Search results for: introductory mathematics

Authors: Maryam Kalkatechi

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The application of algorithms in architecture has been realized as geometric forms which are increasingly being used by architecture firms. The abstraction of ideas in a formulated algorithm is not possible. There is still a gap between design innovation and final built in prescribed formulas, even the most aesthetical realizations. This paper presents the application of erudite design process to conceptualize biomimetic paradigms in architecture. The process is customized to material and tectonics. The first part of the paper outlines the design process elements within four biomimetic pre-concepts. The pre-concepts are chosen from plants family. These include the pine leaf, the dandelion flower; the cactus flower and the sun flower. The choice of these are related to material qualities and natural pattern of the tectonics of these plants. It then focuses on four versions of tectonic comprehension of one of the biomimetic pre-concepts. The next part of the paper discusses the implementation of STEAM in higher education in architecture. This is shown by the relations within the design process and the manifestation of the thinking processes. The A in the SETAM, in this case, is only achieved by the design process, an engaging event as a performing arts, in which the conceptualization and development is realized in final built.

Keywords: biomimetic paradigm, erudite design process, tectonic, STEAM (Science, Technology, Engineering, Arts, Mathematic)

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Jin Koo

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The main purpose of this study is to investigate the comparability of student scores obtained from Test Center (TC) vs. Online-Proctored (OP) Delivery in the three subject areas of Verbal, Reading, and Mathematics for each level (Middle and Upper). Also, this study examines whether there is an interaction effect between test deliveries (TC vs. OP) and gender/ethnicity/ability level in each subject area. The test used in this study is a multiple-choice standardized test for students in grades 5-11. For this study, data were collected during the 2022-23 test administration. This research used a one-factor between-subjects ANOVA and Cohen’s d to compare the TC and OP groups’ test means for each level and each subject area. Also, 2-factor between-subjects ANOVAs were conducted to investigate examinee characteristics: gender (male and female), ethnicity (African-American, Asian, Hispanic, Multi-racial, and White), and ability level (low, average, and high-ability groups). The author found that students’ test scores in some subject areas varied between TC and OP test deliveries by gender, ethnicity, and ability level, meaning that gender, ethnicity, and ability level were related to the score difference. These results will be discussed according to the current testing systems.

Keywords: ability level, ethnicity, gender, online-proctored delivery, standardized test, test center

Procedia PDF Downloads 47

Authors: Omar M. Elmabrouk., Roaa Y. Taha., Najat M. Ebrahim, Sabbreen A. Mohammed

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Power transformers are the most crucial part of power electrical system, distribution and transmission grid. This part is maintained using predictive or condition-based maintenance approach. The diagnosis of power transformer condition is performed based on Dissolved Gas Analysis (DGA). There are five main methods utilized for analyzing these gases. These methods are International Electrotechnical Commission (IEC) gas ratio, Key Gas, Roger gas ratio, Doernenburg, and Duval Triangle. Moreover, due to the importance of the transformers, there is a need for an accurate technique to diagnose and hence predict the transformer condition. The main objective of this technique is to avoid the transformer faults and hence to maintain the power electrical system, distribution and transmission grid. In this paper, the DGA was utilized based on the data collected from the transformer records available in the General Electricity Company of Libya (GECOL) which is located in Benghazi-Libya. The Fuzzy Logic (FL) technique was implemented as a diagnostic approach based on IEC gas ratio method. The FL technique gave better results and approved to be used as an accurate prediction technique for power transformer faults. Also, this technique is approved to be a quite interesting for the readers and the concern researchers in the area of FL mathematics and power transformer.

Keywords: dissolved gas-in-oil analysis, fuzzy logic, power transformer, prediction

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Authors: Darsh N. Patel, Eric Olson

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Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: Wen Chen

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To investigate the interleaving effect of subject matter (mathematics vs. history) and perceptual modality (visual vs. auditory materials) on student’s attention and learning outcomes, the present study collected self-reported data on subjective cognitive load (SCL) and attention level, EEG data, and learning outcomes from micro-lectures. Eighty-one 7th grade students were randomly assigned to four learning conditions: blocked (by subject matter) micro-lectures with auditory textual information (B-A condition), blocked (by subject matter) micro-lectures with visual textual information (B-V condition), interleaved (by subject matter) micro-lectures with auditory textual information (I-A condition), and interleaved micro-lectures by both perceptual modality and subject matter (I-all condition). The results showed that although interleaved conditions may show advantages in certain indices, the I-all condition showed the best overall outcomes (best performance, low SCL, and high attention). This study suggests that interleaving by both subject matter and perceptual modality should be preferred in scheduling and planning classes.

Keywords: cognitive load, interleaving effect, micro-lectures, sustained attention

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Authors: Shana Malio-Satele, Lemalu Silao Vaisola Sefo

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Introductory Statement: South Seas Healthcare is Ōtara’s largest Pacific health provider in South Auckland, New Zealand. Our vision is excellent health and well-being for Pacific people and all communities through strong Pacific values. During the DELTA and Omicron outbreak of COVID-19, our Pacific people, indigenous Māori, and the community of South Auckland were disproportionately affected and faced significant hardship with existing inequities magnified. This study highlights the community-based learnings of harnessing community-based strengths such as indigenous resilience, family-informed experiences and stories that provide critical insights that inform health reform changes that will be sustainable and equitable for all indigenous populations. This study is based on critical learnings acquired during COVID-19 that challenge the deficit narrative common in healthcare about indigenous populations. This study shares case studies of marginalised groups and religious groups and the successful application of indigenous cultural strengths, such as collectivism, positive protective factors, and using trusted relationships to create meaningful change in the way healthcare is delivered. The significance of this study highlights the critical conditions needed to adopt a community-informed way of creating integrated healthcare that works and the role that the community can play in being part of the solution. Methodologies: Key methodologies utilised are indigenous and Pacific-informed. To achieve critical learnings from the community, Pacific research methodologies, heavily informed by the Polynesian practice, were applied. Specifically, this includes; Teu Le Va (Understanding the importance of trusted relationships as a way of creating positive health solutions); The Fonofale Methodology (A way of understanding how health incorporates culture, family, the physical, spiritual, mental and other dimensions of health, as well as time, context and environment; The Fonua Methodology – Understanding the overall wellbeing and health of communities, families and individuals and their holistic needs and environmental factors and the Talanoa methodology (Researching through conversation, where understanding the individual and community is through understanding their history and future through stories). Major Findings: Key findings in the study included: 1. The collectivist approach in the community is a strengths-based response specific to populations, which highlights the importance of trusted relationships and cultural values to achieve meaningful outcomes. 2. The development of a “village model” which identified critical components to achieving health reform change; system navigation, a sense of service that was culturally responsive, critical leadership roles, culturally appropriate support, and the ability to influence the system enablers to support an alternative way of working. Concluding Statement: There is a strong connection between community-based strengths being implemented into healthcare strategies and reforms and the sustainable success of indigenous populations and marginalised communities accessing services that are cohesive, equitably resourced, accessible and meaningful for families. This study highlights the successful community-informed approaches and practices used during the COVID-19 response in New Zealand that are now being implemented in the current health reform.

Keywords: indigenous voice, community voice, health reform, New Zealand

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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: Marcial Blondet, Malena Serrano, Álvaro Rubiños, Elin Mattsson

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In Peru, there are more than two million houses made of adobe (sun dried mud bricks) or rammed earth (35% of the total houses), in which almost 9 million people live, mainly because they cannot afford to purchase industrialized construction materials. Although adobe houses are cheap to build and thermally comfortable, their seismic performance is very poor, and they usually suffer significant damage or collapse with tragic loss of life. Therefore, over the years, researchers at the Pontifical Catholic University of Peru and other institutions have developed many reinforcement techniques as an effort to improve the structural safety of earthen houses located in seismic areas. However, most rural communities live under unacceptable seismic risk conditions because these techniques have not been adopted massively, mainly due to high cost and lack of diffusion. The nylon rope mesh reinforcement technique is simple and low-cost, and two technological transference tools have been developed to diffuse it among rural communities: 1) Scale seismic simulations using a portable shaking table have been designed to prove its effectiveness to protect adobe houses; 2) A step-by-step illustrated construction manual has been developed to guide the complete building process of a nylon rope mesh reinforced adobe house. As a study case, it was selected the district of Pullo: a small rural community in the Peruvian Andes where more than 80% of its inhabitants live in adobe houses and more than 60% are considered to live in poverty or extreme poverty conditions. The research team carried out a one-day workshop in May 2015 and a two-day workshop in September 2015. Results were positive: First, the nylon rope mesh reinforcement procedure was proven simple enough to be replicated by adults, both young and seniors, and participants handled ropes and knots easily as they use them for daily livestock activity. In addition, nylon ropes were proven highly available in the study area as they were found at two local stores in variety of color and size.. Second, the portable shaking table demonstration successfully showed the effectiveness of the nylon rope mesh reinforcement and generated interest on learning about it. On the first workshop, more than 70% of the participants were willing to formally subscribe and sign up for practical training lessons. On the second workshop, more than 80% of the participants returned the second day to receive introductory practical training. Third, community members found illustrations on the construction manual simple and friendly but the roof system illustrations led to misinterpretation so they were improved. The technological transfer tools developed in this project can be used to train rural dwellers on earthquake-resistant self-construction with adobe, which is still very common in the Peruvian Andes. This approach would allow community members to develop skills and capacities to improve safety of their households on their own, thus, mitigating their high seismic risk and preventing tragic losses. Furthermore, proper training in earthquake-resistant self-construction with adobe would prevent rural dwellers from depending on external aid after an earthquake and become agents of their own development.

Keywords: adobe, Peruvian Andes, safe housing, technological transference

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Authors: Kasun P. Wijayaratna, Lauren Gardner, Taha Hossein Rashidi

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Undergraduate students entering university across the last 2 to 3 years tend to be born during the middle years of the 1990s. This generation of students has been exposed to the internet and the desire and dependency on technology since childhood. Brains develop based on environmental influences and technology has wired this generation of student to be attuned to sophisticated complex visual imagery, indicating visual forms of learning may be more effective than the traditional lecture or discussion formats. Furthermore, post-millennials perspectives on career are not focused solely on stability and income but are strongly driven by interest, entrepreneurship and innovation. Accordingly, it is important for educators to acknowledge the generational shift and tailor the delivery of learning material to meet the expectations of the students and the needs of industry. In the context of transport engineering, effectively teaching undergraduate students the basic principles of transport planning, traffic engineering and highway design is fundamental to the progression of the profession from a practice and research perspective. Recent developments in technology have transformed the discipline as practitioners and researchers move away from the traditional “pen and paper” approach to methods involving the use of computer programs and simulation. Further, enhanced accessibility of technology for students has changed the way they understand and learn material being delivered at tertiary education institutions. As a consequence, blended learning approaches, which aim to integrate face to face teaching with flexible self-paced learning resources, have become prevalent to provide scalable education that satisfies the expectations of students. This research study involved the development of a series of ‘Blended Learning’ initiatives implemented within an introductory transport planning and geometric design course, CVEN2401: Sustainable Transport and Highway Engineering, taught at the University of New South Wales, Australia. CVEN2401 was modified by conducting interactive polling exercises during lectures, including weekly online quizzes, offering a series of supplementary learning videos, and implementing a realistic design project that students needed to complete using modelling software that is widely used in practice. These activities and resources were aimed to improve the learning environment for a large class size in excess of 450 students and to ensure that practical industry valued skills were introduced. The case study compared the 2016 and 2017 student cohorts based on their performance across assessment tasks as well as their reception to the material revealed through student feedback surveys. The initiatives were well received with a number of students commenting on the ability to complete self-paced learning and an appreciation of the exposure to a realistic design project. From an educator’s perspective, blending the course made it feasible to interact and engage with students. Personalised learning opportunities were made available whilst delivering a considerable volume of complex content essential for all undergraduate Civil and Environmental Engineering students. Overall, this case study highlights the value of blended learning initiatives, especially in the context of large class size university courses.

Keywords: blended learning, highway design, teaching, transport planning

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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: Nicki Mohammadi, Emma Reford, Natalia Romano Spica, Laura Tabacof, Jenna Tosto-Mancuso, David Putrino, Christopher P. Kellner

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Introductory Statement: The onset of the COVID-19 pandemic demanded an unprecedented need for the rapid development, dispersal, and application of infection testing. However, despite the impressive mobilization of resources, individuals were incredibly limited in their access to tests, particularly during the initial months of the pandemic (March-April 2020) in New York City (NYC). Access to COVID-19 testing is crucial in understanding patients’ illness experiences and integral to the development of COVID-19 standard-of-care protocols, especially in the context of overall access to healthcare resources. Succinct Description of basic methodologies: 18 Patients in a COVID-19 Remote Patient Monitoring Program (Precision Recovery within the Mount Sinai Health System) were interviewed regarding their experience with COVID-19 during the first wave (March-May 2020) of the COVID-19 pandemic in New York City. Patients were asked about their experiences navigating COVID-19 diagnoses, the health care system, and their recovery process. Transcribed interviews were analyzed for thematic codes, using grounded theory to guide the identification of emergent themes and codebook development through an iterative process. Data coding was performed using NVivo12. References for the domain “testing” were then extracted and analyzed for themes and statistical patterns. Clear Indication of Major Findings of the study: 100% of participants (18/18) referenced COVID-19 testing in their interviews, with a total of 79 references across the 18 transcripts (average: 4.4 references/interview; 2.7% interview coverage). 89% of participants (16/18) discussed the difficulty of access to testing, including denial of testing without high severity of symptoms, geographical distance to the testing site, and lack of testing resources at healthcare centers. Participants shared varying perspectives on how the lack of certainty regarding their COVID-19 status affected their course of recovery. One participant shared that because she never tested positive she was shielded from her anxiety and fear, given the death toll in NYC. Another group of participants shared that not having a concrete status to share with family, friends and professionals affected how seriously onlookers took their symptoms. Furthermore, the absence of a positive test barred some individuals from access to treatment programs and employment support. Concluding Statement: Lack of access to COVID-19 testing in the first wave of the pandemic in NYC was a prominent element of patients’ illness experience, particularly during their recovery phase. While for some the lack of concrete results was protective, most emphasized the invalidating effect this had on the perception of illness for both self and others. COVID-19 testing is now widely accessible; however, those who are unable to demonstrate a positive test result but who are still presumed to have had COVID-19 in the first wave must continue to adapt to and live with the effects of this gap in knowledge and care on their recovery. Future efforts are required to ensure that patients do not face barriers to care due to the lack of testing and are reassured regarding their access to healthcare. Affiliations- 1Department of Neurosurgery, Icahn School of Medicine at Mount Sinai, New York, NY 2Abilities Research Center, Department of Rehabilitation and Human Performance, Icahn School of Medicine at Mount Sinai, New York, NY

Keywords: accessibility, COVID-19, recovery, testing

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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

Procedia PDF Downloads 91

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: Mahbuba Kaneez Hasna

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Introductory Statement outlining the background: Little has been written about political ecology of urban gardening, such as a network of knowledge generation, technologies of food production and distribution, food consumption practices, and the regulation of ‘agricultural activities. For urban food gardens to sustain as a long-term food security enterprise, we will need to better understand the anthropological, ecological, political, and institutional factors influencing their development, management, and ongoing viability. Significance of the study: Dhaka as one of the fastest growing city. There are currently no studies regards to Bangladesh on how urban slum dwellerscope with the changing urban environment in the city, where they overcome challenges, and how they cope with the urban ecological cycle of food and vegetable production. It is also essential to understand the importance of their access to confined spaces in the slums they apply their indigenous knowledge. These relationships in nature are important factors in community and conservation ecology. Until now, there has been no significant published academic work on relationships between urban and environmental anthropology, urban planning, geography, ecology, and social anthropology with a focus on urban agriculture and how this contributes to the moral economies, indigenous knowledge, and government policies in order to improve the lives and livelihoods of slum dwellers surrounding parks and open spaces in Dhaka, Bangladesh. Methodology: it have applied participant observation, semi-structured questionnaire-based interviews, and focus group discussions to collect social data. Interviews were conducted with the urban agriculture practitioners who are slum dwellers who carry out their urban agriculture activities. Some of the interviews were conducted with non-government organisations (NGOs) and local and state government officials, using semi-structured interviews. Using these methods developed a clearer understanding of how green space cultivation, local economic self-reliance, and urban gardening are producing distinctive urban ecologies in Dhaka and their policy-implications on urban sustainability. Major findings of the study: The research provided an in-depth knowledge on the challenges that slum dwellers encounter in establishing and maintaining urban gardens, such as the economic development of the city, conflicting political agendas, and environmental constraints in areas within which gardening activities take place. The research investigated (i) How do slum dwellers perform gardening practices from rural areas to open spaces in the city? (ii) How do men and women’s ethno-botanical knowledge contribute to urban biodiversity; (iii) And how do slum dwellers navigate complex constellations of land use policy, competing political agendas, and conflicting land and water tenures to meet livelihood functions provided by their gardens. Concluding statement: Lack of infrastructure facilities such as water supply and sanitation, micro-drains and waste disposal areas, and poor access to basic health care services increase the misery of people in the slum areas. Lack of environmental health awareness information for farmers, such as the risks from the use of chemical pesticides in gardens and from grazing animals in contaminated fields or cropping and planting trees or vegetable in contaminated dumping grounds, can all cause high health risk to humans and their environment.

Keywords: gender, urban agriculture, ecosystem health, urban slum systems

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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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