Concept Of Fraction Research Articles

PENINGKATAN HASIL BELAJAR SISWA TENTANG KONSEP PECAHAN MELALUI PENERAPAN PENDEKATAN REALISTIC MATHEMATIC EDUCATION (RME) DALAM PEMBELAJARAN MATEMATIKA

Fractions are one of the most fundamental concepts in learning mathematics, so that fractions become a very important material in learning mathematics at the elementary school level. However, some students at Seroja Elementary School thought that fraction material was so difficult because they did not understand the concept of fractions well. This can be seen from the results of student learning which shows that the average grade obtained is still low. The method used is classroom action research conducted in three cycles. The research model applied is the model developed by Kemmis and MC Taggart which is generally carried out in four stages, namely (1) planning, (2) implementation, (3) observation, and (4) reflection. The research subjects in an effort to improve student learning outcomes through the application of the RME approach in learning were fourth grade students of Seroja State Elementary School, Serang City, Banten. The results of this study in classroom action research prove that the teacher's ability to apply the RME approach to learning mathematics about the concept of fractions increases and student learning outcomes increase. It can be concluded that there has been an increase in the teacher's ability to apply the RME approach to the concept of fractions in learning elementary mathematics. Furthermore, student learning outcomes regarding the concept of fractions have increased through the application of the RME approach in learning mathematics at SDN Seroja

Examination of pre-service teachers' perceptions of the concept of fraction using the word association test

In this study, it is aimed to examine the perceptions of the mathematics teacher candidates regarding the concept of fraction. 32 teacher candidates participated in the research carried out in the screening model. The word association test was used as a data collection tool and the obtained data were analyzed by content analysis method. According to the results of the analysis, it is seen that the perceptions of teacher candidates regarding the concept of fraction are mostly concentrated in the themes of meanings of fractions, operations in fractions, and representation of fractions. In addition, the themes of numbers, notation, and other mathematical topics in which it is used are other themes that emerged. It was seen that the teacher candidates expressed the quotient meaning at most, they did not mention the percent meaning. It was seen that they mostly expressed the addition operation in fractions and the type of compound fraction. As a result, it is seen that pre-service teachers' perceptions about the concept of fraction are limited. Pre-service teachers can be given a more comprehensive and relational education on the concept of fraction.

Hermeneutic-phenomenological study of the teaching practice of polyvalent teachers

Studies in Math Education have, in the last twenty years, presented substantial results regarding the teaching methodologies used in elementary education. Thus, considering the context of the training of pedagogue teachers who teach Mathematics, we seek with this paper to present a study carried out with a group of polyvalent teachers about their methodological understandings concerning the teaching of fractions. For that, we used the hermeneutic-phenomenological methodology for data analysis, considering the alectic process as an instrument of extraction and interpretation. As results obtained in this study, we highlight the cultural aspects that stress the methodological choice by the teacher, here named cultural crystallization, as well as the gap between the mathematical concept of fraction and the methodological choice for its teaching. In addition to the results obtained through the hermeneutic-phenomenological analysis, the present paper brings possibilities and limitations regarding its use in research in Math Education.

Robust Trajectory Tracking Control for Serial Robotic Manipulators Using Fractional Order-Based PTID Controller

The design of advanced robust control is crucial for serial robotic manipulators under various uncertainties and disturbances in case of the forceful performance needs of industrial robotic applications. Therefore, this work has proposed the design and implementation of a fractional order proportional tilt integral derivative (FOPTID) controller in joint space for a 3-DOF serial robotic manipulator. The proposed controller has been designed based on the fractional calculus concept to fulfill trajectory tracking with high accuracy and also reduce effects from disturbances and uncertainties. The parameters of the controller have been optimized with a GWO–PSO algorithm, which is a hybrid tuning method, by considering the time integral performance criterion. The superior and contribution of the GWO–PSO-based FOPTID controller has been demonstrated by comparing the results with those offered by PID, FOPID and PTID control strategies tuned by the GWO–PSO. The examination of the results showed that the proposed controller, which is based on the GWO–PSO algorithm, demonstrates better trajectory tracking performance and increased robustness against various trajectories, external disturbances, and joint frictions as compared to other controllers under the same operating conditions. In terms of the trajectory tracking performance for robustness, the superiority of the proposed controllers tuned by GWO–PSO has been confirmed by 20.2% to 44.5% reductions in the joint tracking errors. Moreover, for assessing the energy consumption of the tuned controllers, the total energy consumption of the proposed controller for all joints has been remarkably reduced by 2.45% as compared to others. Consequently, the results illustrated that the proposed controller is robust and stable and sustains against the continuous disturbance.

A unified method to simulate electrodeposition and galvanic corrosion using the peridynamic differential operator

This study presents a unified method to model electrodeposition and galvanic corrosion. The governing equations and boundary conditions are recast in their nonlocal form by using the peridynamic differential operator. Electric potential and mass transport equations are solved simultaneously in ANSYS through implicit algorithms for computational efficiency and complex geometry. Deposition and corrosion fronts are established by applying the concept of deposition fraction and examining the concentration values. Element matrices associated with peridynamic interactions are constructed through MATRIX27 elements native to ANSYS. The damping is modeled using combin14 element and the resulting equations are solved in an implicit fashion. Accuracy of this unified method is established by comparison with the published experimental measurements and simulations concerning simple and irregular geometries.

Assessing in vivo flexion-extension quality of motion after cervical disc arthroplasty: a pilot study.

The quality of flexion-extension motion after cervical disc arthroplasty has been a subject of interest due to the number of available devices with different designs and kinematics. Previous studies of motion quality have been limited to measuring the range of motion using two radiographs taken at the extremes of flexion and extension. This is the first study evaluating the in vivo quality of index segment motion using fluoroscopic images collected over the arc of flexion-extension after M6-C cervical disc arthroplasty surgery. Eligible participants had previously undergone a single-level cervical disc arthroplasty surgery for degenerative cervical spine disease performed by the senior author. Study participants underwent dynamic lateral fluoroscopic imaging to capture the C2-C7 motion between maximal flexion and extension. The amount of motion contribution by individual segments to the C2-C7 motion (termed segmental motion fraction) and its variation throughout the arc of flexion-extension were compared between the index and adjacent segments. The shift of centre of rotation during the arc of motion was also assessed. Ten subjects with a mean age of 43.8 years old were recruited, with an average follow-up of 16.2 months at the time of fluoroscopy. The C2-C7 cervical spine had an average flexion-extension range of 66.7 degrees. The contribution of the index segment averaged over the flexion-extension arc of motion was 18.9% (peak contribution 24.4%) for the C5-C6 group; and 15.5% (peak contribution 25.5%) for the C6-C7 group. The mean cranial-caudal location of the centre of rotation progressively shifted in the cranial direction from C2-C3 to C6-C7 motion segment. Our results demonstrated physiologic quality of motion at the index segment and harmony among its neighbouring segments following cervical disc arthroplasty, without gearshift-like intermittent locking of the prosthesis during the arc of flexion-extension motion. This pilot study provides a basis for the design of future long-term studies with larger sample size to compare the quality of motion between different cervical disc prostheses using the concept of segmental motion fraction as a motion-quality metric.

External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

AbstractIn this paper, the linear theory of elasticity for materials with a triple porosity (macro, meso and micro levels of porosities) structure based on the volume fraction concept is considered. The external boundary value problems (BVPs) of steady vibrations of this theory are investigated. Namely, the uniqueness theorem for classical solutions of these BVPs is established. Then, the basic properties of the surface (single‐layer and double‐layer) potentials are given. Finally, on the basis of the properties of potentials, the existence theorems for classical solutions of the above mentioned BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

Estimation of the degree of internal recirculation in Internal Combustion Engines

The concepts of residual gas and admission (or volumetric efficiency) coefficients are used exclusively by specialists in the field of piston Internal Combustion Engines. However, it is preferable to apply the concepts of volume fractions of components of the working mixture consisting of air, fuel, residual, and recirculating gases, for the evaluation of filling. This simplifies and makes it more easy-to-grasp the influence of individual factors on the results of gas exchange processes. The proposed approach makes it possible to take into account the impact on the engine indicators of the molecular weight of the fuel used and the degree of external recirculation, as well as to reduce the number of independent variables. At the same time, the displacement coefficient A proposed by the author characterizes a decrease in filling when an engine with external mixing is switched to a gaseous fuel with a lower molecular weight. A change in the valve timing made it possible to produce an effect on the composition of the working mixture and, thereby, the environmental characteristics of the engine. In the case of external recirculation, it becomes necessary to estimate the summary fraction of neutral combustion products in the working mixture, on which all engine operation depended. This "overall degree of recirculation" can also be determined using the proposed approach.

Critical Standard Normalized Rapid Suppression Hydraulic Index and Its Estimation

As a standard to by which characterize the ability of ships to ascend rapidly, the rapid suppression hydraulic index is the main indicator of the rapid regulatory effect and an important component of channel engineering research. This study reviewed the current determination methods and forms of expression of the rapid suppression hydraulic index and revealed that the existing comprehensive indices of unit energy have obvious disadvantages, such as critical standards not being unified. Based on the balance principle of a ship’s effective propulsion and navigation resistance, according to the unified idea of the critical rapid suppression index, the dimensionless expression of the critical standard normalized rapid suppression hydraulic index was derived. The concepts of flow velocity fraction, slope fraction and their combined rapid suppression index are proposed, and the assessment method of rapid forming and suppressing with the critical standard of 1 is provided. Using an example, we verified the feasibility and convenience of the application of the critical standard normalized rapid suppression hydraulic index in judging rapid formation reaches, navigation obstruction areas and the comparison of the ability of several ship types to ascend rapidly. Based on various ship slope flow rapid suppression indices tested by real ship tests and theoretical analysis through the dimensions, main influencing factors and regression analysis, we introduced the dimensionless power load ratio and established an empirical formula for estimating the flow velocity fraction and slope fraction by the main parameters of the ship type, which can provide a reference for determining the rapid suppression hydraulic index when lacking detailed ship type data. The application scope of the estimated formula is discussed. The methods and data for rapids regulation are provided, which is more convenient for rapids remediation projects, will reduces rapids hindering navigation and then will develop the shipping industry of mountainous rivers to promote the sustainable development of mountainous economic construction.

The Use of Fractional Card Media-Based Concept Attainment Models to Improve Understanding of Fractional Concepts

Purpose of the study: To find out the application of the Concept Attainment model with the help of fractional card media in increasing understanding of the concept of fractions in class II Ahmad Dahlan Elementary School. Methodology: The research was conducted at Ahmad Dahlan Elementary School in the even semester of 2018/2019. The research sample was 22 students. Research data obtained through student learning outcomes and observation sheets. Quantitative data were analyzed using descriptive statistics and Qualitative data were analyzed to determine the learning process using the Concept Attainment learning model based on fractional card media. Main Findings: The results of the study show that the application of the Concept Attainment model assisted by fractional card media can improve understanding of the concept of fractions. By observing the results of understanding the concept of fractions in the first cycle, namely 53.01%, it increased in cycle II to 77.12%. In cycle I the results of the written test evaluation with classical completeness of 63.15% increased in cycle II by 18.66% to 81.81%. Novelty/Originality of this study: The latest research in this research is to combine the concept learning learning model with fraction card media which is generally not widely used, especially for learning fractions in elementary school mathematics, the benefits for students in this action research will then make it easier for them to face more difficult learning levels in the next class and can become a new teaching idea for teachers to facilitate student understanding.

Ionic Liquid-Assisted Selective Extraction and Partitioning of Biomolecules from Macroalgae.

Macroalgae are a promising feedstock for several industries due to their large content of proteins and carbohydrates and the high biomass productivities. A novel extraction and fractionation concept based on ionic liquids (ILs) using Ulva lactuca as model organism is presented. Biomolecules are first extracted by means of IL-assisted mechanical shear, followed by two-phase partitioning or ultrafiltration in order to fractionate proteins and carbohydrates and to recover the IL. Ethyl methyl imidazolium dibutyl phosphate ([Emim][DBP]) is strongly selective to proteins, leading to extraction yields up to 80.4% for proteins and 30.7% for carbohydrates. The complete process, including extraction and ultrafiltration, allowed protein recovery of up to 64.6 and 15.4% of the carbohydrates in the retentate phase, while a maximum of 85.7% of the IL was recovered in the permeate phase. The native structure of the extracted proteins was preserved during extraction and fractionation as shown by gel electrophoresis. Selective extraction of proteins from macroalgae under non-denaturing conditions using ILs followed by the recovery of IL using ultrafiltration is for the first time reported. The proposed extraction-fractionation approach is simple and can be potentially applied for the biorefinery of macroalgae at the commercial scale.

PENGGUNAAN ALAT PERAGA BLOK PECAHAN UNTUK MENINGKATKAN KEMAMPUAN PEMAHAMAN KONSEP PECAHAN PADA PESERTA DIDIK KELAS III SD

This research is motivated by the low ability to understand the concept of fractions in third grade students in learning mathematics in elementary schools. The objectives of this study are (1) to find out the use of fractional block propsfor class III students (2) to determine the improvement of the ability to understand fractions concepts using fractional block propsin class III students. This research method is a quantitative research method with a research design using a pre experimental design (non design) in the form of one group pretest-posttest. This research was conducted at SDN Jati 03, Baleendah District, Bandung Regency, with a population of 62 students and a sample of 35 students. Data collection techniques used observation and tests in the implementation of learning the ability to understand the concept of fractions by using fractional block props. The results showed that (1) the use of fractional block propsin class III can help students be more active in learning and can help the ability to understand fractions concepts so that the ability to understand fractions concepts increases after being given treatment with the use of fractional block props. (2) There is an increase in the ability to understand the concept of fractions in third grade elementary school students after the use of fractional block props can be seen from the results of the average pre-test and post-test in the experimental class, namely 65.74 and 84.80

ANALISIS KEMAMPUAN PEMAHAMAN KONSEP PECAHAN PADA SISWA SMP

This study aims to determine the ability to understand the concept of fractions in grade VII students of SMP Kristen Kusu-Kusu Sereh Ambon. The type of research used is qualitative descriptive research. This research was carried out at SMP Kristen Kusu-Kusu Sereh Ambon, with the data source being class VII-1 students totaling 20 students, and the research subjects selected to be interviewed were three students. Researchers describe students' ability to understand fractional concepts by looking at the results of student answers and interviews. The results of this student's test refer to the question instructions and the student's accuracy in answering. The accuracy of the student's answers is adjusted to the assessment criteria for the test questions and the scoring criteria for the ability to understand fractional concepts with four indicators, namely indicators of the ability to provide examples and non-examples, indicators of the ability to present concepts in various forms of mathematical representation, indicators of the ability to use, utilize and select specific procedures or operations and indicators of the ability to apply concepts or algorithms in problem-solving. Based on the results of the fractional concept comprehension ability test and student interviews, one student met three indicators of concept understanding ability, namely indicators of the ability to provide examples and non-examples, the ability to present concepts in various forms of mathematical representation, and the ability to apply concepts or algorithms in problem-solving, and two students who met one indicator of concept understanding ability, namely indicators of ability to provide an example and non-example.

On Plasma Fractionation Treatment and Its Implications in Cells

Here, we present a novel plasma treatment regime—plasma fractionation, analogous to the concept of dose fractionation in radiotherapy, which could see the application in plasma-based cancer treatment. In plasma fractionation, a single acute dose of plasma is divided into multiple small dosages (fractionated dosages) and administered to the cells in vitro at 24-h intervals. We utilized a helium plasma jet and studied the effects of plasma fractionation in an immortalized keratinocyte line (HaCaT) and a squamous cell carcinoma line (A431). The effects were assessed over three cell seeding densities—8000, 3500, and 1000 cells/well. Our results show that at all seeding densities, plasma fractionation produced lower levels of cell death in both cell types compared to the same dose administered as a single plasma treatment. This highlights the potential of plasma fractionation as a potentially safer method to conduct plasma treatments in the future. We also show that A431 cells were more sensitive to a single acute plasma treatment than HaCaT cells, at cell densities that are subconfluent (1000 cells/well). A similar difference in sensitivity between HaCaT cells and A431 cells was not observed on exogenous treatment with hydrogen peroxide, pointing to the importance of other shorter lived plasma components.

A mathematical model for simulating the transmission dynamics of COVID-19 using the Caputo–Fabrizio fractional-order derivative with nonsingular kernel

The emergence of the new coronavirus variant from the coronaviridae family has become a global concern, and all nations, including Bangladesh, are battling to contain the spread of the disease. In this article, we discuss a COVID-19 vaccination model with the Caputo–Fabrizio (CF) fractional order derivative approach to reveal the complicated action in Bangladesh. We determine the existence and uniqueness properties of the outcomes acquired from our proposed model subjected to the Picard–Lindelöf theorem. We perform the stability analysis by using the fixed-point theorem. We utilize Laplace Transform to evaluate the approximate solution of the model. In the numerical simulation, we consider a new approach called the four-step Adams-Bashforth Predictor–Corrector iteration scheme, which simulates that the fractional order provides more precise results. Finally, several numerical results are displayed with the different numbers of the order of the system. We depict the influence of vaccination in the coronavirus model with different parameter values. By analyzing the transmission dynamics of the virus, we bring to light the importance of several doses of vaccination to prevent disease transmission and contagions. We also conducted the sensitivity analysis for the model parameters to evaluate the impact of those parameters on disease outbreaks. The numerical results demonstrate significant information in the Caputo–Fabrizio fractional derivative concept and provide important insights into predicting disease transmission and control policies.

Study of nonlinear generalized Fisher equation under fractional fuzzy concept

<abstract><p>Fractional calculus can provide an accurate model of many dynamical systems, which leads to a set of partial differential equations (PDE). Fisher's equation is one of these PDEs. This article focuses on a new method that is used for the analytical solution of Fuzzy nonlinear time fractional generalized Fisher's equation (FNLTFGFE) with a source term. While the uncertainty is considered in the initial condition, the proposed technique supports the process of the solution commencing from the parametric form (double parametric form) of a fuzzy number. Next, a joint mechanism of natural transform (NT) coupled with Adomian decomposition method (ADM) is utilized, and the nonlinear term is calculated through ADM. The obtained solution of the unknown function is written in infinite series form. It has been observed that the solution obtained is rapid and accurate. The result proved that this method is more efficient and less time-consuming in comparison with all other methods. Three examples are presented to show the efficiency of the proposed techniques. The result shows that uncertainty plays an important role in analytical sense. i.e., as the uncertainty decreases, the solution approaches a classical solution. Hence, this method makes a very useful contribution towards the solution of the fuzzy nonlinear time fractional generalized Fisher's equation. Moreover, the matlab (2015) software has been used to draw the graphs.</p></abstract>

Izgrađivanje koncepta matematike sa didaktičkim igrama u okruženju koje se odnosi na GeoGebra

In this study, we examine how GeoGebra software can be used for organizing a game-based learning environment and its impact on fraction concept building and the pupils' understanding of the concept. The learning/instruction process was organized in two groups of 9 to 10 years old pupils. The experimental group was offered GeoGebra game-like applets and the learning process was based on them. The control group pupils learned the same subject material in a more traditional fashion. Pupils' understanding of the concept-was assessed using results of regular tests they enrolled in the same environments they were learning. According to the results, the experimental group pupils-demonstrated better understanding of the concepts, and the difference is statistically significant. This implies that GeoGebra software-combined with the game-based learning can give-better results in building and understanding fractions at initial stages.

Neuroeducation and Mathematics: The Formation of New Educational Practices.

Recent research in educational neuroscience has established the correlation between the way the human brain works and the process of perceiving and learning mathematical concepts. In this chapter, a research approach is proposed, based on the principles of educational neuroscience, and focuses on the way students deal with new knowledge in mathematics. Initially, using neuroscientific techniques and a multidimensional approach to new knowledge, data will be collected from students. By collecting neurophysiological measurements and analyzing the data, an attempt will be made to formulate learning paths for a better understanding of fractional concepts, based on the needs of each student.

FRACTIONAL-ORDER MEASLES INFECTION MODEL WITH VACCINATION EFFECTS

The purpose of this work is to investigate the dynamical behavior of a measles disease model adopting fractional and fractal–fractional operators with Mittag-Leffler kernel using two distinct numerical algorithms. First, we discuss the measles model in a fractional framework with Atangana–Baleanu–Caputo derivative and examine some fundamental mathematical assumptions of the considered model. We implement fixed-point theory to explore the existence and uniqueness of model solutions. Next, we apply the novel fractal–fractional concept with Atangana–Baleanu derivative to the measles model and reveal that the model has unique solution. We present the approximate results for the proposed models with graphical illustrations. The results are presented with various choices of fractal and fractional orders. The system behavior to various biological parameters is also investigated. In addition, we compare the considered operators using novel numerical schemes that take into account different [Formula: see text] values.

Analisis Learning Obstacles pada Materi Pecahan Siswa Kelas IV Sekolah Dasar

This study aims to analyze the existence of learning obstacles that occur in students, especially in class IV fraction materials and efforts to overcome these learning obstacles. This research uses descriptive qualitative research method. The sample in this study was 17 grade IV students at SDN Kopo 04 for the academic year 2021/2022 with purposive sampling using a sampling technique. The source of data in this study is the primary data source and for data collection the researchers used test and interview instruments. Data analysis was carried out descriptively by reducing data, presenting data, and drawing conclusions. Based on the results of research and discussion, it was found that a learning obstacle in the ontogenic obstacle category was that students did not understand how to operate addition and subtraction on fractions. Students also experience epistemological obstacles if they are faced with a different problem context from the one exemplified by the teacher in the book and misunderstand the meaning of the question. In addition, there were didactical obstacles where students were not able to place the numerator and denominator, students also did not know the definition of fractions and the concept of fractions as part of a whole and fractions as part of a group, because it was caused by inappropriate teacher teaching. It was also found that efforts to overcome learning obstacles were found such as holding remedials, enrichment, using the RME (Realistic Mathematics Education) learning model, often doing practice questions, and being able to use other learning media besides books. Efforts to overcome the learning obstacles found are expected to be realized to minimize the learning barriers experienced by students.