Subtraction Of Fractions Research Articles

Selecting and Sequencing Students’ Solutions in Orchestrating Mathematical Discussions: Subtraction of Fractions

Selecting and Sequencing Students’ Solutions in Orchestrating Mathematical Discussions: Subtraction of Fractions

Estimating CDMs Using the Slice-Within-Gibbs Sampler.

In this paper, the slice-within-Gibbs sampler has been introduced as a method for estimating cognitive diagnosis models (CDMs). Compared with other Bayesian methods, the slice-within-Gibbs sampler can employ a wide-range of prior specifications; moreover, it can also be applied to complex CDMs with the aid of auxiliary variables, especially when applying different identifiability constraints. To evaluate its performances, two simulation studies were conducted. The first study confirmed the viability of the slice-within-Gibbs sampler in estimating CDMs, mainly including G-DINA and DINA models. The second study compared the slice-within-Gibbs sampler with other commonly used Markov Chain Monte Carlo algorithms, and the results showed that the slice-within-Gibbs sampler converged much faster than the Metropolis-Hastings algorithm and more flexible than the Gibbs sampling in choosing the distributions of priors. Finally, a fraction subtraction dataset was analyzed to illustrate the use of the slice-within-Gibbs sampler in the context of CDMs.

SNOWBALL THROWING SEBAGAI MODEL PEMBELAJARAN GUNA PENINGKATAN KEAKTIFAN BELAJAR SISWA MADRASAH IBTIDAIYYAH BIDANG MATEMATIKA

Classroom action research was motivated by the less active attitude of the Class V students of MI Negeri 4 Gunungkidul. located in MI Negeri 4, located in Dusun Semenrejo, Pulutan Village, Wonosari District, Gunungkidul Regency in learning mathematics. The Snowball Throwing learning model is expected to be able to improve it, especially in the material of addition and subtraction of fractions with different denominators on. This research was conducted during July 2019. Data was collected through observation, interviews and documentation. The research was carried out for two sessions continuously to produce according to expectations where the achievement was achieved through learning as many as 22 students. Therefore it is suggested that the teacher can apply the SbT type of cooperative learning model to other materials. Variations can be made within the framework of cooperative learning that is adapted to the material and conditions

Learning Obstacle the Addition and Subtraction of Fraction in Grade 5 Elementary Schools

The Fraction is a material that is very important for students to learn in elementary school, but various difficulties are shown by students in understanding the material, so this study will analyze the learning obstacle that appears to students in the addition and subtraction material in grade 5 elementary school. The approach in this research uses qualitative and case study methods. The subjects in this study were 5th-grade students of Geger Kalong Girang 1¾2 elementary schools, Bandung City, West Java, Indonesia with a total of 29 students. Data was collected by tests, interviews, and documentation, while for data analysis techniques using data reduction, data presentation, and conclusions. The results of this study indicated that students experience learning obstacles, including 1) ontogenic obstacle, which is the inability of students to understand the purpose of the problems presented; 2) epistemological obstacle, namely the inability of students to understand the concept of fractions is part of the whole and the inability of students to do the addition and subtraction of fractions, and; 3) didactical obstacle caused by the presentation of material and the teacher's way of teaching which is only informal. This research is expected to facilitate students to understand fractions and be a development material in making teaching materials and didactic design of the addition and subtraction fractions based on learning obstacles that appear in this study.

Learning Obstacle the Addition and Subtraction of Fraction in Grade 5 Elementary Schools

The Fraction is a material that is very important for students to learn in elementary school, but various difficulties are shown by students in understanding the material, so this study will analyze the learning obstacle that appears to students in the addition and subtraction material in grade 5 elementary school. The approach in this research uses qualitative and case study methods. The subjects in this study were 5th-grade students of Geger Kalong Girang 1¾2 elementary schools, Bandung City, West Java, Indonesia with a total of 29 students. Data was collected by tests, interviews, and documentation, while for data analysis techniques using data reduction, data presentation, and conclusions. The results of this study indicated that students experience learning obstacles, including 1) ontogenic obstacle, which is the inability of students to understand the purpose of the problems presented; 2) epistemological obstacle, namely the inability of students to understand the concept of fractions is part of the whole and the inability of students to do the addition and subtraction of fractions, and; 3) didactical obstacle caused by the presentation of material and the teacher's way of teaching which is only informal. This research is expected to facilitate students to understand fractions and be a development material in making teaching materials and didactic design of the addition and subtraction fractions based on learning obstacles that appear in this study.

Bayesian Estimation of the DINA Model With Pólya-Gamma Gibbs Sampling.

With the increasing demanding for precision of test feedback, cognitive diagnosis models have attracted more and more attention to fine classify students whether has mastered some skills. The purpose of this paper is to propose a highly effective Pólya-Gamma Gibbs sampling algorithm (Polson et al., 2013) based on auxiliary variables to estimate the deterministic inputs, noisy “and” gate model (DINA) model that have been widely used in cognitive diagnosis study. The new algorithm avoids the Metropolis-Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability. Four simulation studies are conducted and a detailed analysis of fraction subtraction data is carried out to further illustrate the proposed methodology.

Demonstrating Conceptual Understanding of Fraction Arithmetic: An Analysis of Pre-Service Special and General Educators’ Visual Representations

To provide effective fractions instruction, teachers need deep understanding of fraction concepts (i.e., content knowledge) and skill in using visual representations of fractions to support student learning (i.e., pedagogical content knowledge); yet, research indicates that many pre- and in-service teachers lack knowledge in both areas. The present study examines the performance of 55 pre-service teachers (PSTs) on tasks assessing their procedural and conceptual knowledge of fractions, including a test of their ability to generate visual representations and story problems to model fraction multiplication and division. PSTs demonstrated high levels of procedural and conceptual knowledge of fraction addition and subtraction, moderate procedural knowledge for fraction multiplication and division, and relatively weak conceptual knowledge of fraction multiplication and division. Weak conceptual knowledge was related to inability to accurately model fraction multiplication and division using visual representations and story problems. Implications for research and practice are presented.

The identification of students’ didactic obstacles in learning fractions based on the form of the problems

This study aims at knowing whether there are didactic obstacles in learning fractions of students in Yogyakarta based on the form of the problems. Those problems include visual, narrative, and symbolic forms. Materials of fractions consist of the concepts of fractions, equivalent fractions, the order of fractions, decimals, percents, addition of fractions, subtraction of fractions, multiplication of fractions, and division of fractions. The method of this study is survey with expost facto approach. The populations are students of Junior High School grade VII in Yogyakarta. The samples are 151 students from four schools in Yogyakarta. The choice of sample is done by stratified proportional random sampling technique. The instrument is diagnostic test with 27 questions that divide into 9 visual forms, 9 narrative forms, and 9 symbolic forms. Based on the result, students have didactic obstacles in visual forms and narrative forms. While in symbolic forms, students did not have didactic obstacles.

The semantic network supports approximate computation.

The present study used complex approximate and exact arithmetic computation problems to dissociate the brain networks for strategy-based approximate computation and procedure-based exact computation. Twenty-eight college students were scanned with MRI while they were solving complex approximate and exact computation problems, including addition, subtraction, multiplication, and division of multidigit integers and fractions. The neuroimaging data were analyzed using whole brain, region of interest, and functional connectivity approaches. Results showed that approximate computation relative to exact computation elicited greater activation typically in the bilateral inferior frontal gyrus (orbital), middle temporal gyrus, angular gyrus, and dorsomedial prefrontal cortex. The brain regions overlapped with the general semantic network that also supports mathematical problem solving. In contrast, exact computation elicited greater activations in the left rolandic operculum and bilateral hippocampus. Functional connectivity analysis based on the psychophysiological interaction approach showed that approximate computation had stronger connectivity from the left intraparietal sulcus to the semantic areas. In contrast, exact computation had stronger connectivity from the left intraparietal sulcus to the phonological areas. The results suggest that the semantic network supports complex approximate computation and the phonological network supports complex exact computation. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Improvement in Mathematics Learning Outcomes in ‎Fraction Operation Material with Grid Square Unit Media

This research was motivated by MI Ma'arif Kutowinangun fifth grade students who have difficulty in receiving the lessons with materials related to addition and subtraction of various fractions. Especially, when dealing with addition and subtraction of fractions operations with different denominators. This was showed by the results of interviews and observations made by the author. With minimum completeness criteria of 60, from 14 students of V class, only nine of them reached the minimum completeness criteria, and the rest have not been able to achieve the minimum completeness criteria.Based on the above problems, then the author conducted Classroom Action Research (CAR) to determine the improvement of mathematics learning outcomes in fraction operation material with grid square unit media. The research subject was fifth grade students of MI Ma’arif Kutowinangun consisting of 20 students, 11 of them were female and nine of them were male. While, the data collection was obtained through interviews, observation, and evaluation results through written tests which then were analyzed by percentage.Based on this research, there was improvement of student mathematics learning outcomes in fraction operation with grid square unit media. From 20 students who reached the minimum completeness criteria 60 in the first cycle was 16 students or 80%. Then it increased in the second cycle that all fifth grade students of MI Ma'arif Kutowinangun reached the minimum completeness criteria or 100%.

Analisis Learning Obstacles Siswa Pada Materi Pecahan Kelas IV Sekolah Dasar

The purpose of this research to analyze errors of students answer to get a conception of learning obstacles in the fraction material in 4th grade of elementary school. This analysis is important as a basis to prepare teaching materials and to predict of student responses and how to anticipate. This research used the qualitative method. The research subjects were 32 student of 5th grade elementary school who had studied fractions in grade IV in Tasikmalaya Regency. Based on the results of analysis of test and interview data, there are several barriers on student learning. First, didactical obstacles were identified from mistake doing the test problems which is caused by how students studied and materials which used by students such as fraction material that did not clearly define how fractions was and emphasize knowledge procedures, then students do not study fractions through the partitioning process, somewhere partitioning will make learning easier. Second, epistemological obstacles as a result from errors in the processing of questions caused by the limited context of knowledge possessed by students. For example, the definition of fractions which are part of the whole, students are limited to that context without paying attention at the parts as equal/more or less. In addition, procedures of student understanding for example fraction simplification, fraction sequencing, and subtraction and addition of fractions are limited to certain questions. When the questions are different than usual, there are students who didn’t understand the purpose of the problem.

Altıncı Sınıf Öğrencilerinin Kesir İşlemlerinde Yer Verilen Farklı Temsillere Yönelik Tercihleri ve Tercih Ettikleri Temsillerdeki Başarı Durumları

Normal 0 21 false false false TR X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Calibri",sans-serif; mso-bidi-font-family:"Times New Roman";} The aim of this study is to determine the representation preferences (numerical, area model, number line and verbal) of the sixth-year students for the addition and subtraction of fractions and to reveal their successes in their preferences. Being descriptive in nature, this research has been conducted as a survey study. The study group consists of 59 students, 31 of whom are boys and 28 of whom are girls, who are in the sixth grade of three middle schools affiliated to MoNE in the city of Kastamonu. A purposeful sampling selection method was used to select participants. The data were collected by " Multiple Representations in Fraction Operations Test " and analyzed in accordance with predefined transition criteria. Representation preferences of students and interpretations of their success in their preferences were presented through descriptive statistics (percentage and frequency). While area model representations take the first place in preferences, verbal representations are the least preferred type of representation. When students’ performances in the representations are examined, the most successful representations of students in addition and subtraction of fractions are numerical and area model representations. On the other hand, it has been seen that the achievement status of students in the verbal and numerical representation types is considerably low.

Pre-service primary Mathematics teachers’ understanding of fractions: An action–process–object–schema perspective

Background: The concept of rational numbers is one of the learner’s first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study was set up to apply Action–Process–Object–Schema theory to study primary teachers’ understanding of addition and subtraction of fractions. Setting: The participants of this study comprised 60 undergraduate full-time students, studying to become teachers. The participants were enrolled in a foundational course in Mathematics because they had not passed Mathematics at Grade 12 level. This course was intended to help deepen their understanding of basic numeracy, allowing them to continue with further courses if they wanted to specialise in teaching primary mathematics Methods: Data were collected using written responses of the pre-service students to two tasks that focused on operations with fractions. Ten students volunteered to be interviewed of which three are drawn upon in this article. Results: Many of the pre-service teachers coped well with addition and subtraction of common fractions with the same denominator. However, more than 52% struggled to carry out these operations on common fractions with different denominators, showing that their conceptions had not developed into object-level structures. Conclusion: It is evident that the incorrect procedures have become embedded in the students mental schema. It is crucial that programmes for upgrading pre-service teachers should include opportunities for teachers to interrogate their personal understandings of the basic mathematics concepts.

Learning fraction through the context of Asian Games 2018

In August 2018, Indonesia will host Asian Games in two cities namely Jakarta and Palembang. As the researchers stay in the city of Palembang, we use this event as the context for designing mathematics lesson materials. This paper shares the results of the design research method, which aims to developing Learning Trajectory for primary school students. Three phases of design research were used namely preparing for an experiment, teaching experiment, and finally retrospective analysis. As the result, this research produces Local Instructional Theory (LIT) on fraction through the contexts of Asian Games 2018 sports namely swimming, shot put, rowing, running, and hurdles. The swimming context could stimulate students’ informal knowledge about the meaning of fractions. By using shot-put context can assist students in learning the subtraction of fractions. Furthermore, running context can help students understand the division of fractions. Meanwhile, rowing context can help students understand addition and subtraction of fractions. Lastly, the context of hurdles can help students to realize their knowledge about the concept of multiplication of fractions with natural numbers. Therefore, this study contributes positively to the various parties on how to teach fractions using the contexts in the learning process of Indonesian Realistic Mathematics Education.

Bayesian DINA Modeling Incorporating Within-Item Characteristic Dependency.

The within-item characteristic dependency (WICD) means that dependencies exist among different types of item characteristics/parameters within an item. The potential WICD has been ignored by current modeling approaches and estimation algorithms for the deterministic inputs noisy "and" gate (DINA) model. To explicitly model WICD, this study proposed a modified Bayesian DINA modeling approach where a bivariate normal distribution was employed as a joint prior distribution for correlated item parameters. Simulation results indicated that the model parameters were well recovered and that explicitly modeling WICD improved model parameter estimation accuracy, precision, and efficiency. In addition, when potential item blocks existed, the proposed modeling approach still demonstrated good performance and high robustness. Furthermore, the fraction subtraction data were analyzed to illustrate the application and advantage of the proposed modeling approach.

Comparison of Cognitive Diagnosis Models under Changing Conditions: DINA, RDINA, HODINA and HORDINA

The application of CDMs to fraction subtraction data revealed problems on the classification of examinees, latent class sizes, and the use of higher-order models. Additionally, selecting the most appropriate model assumes critical importance if there are several appropriate models available for the data. In the present study, DINA–RDINA and HODINA–HORDINA models were compared under changing conditions (i.e., number of attributes, g and s item parameter values, and number of items) with simulated and real data. The results show that for conditions where the g–s parameter values and the number of attributes were low (0.1 and 3, respectively), the reparameterized models generated values that were virtually identical to those obtained using DINA models. However, when the g–s parameter values and the number of attributes were increased (0.5 and 5, respectively), the parameter estimations obtained from the models, latent class estimates, AIC, and BIC show differences through the values from the models.

Use of Angle Model to Understand Addition and Subtraction of Fractions

Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and learning (TMATL) of operations of fraction. With the hope of engaging the reformed mathematical approach of teaching and learning (RMATL) this study investigated the following: How can trainee teachers use the angle model in RMATL operations of fractions? What are the perceptions of trainee teachers in the use of the angle model which engages RMATL to teach the operations of fractions? With the goal to fill the mentioned gap in which learners struggle to perform operations involving fractions, we observed and analysed worksheets on operation with fractions students wrote. Observations and interviews with trainee teachers of lower primary revealed poor performance in problems related to operations with fractions. Observed patterns supported by cognitivism revealed that invented methods or strategies on which RMATL is anchored are suitable enough to engage learner–centred teaching and learning which can prevent the abstractness of the concept of operations with fractions.

Towards the Solution of Abysmal Performance of Fraction in Navrongo Presbyterian Primary School: Comparing the Sets of Objects and Paper Folding Designed Interventions

This is an interventional study sought to find the difference in the performance of pupils who were taught using sets of objects (sets model) and paper folding activities, to solve word problems involving addition and subtraction of proper fractions. A total of thirty pupils, of Navrongo Presbyterian Primary School Basic Five A, were used in the study. A well-structured lesson, with teaching and learning materials, was used. A pretest and posttest assessments were deployed to ascertain the effect of the interventional teaching strategies. Prior, to the intervention of the study, 73.3% of the pupils (total of 30) scored below the average mark ranging from 5-7. These represented the experimental group of the study. 26.7% of the pupils (control group) scored the average mark. However, after the intervention, both strategies (sets of objects and paper folding activities) showed remarkable performance. Although both strategies showed remarkable performance in pupils, 59% of the experimental group (total of 22 pupils) scored above the average mark in the paper folding as compared to 50% of the experimental group who scored above the average mark in the usage of sets model. While 87.5% of the control group scored above the average marks ranging from 8-10 during the paper folding activities, 62.5% of the control group scored above the average marks from 8-10 during the use of sets model. The posttest results of both the control and experimental groups taught using paper folding performed far better compared to sets model. The study has shown that pupils’ level of performance had improved drastically with the help of paper folding method. In conclusion, paper folding activities help pupils to appreciate word problems involving addition and subtraction of proper fractions.

PMR Application to increase Activity and Results of Learning about Reduction Additive Fractions in Elementary School

Learning mathematics in elementary school should be oriented to the creation of activities that encourage the acquisition of an understanding of mathematical concepts more profound by the students. Based on observations and interviews conducted in SDN Sukosari 01 Bondowoso, it is known that teachers have many students actively involved in learning. The lack of use of methods or models of innovative learning in every learning math become one of the causes of low student learning activities that adversely affects the learning results. To overcome these problems is used Realistic Mathematics Approach (PMR) to enhance the activity and student learning outcomes. The purpose of this study is to describe the application of PMR on the subject of addition and subtraction of fractions to increase the activity and student learning outcomes in class V SDN Sukosari 01 Bondowoso at 2016/2017. This type of research is the Classroom Action Research conducted as many as two cycles and each cycle consisting of 2 meetings and 4 stages, including planning, implementation, observation and reflection. Data collection methods used in this research is observation, interviews, tests, questionnaires and documentation. Based on the analysis, the average percentage of students in the classical learning activities in the first cycle increased from 62.92% to 77.42%. In the second cycle, the average student learning outcomes also increased from 65.11 into 75.54. Based on these results, it can be seen that the implementation of PMR can increase the activity and student learning outcomes.

Developing Learning Materials in Addition and Subtraction of Fractions with Realistic Mathematics Approach for Students Grade 4

This study aims to describe the development process of learning materials that consists of lesson plan, student activity sheet, and fraction card. The study focuses on teaching addition and subtraction of fractions through realistic mathematics education. The development process used the Four-D model which consists of four steps: define, design, develop, and disseminate. In the first step (define), the teacher established the terms of learning by determining fundamental problem, analyzing students, and specifying instructional objectives. In the second step (design), the prototype of learning materials was constructed as a test standard, choosing the proper media and selecting the format. On the third step (develop), the learning materials were validated by the experts and then revised. Once the learning materials were ready they were tested in classroom. The teacher then collected data to measure the quality of the learning materials. The last step, dissemination, was the implementation of learning materials on a broad scale. From this step, the teacher collected data to measure the effectiveness of the learning. This study generated good learningmaterials and supported students Grade 4 to learn about addition and subtraction of fractions. While the results are providing some promising directions, a much larger study would be needed to determine if the results are due to the approach or due to the teachers’ enthusiasm or what is known as the Hawthorne Effect.