Search results for: fuzzy mathematics

Authors: Takuro Kida, Yuichi Kida

Abstract:

In this paper, it is shown a base of the new trend of algorithm mathematically that treats a historical reason of continuous discrimination in the world as well as its solution by introducing new concepts of parallel world that includes an invisible set of errors as its companion. With respect to a matrix operator-filter bank that the matrix operator-analysis-filter bank H and the matrix operator-sampling-filter bank S are given, firstly, we introduce the detail algorithm to derive the optimum matrix operator-synthesis-filter bank Z that minimizes all the worst-case measures of the matrix operator-error-signals E(ω) = F(ω) − Y(ω) between the matrix operator-input-signals F(ω) and the matrix operator-output-signals Y(ω) of the matrix operator-filter bank at the same time. Further, feedback is introduced to the above approximation theory, and it is indicated that introducing conversations with feedback do not superior automatically to the accumulation of existing knowledge of signal prediction. Secondly, the concept of category in the field of mathematics is applied to the above optimum signal approximation and is indicated that the category-based approximation theory is applied to the set-theoretic consideration of the recognition of humans. Based on this discussion, it is shown naturally why the narrow perception that tends to create isolation shows an apparent advantage in the short term and, often, why such narrow thinking becomes intimate with discriminatory action in a human group. Throughout these considerations, it is presented that, in order to abolish easy and intimate discriminatory behavior, it is important to create a parallel world of conception where we share the set of invisible error signals, including the words and the consciousness of both worlds.

Keywords: matrix filterbank, optimum signal approximation, category theory, simultaneous minimization

Procedia PDF Downloads 145

Authors: Yeşim Özer Özkan, Fatma Büşra Fincan

Abstract:

Biased sample is a regression of an observation, design process and all of the specifications lead to tendency of a side or the situation of leaving from the objectivity. It is expected that, test items are answered by the students who come from different social groups and the same ability not to be different from each other. The importance of the expectation increases especially during student selection and placement examinations. For example, all of the test items should not be beneficial for just a male or female group. The aim of the research is an investigation of item bias whether or not the exam included in 2014 free boarding and scholarship examination in terms of gender variable. Data which belong to 5th, 6th, and 7th grade the secondary education students were obtained by the General Directorate of Measurement, Evaluation and Examination Services in Turkey. 20% students were selected randomly within 192090 students. Based on 38418 students’ exam paper were examined for determination item bias. Winsteps 3.8.1 package program was used to determine bias in analysis of data, according to Rasch Model in respect to gender variable. Mathematics items tests were examined in terms of gender bias. Firstly, confirmatory factor analysis was applied twenty-five math questions. After that, NFI, TLI, CFI, IFI, RFI, GFI, RMSEA, and SRMR were examined in order to be validity and values of goodness of fit. Modification index values of confirmatory factor analysis were examined and then some of the items were omitted because these items gave an error in terms of model conformity and conceptual. The analysis shows that in 2014 free boarding and scholarship examination exam does not include bias. This is an indication of the gender of the examination to be made in favor of or against different groups of students.

Keywords: gender, item bias, placement test, Rasch model

Procedia PDF Downloads 231

Authors: Danielle Schneider, Ying Xie

Abstract:

Middle school science, technology, engineering, and math (STEM) teachers experience an exceptional challenge in the expectation to incorporate curricula that builds strong spatial reasoning skills on rudimentary geometry concepts. Because spatial ability is so closely tied to STEM students’ success, researchers are tasked to determine effective instructional practices that create an authentic learning environment within the immersive virtual reality learning environment (IVRLE). This study looked to investigate the effect of the IVRLE on middle school STEM students’ spatial reasoning skills as a methodology to benefit the STEM middle school students’ spatial reasoning skills. This experimental study was comprised of thirty 7th-grade STEM students divided into a treatment group that was engaged in an immersive VR platform where they engaged in building an object in the virtual realm by applying spatial processing and visualizing its dimensions and a control group that built the identical object using a desktop computer-based, computer-aided design (CAD) program. Before and after the students participated in the respective “3D modeling” environment, their spatial reasoning abilities were assessed using the Middle Grades Mathematics Project Spatial Visualization Test (MGMP-SVT). Additionally, both groups created a physical 3D model as a secondary measure to measure the effectiveness of the IVRLE. The results of a one-way ANOVA in this study identified a negative effect on those in the IVRLE. These findings suggest that with middle school students, virtual reality (VR) proved an inadequate tool to benefit spatial relation skills as compared to desktop-based CAD.

Keywords: virtual reality, spatial reasoning, CAD, middle school STEM

Procedia PDF Downloads 86

Authors: Kizito Ugochukwu Nwajeri

Abstract:

This paper explores the application of hybrid block methods for solving boundary value problems (BVPs), which are prevalent in various fields such as science, engineering, and applied mathematics. Traditionally, numerical approaches such as finite difference and shooting methods, often encounter challenges related to stability and convergence, particularly in the context of complex and nonlinear BVPs. To address these challenges, we propose a hybrid block method that integrates features from both single-step and multi-step techniques. This method allows for the simultaneous computation of multiple solution points while maintaining high accuracy. Specifically, we employ a combination of polynomial interpolation and collocation strategies to derive a system of equations that captures the behavior of the solution across the entire domain. By directly incorporating boundary conditions into the formulation, we enhance the stability and convergence properties of the numerical solution. Furthermore, we introduce an adaptive step-size mechanism to optimize performance based on the local behavior of the solution. This adjustment allows the method to respond effectively to variations in solution behavior, improving both accuracy and computational efficiency. Numerical tests on a variety of boundary value problems demonstrate the effectiveness of the hybrid block methods. These tests showcase significant improvements in accuracy and computational efficiency compared to conventional methods, indicating that our approach is robust and versatile. The results suggest that this hybrid block method is suitable for a wide range of applications in real-world problems, offering a promising alternative to existing numerical techniques.

Keywords: hybrid block methods, boundary value problem, polynomial interpolation, adaptive step-size control, collocation methods

Procedia PDF Downloads 36

Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

Abstract:

Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

Procedia PDF Downloads 499

Authors: R. M. Kashim

Abstract:

The study investigated primary school teachers’ conceptual and procedural knowledge of rational numbers and its effects on pupil’s achievement in rational numbers. Specifically, primary school teachers’ level of conceptual knowledge about rational numbers, primary school teachers’ level of procedural knowledge about rational numbers, and the effects of teachers conceptual and procedural knowledge on their pupils understanding of rational numbers in primary schools is investigated. The study was carried out in Bauchi metropolis in the Bauchi state of Nigeria. The design of the study was a multi-stage design. The first stage was a descriptive design. The second stage involves a pre-test, post-test only quasi-experimental design. Two instruments were used for the data collection in the study. These were Conceptual and Procedural knowledge test (CPKT) and Rational number achievement test (RAT), the population of the study comprises of three (3) mathematics teachers’ holders of Nigerian Certificate in Education (NCE) teaching primary six and 210 pupils in their intact classes were used for the study. The data collected were analyzed using mean, standard deviation, analysis of variance, analysis of covariance and t- test. The findings indicated that the pupils taught rational number by a teacher that has high conceptual and procedural knowledge understand and perform better than the pupil taught by a teacher who has low conceptual and procedural knowledge of rational number. It is, therefore, recommended that teachers in primary schools should be encouraged to enrich their conceptual knowledge of rational numbers. Also, the superiority performance of teachers in procedural knowledge in rational number should not become an obstruction of understanding. Teachers Conceptual and procedural knowledge of rational numbers should be balanced so that primary school pupils will have a view of better teaching and learning of rational number in our contemporary schools.

Keywords: conceptual, procedural knowledge, rational number, pupils

Procedia PDF Downloads 453

Authors: Sameer Jung Karki, Gokhan Saygili

Abstract:

The allowable bearing capacity of foundation systems is determined by applying a factor of safety to the ultimate bearing capacity. Conventional ultimate bearing capacity calculations routines are based on deterministic input parameters where the nonuniformity and inhomogeneity of soil and site properties are not accounted for. Hence, the laws of mathematics like probability calculus and statistical analysis cannot be directly applied to foundation engineering. It’s assumed that the Factor of Safety, typically as high as 3.0, incorporates the uncertainty of the input parameters. This factor of safety is estimated based on subjective judgement rather than objective facts. It is an ambiguous term. Hence, a probabilistic analysis of the bearing capacity of an isolated footing on a clayey soil is carried out by using the Monte Carlo Simulation method. This simulated model was compared with the traditional discrete model. It was found out that the bearing capacity of soil was found higher for the simulated model compared with the discrete model. This was verified by doing the sensitivity analysis. As the number of simulations was increased, there was a significant % increase of the bearing capacity compared with discrete bearing capacity. The bearing capacity values obtained by simulation was found to follow a normal distribution. While using the traditional value of Factor of safety 3, the allowable bearing capacity had lower probability (0.03717) of occurring in the field compared to a higher probability (0.15866), while using the simulation derived factor of safety of 1.5. This means the traditional factor of safety is giving us bearing capacity that is less likely occurring/available in the field. This shows the subjective nature of factor of safety, and hence probability method is suggested to address the variability of the input parameters in bearing capacity equations.

Keywords: bearing capacity, factor of safety, isolated footing, montecarlo simulation

Procedia PDF Downloads 187

Authors: Mei-Chun. Chang

Abstract:

STEAM (Science, Technology, Engineering, Art, and Mathematics) represents a cross-disciplinary and learner-centered teaching model that cultivates students to link theory with the presentation of real situations, thereby improving their various abilities. This study explores students' learning performance after using the 6E model in STEAM teaching for a professional course in the digital media design department of technical colleges, as well as the difficulties and countermeasures faced by STEAM curriculum design and its implementation. In this study, through industry experts’ work experience, activity exchanges, course teaching, and experience, learners can think about the design and development value of virtual idol products that meet the needs of users and to employ AR/VR technology to innovate their product applications. Applying action research, the investigation has 35 junior students from the department of digital media design of the school where the researcher teaches as the research subjects. The teaching research was conducted over two stages spanning ten weeks and 30 sessions. This research collected the data and conducted quantitative and qualitative data sorting analyses through ‘design draft sheet’, ‘student interview record’, ‘STEAM Product Semantic Scale’, and ‘Creative Product Semantic Scale (CPSS)’. Research conclusions are presented, and relevant suggestions are proposed as a reference for teachers or follow-up researchers. The contribution of this study is to teach college students to develop original virtual idols and product designs, improve learning effectiveness through STEAM teaching activities, and effectively cultivate innovative and practical cross-disciplinary design talents.

Keywords: STEAM, 6E model, virtual idol, learning effectiveness, practical courses

Procedia PDF Downloads 127

Authors: Wann-Ming Wey

Abstract:

In recent years, in addition to face the external threats such as energy shortages and climate change, traffic congestion and environmental pollution have become anxious problems for many cities. Considering private automobile-oriented urban development had produced many negative environmental and social impacts, the transit-oriented development (TOD) has been considered as a sustainable urban model. TOD encourages public transport combined with friendly walking and cycling environment designs, however, non-motorized modes help improving human health, energy saving, and reducing carbon emissions. Due to environmental changes often affect the planners’ decision-making; this research applies dynamic network process (DNP) which includes the time dependent concept to promoting friendly walking and cycling environmental designs as an advanced planning support system for environment improvements. This research aims to discuss what kinds of design strategies can improve a friendly walking and cycling environment under TOD. First of all, we collate and analyze environment designing factors by reviewing the relevant literatures as well as divide into three aspects of “safety”, “convenience”, and “amenity” from fifteen environment designing factors. Furthermore, we utilize fuzzy Delphi Technique (FDT) expert questionnaire to filter out the more important designing criteria for the study case. Finally, we utilized DNP expert questionnaire to obtain the weights changes at different time points for each design criterion. Based on the changing trends of each criterion weight, we are able to develop appropriate designing strategies as the reference for planners to allocate resources in a dynamic environment. In order to illustrate the approach we propose in this research, Taipei city as one example has been used as an empirical study, and the results are in depth analyzed to explain the application of our proposed approach.

Keywords: environment planning support systems, walking and cycling, transit-oriented development (TOD), dynamic network process (DNP)

Procedia PDF Downloads 345

Authors: Yu Chen, Xiaoguang Yang, Lin Lin

Abstract:

Traffic engineering construction is an important infrastructure for economic and social development. In the process of construction and operation, the ability to make a correct evaluation of the project's environmental impact appears to be crucial to the rational operation of existing transportation projects, the correct development of transportation engineering construction and the adoption of corresponding measures to scientifically carry out environmental protection work. Most of the existing research work on ecological and environmental impact assessment is limited to individual aspects of the environment and less to the overall evaluation of the environmental system; in terms of research conclusions, there are more qualitative analyses from the technical and policy levels, and there is a lack of quantitative research results and quantitative and operable evaluation models. In this paper, a comprehensive analysis of the ecological and environmental impacts of transportation construction projects is conducted, and factors such as the accessibility of data and the reliability of calculation results are comprehensively considered to extract indicators that can reflect the essence and characteristics. The qualitative evaluation indicators were screened using the expert review method, the qualitative indicators were measured using the fuzzy statistics method, the quantitative indicators were screened using the principal component analysis method, and the quantitative indicators were measured by both literature search and calculation. An environmental impact evaluation index system with the general objective layer, sub-objective layer and indicator layer was established, dividing the environmental impact of the transportation construction project into two periods: the construction period and the operation period. On the basis of the evaluation index system, the index weights are determined using the hierarchical analysis method, and the individual indicators to be evaluated are dimensionless, eliminating the influence of the original background and meaning of the indicators. Finally, the thesis uses the above research results, combined with the actual engineering practice, to verify the correctness and operability of the evaluation method.

Keywords: transportation construction projects, ecological and environmental impact, analysis and evaluation, indicator evaluation system

Procedia PDF Downloads 108

Authors: Takuro Kida, Yuichi Kida

Abstract:

We show a base of the new trend of algorithm mathematically that treats a historical reason of continuous discrimination in the world as well as its solution by introducing new concepts of parallel world that includes an invisible set of errors as its companion. With respect to a matrix operator-filter bank that the matrix operator-analysis-filter bank H and the matrix operator-sampling-filter bank S are given, firstly, we introduce the detailed algorithm to derive the optimum matrix operator-synthesis-filter bank Z that minimizes all the worst-case measures of the matrix operator-error-signals E(ω) = F(ω) − Y(ω) between the matrix operator-input-signals F(ω) and the matrix operator-output signals Y(ω) of the matrix operator-filter bank at the same time. Further, feedback is introduced to the above approximation theory and it is indicated that introducing conversations with feedback does not superior automatically to the accumulation of existing knowledge of signal prediction. Secondly, the concept of category in the field of mathematics is applied to the above optimum signal approximation and is indicated that the category-based approximation theory is applied to the set-theoretic consideration of the recognition of humans. Based on this discussion, it is shown naturally why the narrow perception that tends to create isolation shows an apparent advantage in the short term and, often, why such narrow thinking becomes intimate with discriminatory action in a human group. Throughout these considerations, it is presented that, in order to abolish easy and intimate discriminatory behavior, it is important to create a parallel world of conception where we share the set of invisible error signals, including the words and the consciousness of both worlds.

Keywords: signal prediction, pseudo inverse matrix, artificial intelligence, conditional optimization

Procedia PDF Downloads 158

Authors: Foster Chilufya

Abstract:

This study sought to determine factors that affect academic performance of mature age students in Science Education at University of Zambia. It was guided by Maslow’s Hierarchy of Needs. The theory provided relationship between achievement motivation and academic performance. A descriptive research design was used. Both Qualitative and Quantitative research methods were used to collect data from 88 respondents. Simple random and purposive sampling procedures were used to collect from the respondents. Concerning factors that motivate mature-age students to choose Science Education Programs, the following were cited: need for self-actualization, acquisition of new knowledge, encouragement from friends and family members, good performance at high school and diploma level, love for the sciences, prestige and desire to be promoted at places of work. As regards factors that affected the academic performance of mature-age students, both negative and positive factors were identified. These included: demographic factors such as age and gender, psychological characteristics such as motivation and preparedness to learn, self-set goals, self esteem, ability, confidence and persistence, student prior academic performance at high school and college level, social factors, institutional factors and the outcomes of the learning process. In order to address the factors that negatively affect academic performance of mature-age students, the following measures were identified: encouraging group discussions, encouraging interactive learning process, providing a conducive learning environment, reviewing Science Education curriculum and providing adequate learning materials. Based on these factors, it is recommended that, the School of Education introduces a program in Science Education specifically for students training to be teachers of science. Additionally, introduce majors in Physics Education, Biology Education, Chemistry Education and Mathematics Education relevant to what is taught in high schools.

Keywords: academic, performance, in-service, science

Procedia PDF Downloads 312

Authors: Saeid Haghjoo, Ebrahim Reyhani, Fahimeh Kolahdouz

Abstract:

The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.

Keywords: average rate of change, context problems, derivative, numerical representation, SOLO taxonomy

Procedia PDF Downloads 93

Authors: Nilda San Miguel, Elymar Pascual

Abstract:

The main focus of this study is exploring the effective approaches in teaching Mathematics that is being applied in public schools, s.y. 2018-2019. This research was written as connected output to the district-wide School Learning Action Cell (DISLAC) on Math teaching approaches which was recently conducted in Victoria, Laguna. Fifty-four math teachers coming from 17 schools in Victoria became the respondents of this study. Qualitative method of doing research was applied. Teachers’ responses to the following concerns were gathered, analyzed and interpreted: (1) evaluation of the recently conducted DISLAC, (2) status of the use of different approaches, (3) perception on the effective use of approaches, (4) preference of approach to explore in classroom sessions, (5) factors affecting the choice of approach, (6) difficulties encountered, (7) and perceived benefit to learners. Results showed that the conduct of DISLAC was very highly satisfactory (mean 4.41). Teachers looked at collaborative approach as very highly effective (mean 4.74). Fifty-two percent of the teachers is using collaborative approach, 17% constructivist, 11% integrative, 11% inquiry-based, and 9% reflective. Reflective approach was chosen to be explored by most of the respondents (29%) in future sessions. The difficulties encountered by teachers in using the different approaches are: (1) learners’ difficulty in following instructions, (2) lack of focus, (3) lack of willingness and cooperation, (4) teachers’ lack of mastery in using different approaches, and (5) lack of time of doing visual aids because of time mismanagement. Teachers deemed the use of various teaching approaches can help the learners to have (1) mastery of competency, (2) increased communication, (3) improved confidence, (4) facility in comprehension, and (5) better academic output. The result obtained from this study can be used as an input for SLACs. Recommendations at the end of the study were given to school/district heads and future researchers.

Keywords: approaches, collaborative, constructivism, inquiry-based, integrative, reflective

Procedia PDF Downloads 283

Authors: Narupot Putwattana

Abstract:

Changes in global situation such as environmental and economic crisis brought the new perspective for science education called integrative biology. STEM has been increasingly mentioned for several educational researches as the approach which combines the concept in Science (S), Technology (T), Engineering (E) and Mathematics (M) to apply in teaching and learning process so as to strengthen the 21st-century skills such as creativity and critical thinking. Recent studies demonstrated STEM as the pedagogy which described the engineering process along with the science classroom activities. So far, pedagogical contents for STEM explaining the content in biology have been scarce. A qualitative literature review was conducted so as to gather the articles based on electronic databases (google scholar). STEM education, engineering design, teaching and learning of biology were used as main keywords to find out researches involving with the application of STEM in biology teaching and learning process. All articles were analyzed to obtain appropriate teaching and learning model that unify the core concept of biology. The synthesized model comprised of engineering design, inquiry-based learning, biological prototype and biologically-inspired design (BID). STEM content and context integration were used as the theoretical framework to create the integrative biology instructional model for STEM education. Several disciplines contents such as biology, engineering, and technology were regarded for inquiry-based learning to build biological prototype. Direct and indirect integrations were used to provide the knowledge into the biology related STEM strategy. Meanwhile, engineering design and BID showed the occupational context for engineer and biologist. Technological and mathematical aspects were required to be inspected in terms of co-teaching method. Lastly, other variables such as critical thinking and problem-solving skills should be more considered in the further researches.

Keywords: biomimicry, engineering approach, STEM education, teaching and learning model

Procedia PDF Downloads 257

Authors: Kara Rosenblatt, Kevin Badgett, James Eldridge

Abstract:

There is a preponderance of information regarding the overall effectiveness of charter schools and their ability to increase academic achievement compared to traditional district schools. Most research on the topic is focused on comparing long and short-term outcomes, academic achievement in mathematics and reading, and locale (i.e., urban, v. Rural). While the lingering unanswered questions regarding effectiveness continue to loom for school leaders, data on charter schools suggests that enrollment increases by 10% annually and that charter schools educate more than 2 million U.S. students across 40 states each year. Given the increasing share of U.S. students educated in charter schools, it is important to better understand possible differences in student achievement defined in multiple ways for students in charter schools and for those in Independent School District (ISD) settings in the state of Texas. Data were retrieved from the Texas Education Agency’s (TEA) repository that includes data organized annually and available on the TEA website. Specific data points and definitions of achievement were based on characterizations of achievement found in the relevant literature. Specific data points include but were not limited to graduation rate, student performance on standardized testing, and teacher-related factors such as experience and longevity in the district. Initial findings indicate some similarities with the current literature on long-term student achievement in English/Language Arts; however, the findings differ substantially from other recent research related to long-term student achievement in social studies. There are a number of interesting findings also related to differences between achievement for students in charters and ISDs and within different types of charter schools in Texas. In addition to findings, implications for leadership in different settings will be explored.

Keywords: charter schools, ISDs, student achievement, implications for PK-12 school leadership

Procedia PDF Downloads 129

Authors: Xiaobin Liang, Wei Liang, Laibin Zhang, Xiaoyan Guo

Abstract:

Pipelines pass through coal mined gobs inevitably in the mining area, the stability of which has great influence on the safety of pipelines. After extensive literature study and field research, it was found that there are a few risk assessment methods for coal mined gob pipelines, and there is a lack of data on the gob sites. Therefore, the fuzzy comprehensive evaluation method is widely used based on expert opinions. However, the subjective opinions or lack of experience of individual experts may lead to inaccurate evaluation results. Hence the accuracy of the results needs to be further improved. This paper presents a comprehensive approach to achieve this purpose by combining bow-tie model and cloud inference. The specific evaluation process is as follows: First, a bow-tie model composed of a fault tree and an event tree is established to graphically illustrate the probability and consequence indicators of pipeline failure. Second, the interval estimation method can be scored in the form of intervals to improve the accuracy of the results, and the censored mean algorithm is used to remove the maximum and minimum values of the score to improve the stability of the results. The golden section method is used to determine the weight of the indicators and reduce the subjectivity of index weights. Third, the failure probability and failure consequence scores of the pipeline are converted into three numerical features by using cloud inference. The cloud inference can better describe the ambiguity and volatility of the results which can better describe the volatility of the risk level. Finally, the cloud drop graphs of failure probability and failure consequences can be expressed, which intuitively and accurately illustrate the ambiguity and randomness of the results. A case study of a coal mine gob pipeline carrying natural gas has been investigated to validate the utility of the proposed method. The evaluation results of this case show that the probability of failure of the pipeline is very low, the consequences of failure are more serious, which is consistent with the reality.

Keywords: bow-tie model, natural gas pipeline, coal mine gob, cloud inference

Procedia PDF Downloads 251

Authors: Caiwei Zhu, Remke Klapwijk

Abstract:

Spatial thinking, a way of thinking based on the understanding and reasoning of spatial concepts and representations, is embedded in science, technology, engineering, arts, and mathematics (STEAM) learning. Aside from many studies that successfully used targeted training to improve students’ spatial thinking skills, few have closely examined how spatial thinking can be trained in classroom settings. Design and technology education, which receives increasing attention towards its integration into formal curriculums, inherently encompasses a wide range of spatial activities, such as constructing mental representations of design ideas, mentally transforming objects and materials to form designs, visually communicating design plans through annotated drawings, and creating 2D and 3D design artifacts. Among different design topics, biomimicry offers a unique avenue for students to recognize and analyze the shapes and structures in nature. By mapping the forms of plants and animals onto functions, students gain inspiration to solve human design challenges. This study is one of the first to highlight opportunities for training spatial thinking in a biomimicry design project for primary school students. Embracing methodological principles of educational design-based research, this case study is conducted along with iterations in the design of the intervention and collaboration with teachers. Data are harvested from small groups of 10- to 12-year-olds at an international school in the Netherlands. Classroom videos, semi-structured interviews with students, design drawings and artifacts, formative assessment, and the pre- and post-intervention spatial test triangulate evidence for students' spatial thinking. In addition to contributing to a theory of integrating spatial thinking in the primary curriculum, mechanisms underlying such improvement in spatial thinking are explored and discussed.

Keywords: biomimicry, design and technology education, primary education, spatial thinking

Procedia PDF Downloads 77

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

Abstract:

The role of images/illustrations in communicating meanings and triggering emotions assumes an increasingly relevant role in contemporary texts, regardless of the age group for which they are intended or the nature of the texts that host them. It is no coincidence that children's books are full of illustrations and that the image/text ratio decreases as the age group grows. The vast majority of children's books can be considered multimodal texts containing text and images/illustrations interacting with each other to provide the young reader with a broader and more creative understanding of the book's narrative. This interaction is very diverse, ranging from images/illustrations that are not essential for understanding the storytelling to those that contribute significantly to the meaning of the story. Usually, these books are also read by adults, namely by parents, educators, and teachers who act as mediators between the book and the children, explaining aspects that are or seem to be too complex for the child's context. It should be noted that there are books labeled as children's books that are clearly intended for both children and adults. In this work, following a qualitative and interpretative methodology based on written productions, participant observation, and field notes, we will describe the perceptions of future teachers of the 1st cycle of basic education, attending a master's degree at a Portuguese university, about the role of the image in literary and non-literary texts, namely in mathematical texts, and how these can constitute precious resources for emotional regulation and for the design of creative didactic situations. The analysis of the collected data allowed us to obtain evidence regarding the evolution of the participants' perception regarding the crucial role of images in children's literature, not only as an emotional regulator for young readers but also as a creative source for the design of meaningful didactical situations, crossing other scientific areas, other than the mother tongue, namely mathematics.

Keywords: children’s literature, emotions, multimodal texts, soft skills

Procedia PDF Downloads 94

Authors: Deniz Ünal Özpalamutcu, Burcu Altman

Abstract:

Actuaria uses mathematics, statistic and financial information when analyzing the financial impacts of uncertainties, risks, insurance and pension related issues. In other words, it deals with the likelihood of potential risks, their financial impacts and especially the financial measures. Handling these measures require some long-term payment and investments. So, it is obvious it is inevitable to plan the periodic payments with equal time intervals considering also the changing value of money over time. These series of payment made specific intervals of time is called annuity or rant. In literature, rants are classified based on start and end dates, start times, payments times, payments amount or frequency. Classification of rants based on payment amounts changes based on the constant, descending or ascending payment methods. The literature about handling the annuity is very limited. Yet in a daily life, especially in today’s world where the economic issues gained a prominence, it is very crucial to use the variable annuity method in line with the demands of the customers. In this study, the types of annuities with flexible payment are discussed. In other words, we focus on calculating payment amount of a period by adding a certain percentage of previous period payment was studied. While studying this problem, formulas were created considering both start and end period payments for cash value and accumulated. Also increase of each period payment by r interest rate each period payments calculated with previous periods increases. And the problem of annuities (rants) of which each period payment increased with previous periods’ increase by r interest rate has been analyzed. Cash value and accumulated value calculation of this problem were studied separately based on the period start/end and their relations were expressed by formulas.

Keywords: actuaria, annuity, flexible payment, rant

Procedia PDF Downloads 222

Authors: Sudhir Kumar Tewatia, Kanishck Tewatia, Anttriksh Tewatia

Abstract:

Advancements in soil consolidation are discussed, and further improvements are proposed with particular reference to Tewatia’s Y-Y’ Approach, which is called the Settlement versus Rate of Settlement Approach in consolidation. A branch of calculus named Y-Y' (or y versus dy/dx) is suggested (as compared to the common X-Y', x versus dy/dx, dy/dx versus x or Newton-Leibniz branch) that solves some complicated/unsolved theoretical and practical problems in physical sciences (Physics, Chemistry, Mathematics, Biology, and allied sciences) and engineering in an amazingly simple and short manner, particularly when independent variable X is unknown and X-Y' Approach can’t be used. Complicated theoretical and practical problems in 1D, 2D, 3D Primary and Secondary consolidations with non-uniform gradual loading and irregularly shaped clays are solved with elementary school level Y-Y' Approach, and it is interesting to note that in X-Y' Approach, equations become more difficult while we move from one to three dimensions, but in Y-Y' Approach even 2D/3D equations are very simple to derive, solve, and use; rather easier sometimes. This branch of calculus will have a far-reaching impact on understanding and solving the problems in different fields of physical sciences and engineering that were hitherto unsolved or difficult to be solved by normal calculus/numerical/computer methods. Some particular cases from soil consolidation that basically creeps and diffusion equations in isolation and in combination with each other are taken for comparison with heat transfer. The Y-Y’ Approach can similarly be applied in wave equations and other fields wherever normal calculus works or fails. Soil mechanics uses mathematical analogies from other fields of physical sciences and engineering to solve theoretical and practical problems; for example, consolidation theory is a replica of the heat equation from thermodynamics with the addition of the effective stress principle. An attempt is made to give them mathematical analogies.

Keywords: calculus, clay, consolidation, creep, diffusion, heat, settlement

Procedia PDF Downloads 96

Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

Abstract:

Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. In particular, the usual rules of associativity, commutativity and distributivity hold. Fields also appear in many other areas of mathematics; see the examples below. When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a commutative field or a rational domain. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a division ring ordivision algebra or sometimes a skew field. Also non-commutative field is still widely used. In French, fields are called corps (literally, body), generally regardless of their commutativity. When necessary, a (commutative) field is called corps commutative and a skew field-corps gauche. The German word for body is Körper and this word is used to denote fields; hence the use of the blackboard bold to denote a field. The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher. An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental. The aim of Galois Theory is the study of algebraic extensions of a field. Given a field k, various kinds of closures of k may be introduced. For example, the algebraic closure, the separable closure, the cyclic closure et cetera. The idea is always the same: If P is a property of fields, then a P-closure of k is a field K containing k, having property, and which is minimal in the sense that no proper subfield of K that contains k has property P. For example if we take P (K) to be the property ‘every non-constant polynomial f in K[t] has a root in K’, then a P-closure of k is just an algebraic closure of k. In general, if P-closures exist for some property P and field k, they are all isomorphic. However, there is in general no preferable isomorphism between two closures.

Keywords: field theory, mechanic maths, supertech, rolltech

Procedia PDF Downloads 375

Authors: Neslihan Sahin Celik, Ali Eraslan

Abstract:

Mathematical model and modeling are one of the topics that have been intensively discussed in recent years. In line with the results of the PISA studies, researchers in many countries have begun to question how much students in school-education system are prepared to solve the real-world problems they encounter in their future professional lives. As a result, many mathematics educators have begun to emphasize the importance of new skills and understanding such as constructing, Hypothesizing, Describing, manipulating, predicting, working together for complex and multifaceted problems for success in beyond the school. When students increasingly face this kind of situations in their daily life, it is important to make sure that students have enough experience to work together and interpret mathematical situations that enable them to think in different ways and share their ideas with their peers. Thus, model eliciting activities are one of main tools that help students to gain experiences and the new skills required. This research study was carried on the town center of a big city located in the Black Sea region in Turkey. The participants were eighth-grade students in a middle school. After a six-week preliminary study, three students in an eighth-grade classroom were selected using criterion sampling technique and placed in a focus group. The focus group of three students was videotaped as they worked on a model eliciting activity, the Summer Job Problem. The conversation of the group was transcribed, examined with students’ written work and then qualitatively analyzed through the lens of Blum’s (1996) modeling processing cycle. The study results showed that eighth grade students can successfully work with the model eliciting, develop a model based on the two parameters and review the whole process. On the other hand, they had difficulties to relate parameters to each other and take all parameters into account to establish the model.

Keywords: middle school, modeling, mathematical modeling, summer job problem

Procedia PDF Downloads 338

Authors: Michael N. O'Sullivan, Con Sheahan

Abstract:

Mass customization is the idea of offering custom products or services to satisfy the needs of each individual customer while maintaining the efficiency of mass production. Technologies like 3D printing and artificial intelligence have many start-ups hoping to capitalize on this dream of creating personalized products at an affordable price, and well established companies scrambling to innovate and maintain their market share. However, the majority of them are failing as they struggle to understand one key question – where does customization make sense? Customization and personalization only make sense where the value of the perceived benefit outweighs the cost to implement it. In other words, will people pay for it? Looking at the Kano Model makes it clear that it depends on the product. In products where customization is an inherent need, like prosthetics, mass customization technologies can be highly beneficial. However, for products that already sell as a standard, like headphones, offering customization is likely only an added bonus, and so the product development team must figure out if the customers’ perception of the added value of this feature will outweigh its premium price tag. This can be done through the use of a ‘serious game,’ whereby potential customers are given a limited budget to collaboratively buy and bid on potential features of the product before it is developed. If the group choose to buy customization over other features, then the product development team should implement it into their design. If not, the team should prioritize the features on which the customers have spent their budget. The level of customization purchased can also be translated to an appropriate production method, for example, the most expensive type of customization would likely be free-form design and could be achieved through digital fabrication, while a lower level could be achieved through short batch production. Twenty-five teams of final year students from design, engineering, construction and technology tested this methodology when bringing a product from concept through to production specification, and found that it allowed them to confidently decide what level of customization, if any, would be worth offering for their product, and what would be the best method of producing it. They also found that the discussion and negotiations between players during the game led to invaluable insights, and often decided to play a second game where they offered customers the option to buy the various customization ideas that had been discussed during the first game.

Keywords: Kano model, mass customization, new product development, serious game

Procedia PDF Downloads 136

Authors: Jeff Chak-Fu Wong, Tony Chun Yin Yip

Abstract:

The transition from secondary school to university seems exciting for many first-year students but can be more challenging than expected. Enabling instructors to know students’ learning habits and styles enhances their understanding of the students’ learning backgrounds, allows teachers to provide better support for their students, and has therefore high potential to improve teaching quality and learning, especially in any mathematics-related courses. The aim of this research is to collect students’ data using online surveys, to analyze students’ factors using learning analytics and educational data mining and to discover the characteristics of the students at risk of falling behind in their studies based on students’ previous academic backgrounds and collected data. In this paper, we use correlation-based distance methods and mutual information for measuring student factor relationships. We then develop a factor network using the Minimum Spanning Tree method and consider further study for analyzing the topological properties of these networks using social network analysis tools. Under the framework of mutual information, two graph-based feature filtering methods, i.e., unsupervised and supervised infinite feature selection algorithms, are used to analyze the results for students’ data to rank and select the appropriate subsets of features and yield effective results in identifying the factors affecting students at risk of failing. This discovered knowledge may help students as well as instructors enhance educational quality by finding out possible under-performers at the beginning of the first semester and applying more special attention to them in order to help in their learning process and improve their learning outcomes.

Keywords: students' academic performance, correlation-based distance method, social network analysis, feature selection, graph-based feature filtering method

Procedia PDF Downloads 131

Authors: Pontus Backstrom

Abstract:

In the educational literature on peer effects, attention has been brought to the fact that the mechanisms creating peer effects are still to a large extent hidden in obscurity. The hypothesis in this study is that the Frame Factor Theory can be used to explain these mechanisms. At heart of the theory is the concept of “time needed” for students to learn a certain curricula unit. The relations between class-aggregated time needed and the actual time available, steers and hinders the actions possible for the teacher. Further, the theory predicts that the timing and pacing of the teachers’ instruction is governed by a “criterion steering group” (CSG), namely the pupils in the 10th-25th percentile of the aptitude distribution in class. The class composition hereby set the possibilities and limitations for instruction, creating peer effects on individual outcomes. To test if the theory can be applied to the issue of peer effects, the study employs multilevel structural equation modelling (M-SEM) on Swedish TIMSS 2015-data (Trends in International Mathematics and Science Study; students N=4090, teachers N=200). Using confirmatory factor analysis (CFA) in the SEM-framework in MPLUS, latent variables are specified according to the theory, such as “limitations of instruction” from TIMSS survey items. The results indicate a good model fit to data of the measurement model. Research is still in progress, but preliminary results from initial M-SEM-models verify a strong relation between the mean level of the CSG and the latent variable of limitations on instruction, a variable which in turn have a great impact on individual students’ test results. Further analysis is required, but so far the analysis indicates a confirmation of the predictions derived from the frame factor theory and reveals that one of the important mechanisms creating peer effects in student outcomes is the effect the class composition has upon the teachers’ instruction in class.

Keywords: compositional effects, frame factor theory, peer effects, structural equation modelling

Procedia PDF Downloads 135

Authors: Abdullah Al Farwan, Ya Zhang

Abstract:

In today’s educational arena, it is critical to understand educational data and be able to evaluate important aspects, particularly data on student achievement. Educational Data Mining (EDM) is a research area that focusing on uncovering patterns and information in data from educational institutions. Teachers, if they are able to predict their students' class performance, can use this information to improve their teaching abilities. It has evolved into valuable knowledge that can be used for a wide range of objectives; for example, a strategic plan can be used to generate high-quality education. Based on previous data, this paper recommends employing data mining techniques to forecast students' final grades. In this study, five data mining methods, Decision Tree, JRip, Naive Bayes, Multi-layer Perceptron, and Random Forest with wrapper feature selection, were used on two datasets relating to Portuguese language and mathematics classes lessons. The results showed the effectiveness of using data mining learning methodologies in predicting student academic success. The classification accuracy achieved with selected algorithms lies in the range of 80-94%. Among all the selected classification algorithms, the lowest accuracy is achieved by the Multi-layer Perceptron algorithm, which is close to 70.45%, and the highest accuracy is achieved by the Random Forest algorithm, which is close to 94.10%. This proposed work can assist educational administrators to identify poor performing students at an early stage and perhaps implement motivational interventions to improve their academic success and prevent educational dropout.

Keywords: classification algorithms, decision tree, feature selection, multi-layer perceptron, Naïve Bayes, random forest, students’ academic performance

Procedia PDF Downloads 169

Authors: Atnafu Ashenef Wondim

Abstract:

In today’s highly competitive business environment, employees are considered a source of competitive advantage. Researchers have looked into job autonomy's effect on organizational commitment and declared superior organizational performance strongly depends on the effort and commitment of employees. The purpose of this study was to explore the relationship between job autonomy and organizational commitment from newcomer’s point of view. The mediation role of employee engagement (physical, emotional, and cognitive) was also examined in the case of Ethiopian Commercial Banks. An exploratory survey research design with mixed-method approach that included partial least squares structural equation modeling and Fuzzy-Set Qualitative Comparative Analysis technique were using to address the sample size of 348 new employees. In-depth interviews with purposive and convenientsampling techniques are conducted with new employees (n=43). The results confirmed that job autonomy had positive, significant direct effects on physical engagement, emotional engagement, and cognitive engagement (path coeffs. = 0.874, 0.931, and 0.893).The results showed thatthe employee engagement driver, physical engagement, had a positive significant influence on affective commitment (path coeff. = 0.187) and normative commitment (path coeff. = 0.512) but no significant effect on continuance commitment. Employee engagement partially mediates the relationship between job autonomy and organizational commitment, which means supporting the indirect effects of job autonomy on affective, continuance, and normative commitment through physical engagement. The findings of this study add new perspectives by positioning it within a complex organizational African setting and by expanding the job autonomy and organizational commitment literature, which will benefit future research. Much of the literature on job autonomy and organizational commitment has been conducted within a well-established organizational business context in Western developed countries.The findings lead to fresh information on job autonomy and organizational commitment implementation enablers that can assist in the formulation of a better policy/strategy to efficiently adopt job autonomy and organizational commitment.

Keywords: employee engagement, job autonomy, organizational commitment, social exchange theory

Procedia PDF Downloads 33

Authors: Neslihan Şahin Çelik, Ali Eraslan

Abstract:

In recent years, mathematics educators have frequently stressed the necessity of instructing students about models and modeling approaches that encompass cognitive and metacognitive thought processes, starting from the first years of school and continuing on through the years of higher education. The purpose of this study is to examine the thought processes of 4th-grade primary school students in their modeling activities and to explore the difficulties encountered in these processes, if any. The study, of qualitative design, was conducted in the 2015-2016 academic year at a public state-school located in a central city in the Black Sea Region of Turkey. A preliminary study was first implemented with designated 4th grade students, after which the criterion sampling method was used to select three students that would be recruited into the focus group. The focus group that was thus formed was asked to work on the model eliciting activity of the Paper Airplane Problem and the entire process was recorded on video. The Paper Airplane Problem required the students to determine the winner with respect to: (a) the plane that stays in the air for the longest time; (b) the plane that travels the greatest distance in a straight-line path; and (c) the overall winner for the contest. A written transcript was made of the video recording, after which the recording and the students' worksheets were analyzed using the Blum and Ferri modeling cycle. The results of the study revealed that the students tested the hypotheses related to daily life that they had set up, generated ideas of their own, verified their models by making connections with real life, and tried to make their models generalizable. On the other hand, the students had some difficulties in terms of their interpretation of the table of data and their ways of operating on the data during the modeling processes.

Keywords: primary school students, model eliciting activity, mathematical modeling, modeling process, paper airplane problem

Procedia PDF Downloads 360

Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

Abstract:

Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

Procedia PDF Downloads 109