjects. Learning other science subjects like their hearing counterparts will enable the SHISL to go higher in studies and increase their height to pluck a fruit of the tree of employment.

Keywords: students with hearing impairment using sign language, hearing impairment, language subjects, science subjects, e-learning

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Authors: Lida Balilan, Dariush Sattarzadeh, Rana Koorepaz

Abstract:

In the Ilkhanid era, the mystical school of Tabriz manifested itself as an art school in various aspects, including miniatures, architecture, urban planning and design, simultaneously with the expansion of the many sciences of its time. In this era, mysticism, both in form and in poetry and prose, as well as in works of art reached its peak. Mysticism, as an inner belief and thought, brought the audience to the artistic and aesthetical view using allegorical and symbolic expression of the religion and had a direct impact on the formation of the intellectual and cultural layers of the society. At the same time, Mystic school of Tabriz could create a symbolic and allegorical language to create magnificent works of architecture with the expansion of science in various fields and using various sciences such as mathematics, geometry, science of numbers and by Abjad letters. In this era, geometry is the middle link between mysticism and architecture and it is divided into two categories, including intellectual and sensory geometry and based on its function. Soltaniyeh dome is one of the prominent buildings of the Tabriz school with the shrine land use. In this article, information is collected using a historical-interpretive method and the results are analyzed using an analytical-comparative method. The results of the study suggest that the designers and builders of the Soltaniyeh dome have used shapes, colors, numbers, letters and words in the form of motifs, geometric patterns as well as lines and writings in levels and layers ranging from plans to decorations and arrays for architectural symbolization and encryption to express and transmit mystical ideas.

Keywords: geometry, Tabriz school, mystical thoughts, dome of Soltaniyeh

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Authors: Derya Duran, Christine Jacknick

Abstract:

Despite a growing body of research on classroom, especially language classroom interactions, much more is yet to be discovered on how interaction is organized in higher education settings. This study investigates how the discourse marker 'I mean' in teacher questioning turns functions as a resource to promote student participation as well as to enhance collective understanding in whole-class discussions. This paper takes a conversation analytic perspective, drawing on 30-hour video recordings of classroom interaction in an English as a medium of instruction university in Turkey. Two content classrooms (i.e., Guidance) were observed during an academic term. The course was offered to 4th year students (n=78) in the Faculty of Education; students were majoring in different subjects (i.e., Early Childhood Education, Foreign Language Education, Mathematics Education). Results of the study demonstrate the multi-functionality of discourse marker 'I mean' in teacher questioning turns. In the context of English as a medium of instruction classrooms where possible sources of confusion may occur, we found that 'I mean' is primarily used to indicate upcoming adjustments. More specifically, it is employed for a variety of interactional purposes such as elaboration, clarification, specification, reformulation, and reference to the instructional activity. The study sheds light on the multiplicity of functions of the discourse marker in academic interactions and it uncovers how certain linguistic resources serve functions to the organization of repair such as the maintenance of understanding in classroom interaction. In doing so, it also shows the ways in which participation is routinely enacted in shared interactional events through linguistic resources.

Keywords: conversation analysis, discourse marker, English as a medium of instruction, repair

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Authors: Amir Hossein Allahdadi

Abstract:

The mystical and intuitive look of Islamic artists inspired by the Koranic and mystical principles and also based on the geometry and mathematics has left unique works whose range extends across the borders of Islam. The relationship between Islamic art and music in the traditional art is of one of the concepts that can be traced back to the other arts by detection of its components. One of the links is the art of painting whose subtleties that can be applicable to both architecture and music. So, architecture and music links can be traced in other arts with a traditional foundation in order to evaluate the equivalents of traditional arts. What is the relationship between physical space of architecture and nonphysical space of music? What is musical architecture? What is the music that tends to architecture? These questions are very small samples of the questions that arise in this category, and these questions and concerns remain as long as the music is played and the architecture is made. Efforts have been made in this area, references compiled and plans drawn. As an example, we can refer to views of ‘Mansour Falamaki’ in the book of architecture and music, as well as the book transition from mud to heart by ‘Hesamodin Seraj’. The method is such that a certain melody is given to an architect and it is tried to design a specified architecture using a certain theme. This study is not to follow the architecture of a particular type of music and the formation of a volume based on a sound. In this opportunity, it is tried to briefly review the relationship between music and architecture in the Iranian original and traditional arts, using the basic definitions of arts. The musician plays, the architect designs, the actor forms his desired space and painter displays his multi-dimensional world in the form of two-dimensions. The expression language is different, but all of them can be gathered in a form, a form which has no clear boundaries. In fact, in any original art, the artist applies his art as a tool to express his insights which are nothing but achieving the world beyond this place and time.

Keywords: architecture, music, geometric proportions, mathematical proportions

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Authors: Giulia I. Pintea

Abstract:

The Roma people are a nomadic ethnic group native to India, and they are one of the most prevalent minorities in Europe. In the past, Roma were enslaved and they were imprisoned in concentration camps during the Holocaust; today, Roma are subject to hate crimes and are denied access to healthcare, education, and proper housing. The aim of this project is to analyze how the public perception of the Roma people may be influenced by antiziganist and pro-Roma institutions in Europe. In order to carry out this project, we used social network analysis to build two large social networks: The antiziganist network, which is composed of institutions that oppress and racialize Roma, and the pro-Roma network, which is composed of institutions that advocate for and protect Roma rights. Measures of centrality, density, and modularity were obtained to determine which of the two social networks is exerting the greatest influence on the public’s perception of Roma in European societies. Furthermore, data on hate crimes on Roma were gathered from the Organization for Security and Cooperation in Europe (OSCE). We analyzed the trends in hate crimes on Roma for several European countries for 2009-2015 in order to see whether or not there have been changes in the public’s perception of Roma, thus helping us evaluate which of the two social networks has been more influential. Overall, the results suggest that there is a greater and faster exchange of information in the pro-Roma network. However, when taking the hate crimes into account, the impact of the pro-Roma institutions is ambiguous, due to differing patterns among European countries, suggesting that the impact of the pro-Roma network is inconsistent. Despite antiziganist institutions having a slower flow of information, the hate crime patterns also suggest that the antiziganist network has a higher impact on certain countries, which may be due to institutions outside the political sphere boosting the spread of antiziganist ideas and information to the European public.

Keywords: applied mathematics, oppression, Roma people, social network analysis

Procedia PDF Downloads 250