Division Of Fractions Research Articles

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.

Enhance elementary school students to learn mathematics: Case of the use of mother tongue-base language (MTBL) students

The study of using Mother Tongue-Based Language (MTBL) in remediation on Least Learned Competencies in Elementary Mathematics to two sections in Grade VI at Tambo Central School was carried out. Both groups were exposed to team-assisted individualized remediation. The data needed for this study were obtained through 30-item achievement test and seventeen (17) Learning Materials constructed by the researcher which were construct-validated and evaluated by mathematics experts. Identified competencies of the materials were based on the National Achievement Test result and in the K to 12 Curriculum on Rational Numbers. The findings of the study revealed that the use of MTBL in team-assisted individualized remediation evidently improved the performance of the respondents in the three competencies on fractions namely comprehension of fractions; multiplication of fractions and its applications; and division of fractions and its applications.

Fourth to Sixth Grade Teachers’ Invented Real World Problems and Pictorial Representations for Fraction Division

Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their own understanding as well as how to incorporate multiple representations in their instruction. This naturalistic inquiry study investigated fourth to sixth grade teachers’ invented real-world problems and pictorial representations for fraction division. The teachers completed a written assessment focused on conceptual understanding of fraction operations through multiple representations at the beginning and conclusion of a weeklong professional development experience. The questions on the assessment were taken or modified from prior research studies. The results in this paper focus specifically on a task in which the teachers had to develop a real world story problem for 2½ ÷ ¾ and solve the problem by drawing a pictorial representation. The teachers showed statistically significant improvement on developing appropriate real-world problems and using pictorial representations to solve their problems. Implications for teachers’ usage of multiple representations are discussed along with needed structures for professional development targeted on fractions.

Pre-Service Teachers Making Sense of Fraction Division with Remainders

This study reports an analysis of how pre-service teachers (n=34) made sense of fraction division with remainders using pictorial modeling strategies, and how small-group and whole-class discussion helped them develop conceptual understanding. One and a half class sessions were video recorded, and 12 interviews were conducted. Results indicate that pre-service teachers can develop a conceptual understanding of fraction division with remainders using modeling strategies, and their understanding emerges in three levels: a) level one: ignoring the remainder or labeling it incorrectly; b) level two: interpreting the remainder in the original unit but not relating it to the new unit; and c) level three: interpreting the remainder both in the original unit and the new unit flexibly.

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).

Building a computerized dynamic representation as an instrument for mathematical explanation of division of fractions

ABSTRACTThis study describes a teaching process that offers teachers and pupils ways of constructing the division operation through illustration based on defining the reference unit (divisor), the reference whole1 and the dividend. We introduce a computerized dynamic environment, using an Excel spreadsheet, in which both teachers and pupils can independently construct the solution process in a manner that leads to meaningful learning. Nine pairs of teachers and pupils underwent an intervention process using Excel, comparing pupils’ understanding of division of fractions before and after the learning process. Findings from the pupils indicate the Excel software enabled them to portray and construct the meaning of the division process while applying accurate mathematical terms. Specifically, they could thoroughly understand the meaning of a word problem, so as to explain another student’s mistake. Furthermore, teachers’ analyses of the pupils’ work indicate that the use of this computerized dynamic environment helped the teachers develop mathematical knowledge, pedagogical knowledge and technological pedagogical knowledge.

A design of a 5.6 GHz frequency synthesizer with switched bias LIT VCO and low noise on‐chip LDO regulator for 5G applications

A design of a 5.6 GHz frequency synthesizer with switched bias LIT VCO and low noise on‐chip LDO regulator for 5G applications

Overcoming Errors in Fraction Computation by Emphasizing Unit Fractions, Length Drawings, and Student Explanations

This paper addresses the perceived opacity of fraction computation by summarizing results of classroom design experiments focused on making fraction concepts and computation meaningful to students and teachers. A nurturing Math Talk classroom environment, in which students made and explained math drawings supported sense-making by students and teachers. Students were able to make drawings of length models connected to symbolic computations for all fraction operations, and most students were able to explain their thinking. Correct performance on computations was considerably higher than that of U.S. students using traditional textbooks and was more comparable to performance of East Asian students. The paper shows the length drawings for each fraction operation and summarizes the nature of students' errors and how to overcome these. Length drawings (bar and number line models) connected to fraction symbols and words can focus students on unit fractions in all operations. Important difficulties to overcome are that fraction notation does not differentiate the roles of the numerator and denominator, and the notation shows the number but not the size of unit fractions. Multiplying fractions by multiplying each unit fraction and not the whole fraction magnitude is a general method, and division of fractions can begin by dividing numerators and denominators.

A comparison of the instructional content on division of fractions in Turkish and Singaporean textbooks

ABSTRACTThis study has compared Turkish and Singaporean textbooks with respect to the instructional content of the unit on division in fractions, which is a challenging topic for many students. Two Turkish textbooks were compared against two Singaporean books, My Pals Are Here and Targeting Mathematics. In Turkish and Singaporean mathematics books, the contents of the unit on division in fractions are based on students’ conceptual understanding and the development of operational fluency. When compared to Singaporean textbooks, Turkish books included more solution methods. However, the solutions in Turkish books displayed no relationship between visual and symbolic representation. Both Turkish and Singaporean books used only area models (circle, rectangle) in teaching the topic of division in fractions, and included measurement and equal sharing problems with step by step solution explanations. In sum, it may be claimed that Singaporean books caused students to use fewer solution strategies but offered more opportunities for grasping the relationship between division and multiplication in fractions.

AN EXAMINATION OF MEANINGS AND ERROR TYPES ASSOCIATED WITH PRE-SERVICE ELEMENTARY TEACHERS' POSED PROBLEMS FOR THE MULTIPLICATION AND DIVISION OF FRACTIONS

The current study aims to examine meanings and error types associated with pre-service elementary teachers’ semi-structured problems for the multiplication and division of fractions. A total of 83 junior pre-service elementary teachers were recruited in the spring semester of the 2016-2017 academic year. A researcher-developed Problem Posing Test consisting of eight items was used to collect the data of this study. The findings indicated that the pre-service elementary teachers were not proficient in posing appropriate problems for the multiplication and division of fractions. Furthermore, while the most frequent error type found was a failure in expressing the multiplication operation in the question root for the multiplication of fractions, it was assigning natural number meaning to fractions for the division of fractions. Article visualizations:

Constant envelope FrFT OFDM: Spectral and energy efficiency analysis

Constant envelope with a fractional Fourier transformorthogonal frequency division multiplexing (CE-FrFT-OFDM) is a special case of a constant envelope OFDM (CE-OFDM), both being energy efficient wireless communication techniques with a 0 dB peak to average power ratio (PAPR). However, with the proper selection of fractional order, the first technique has a high bit error rate (BER) performance in the frequency-time selective channels. This paper performs further analysis of CE-FrFT-OFDM by examining its spectral efficiency (SE) and energy efficiency (EE) and compare to the famous OFDM and FrFT-OFDM techniques. Analytical and comprehensive simulations conducted show that, the CE-FrFT-OFDM has five times the EE of OFDM and FrFT-OFDM systems with a slightly less SE. Increasing CE-FrFT-OFDM's transmission power by increasing its amplitude to 1.7 increases its SE to match that of the OFDM and FrFT-OFDM systems while slightly reducing its EE by 20% to be four times that of OFDM and FrFTOFDM systems. OFDM and FrFT-OFDM's amplitude fluctuations cause rapid changing output back-off (OBO) power requirements and further reduce power amplifier (PA) efficiency while CE-FrFTOFDM stable operational linear range makes it a better candidate and outperforms the other techniques when their OBO exceeds 1.7. Higher EE and low BER in time-frequency selective channel are attracting features for CE-FrFT-OFDM deployment in mobile devices.

P‐87: Time‐Multiplexing Parallax Barrier with Fractional Time Division

This paper proposes an autostereoscopic display based on time‐multiplexing parallax barrier with fractional numbers of time‐division. We analyze the effect of fractional time‐division to find the conditions where flickers do not stand out even when the number of time‐division is fractional.

PENINGKATAN AKTIVITAS DAN HASIL BELAJAR MATEMATIKA MELALUI PEMBELAJARAN KOOPERATIF TIPE THINK-PAIR-SHARE (TPS) DI KELAS VC SD NEGERI 47 KOTA JAMBI

The purpose of this study are to increase students’ learning activities in the learning process of mathematics by applying the type of Think-Pair-Share (TPS) cooperative learning and to improve students’ learning outcomes in mathematics. This research was carried out in the fifth grade Students in Elemntary School 47 Jambi during the first semester of 2017/2018 Academic Year. The action was carried out in 2 cycles with the subject matter covered in cycle I was about explaining and reducing two fractions with different denominators and in cycle II about multiplication and division of decimal fractions. Data was collected by observation methods using observation sheets and student learning outcomes was collected using tests. The results of the study based on data analysis showed an increase in learning outcomes from 64.29% wich is sufficient category in the first cycle to be a good category in the second cycle with 83.93%. For student learning outcome there was an improvement from 50% with inactive categories to 90% with very active categories.. The results of this study indicate that the application of the Think-Pair-Share (TPS) Cooperative Learning model can be used to improve student learning outcomes.

Making sense of fraction division: domain and representation knowledge of preservice elementary teachers on a fraction division task

The mathematical domain of fraction division continues to be an area of great difficulty for many teachers and preservice teachers (Lo and Luo, Journal for Mathematics Teacher Education 15:481–500, 2012; Newton, American Educational Research Journal 45:1080–1110, 2008; Rizvi and Lawson, International Education Journal 8(2):377–392, 2007; Young and Zientek, Investigations in Mathematics Learning 4(1):1-23, 2011). In this study, preservice teachers were given a fraction division task that sought to investigate their own personal approaches to solving a fraction division problem. Their results were contrasted with their ability to interpret student work on the same task. The purpose was to uncover information and gain greater insight into conceptualizations of fraction division they used and links or connections they made among verbal, diagrammatic, and algebraic representations as they solved the task themselves and then analyzed sample student solutions to the same task. Our findings have implications for future research and instruction on fraction division.

Performance evaluation of fractional OFDM for extending transmission distance without reducing spectral efficiency

The performance of a fractional orthogonal frequency division multiplexing (FrOFDM) system is examined considering spectral efficiency (SE). While FrOFDM can reduce peak-to-average power ratio, which is a drawback in OFDM, its bandwidth is expanded. Simulations were performed to evaluate the increasing amount of transmission distance from the signal-to-noise ratio of the received signals with keeping the best SE of OFDM. Simulation results show that FrOFDM can increase the transmission distance without reducing SE.

Peningkatan aktivitas dan hasil belajar matematika melalui pembelajaran kooperatif tipe Think Pair Share di kelas VC SD Negeri 47 Jambi

The purpose of this study are to increase students’ learning activities in the learning processof mathematics by applying the type of Think-Pair-Share (TPS) cooperative learning and toimprove students’ learning outcomes in mathematics. This research was carried out in thefifth grade Students in Elemntary School 47 Jambi during the first semester of 2017/2018Academic Year. The action was carried out in 2 cycles with the subject matter covered incycle I was about explaining and reducing two fractions with different denominators and incycle II about multiplication and division of decimal fractions. Data was collected byobservation methods using observation sheets and student learning outcomes was collectedusing tests. The results of the study based on data analysis showed an increase in learningoutcomes from 64.29% wich is sufficient category in the first cycle to be a good category inthe second cycle with 83.93%. For student learning outcome there was an improvement from50% with inactive categories to 90% with very active categories.. The results of this studyindicate that the application of the Think-Pair-Share (TPS) Cooperative Learning model canbe used to improve student learning outcomes.Keywords: learning process, Think-Pair-Share.

The Middle School Mathematics Teachers' Subject Matter Knowledge: The Context of Division of Fractions.

In this study, the middle school mathematics teachers’ knowledge of division of fractions was investigated through the strategies that they proposed and the problems that they posed for division of fractions. The data was collected from 22 middle school mathematics teachers through the task and semi-structured interviews. The data of this case study was analyzed by content analysis approach. According to the findings, 5 alternative strategies were proposed by 22 teachers to divide fractions. Among these strategies, the most commonly used was invert and multiply strategy and the least are converting fractions into decimal and converting to equation. In relation to the problems that the teachers posed, the findings revealed that more than half of the teachers could not propose appropriate problems. In other words, the teachers had difficulty in generating an appropriate story problem to illustrate division of fractions. These results and implications are discussed and the recommendations are presented in accordance with the findings of the study. Article visualizations:

Number lines, but not area models, support children’s accuracy and conceptual models of fraction division

The Common Core State Standards in Mathematics recommends that children should use visual models to represent fraction operations, such as fraction division. However, there is little experimental research on which visual models are the most effective for helping children to accurately solve and conceptualize these operations. In the current study, 123 fifth and sixth grade students solved fraction division problems in one of four visual model conditions: number lines, circular area models, rectangular area models, or no visual model at all. Children who solved the problems accompanied by a number line were more accurate and showed evidence of consistently producing sound conceptual models across the majority of problems than did children who completed problems with either area model or no visual model at all. These findings are particularly striking given that children have experienced partitioning area models into equal shares as early as first grade, thus circles and rectangles were likely familiar to children. The number line advantage may stem from the fact that they afford the ability to represent both operand magnitudes in relation to one another and relative to a common endpoint. Future work should investigate the optimal order that instructors should introduce various visual models to promote children’s representational fluency across number lines and area models.

Peningkatan hasil belajar matematika materi menggunakan pecahan dalam pemecahan masalah dengan pendekatan Contextual Teaching Learning (CTL)

<p class="Abstrak">Learning mathematics using fractions in problem-solving is boring for students. For this reason, researchers are interested in improving the process of learning mathematics, especially learning Using Fractions in Problem Solving with the Contextual Teaching Learning (CTL) approach. The CTL approach is felt to be able to overcome the existing problems. This study aims to describe the planning, implementation, and assessment of mathematics learning outcomes improvement using fractions in problem-solving with a contextual approach. The implementation of this research uses a qualitative and quantitative approach using a class action research design which includes: (1) Planning, (2) Implementation, (3) Observation and (4) Reflection. The study was conducted in 2 cycles. Research data in the form of information about the process and action data obtained from observations, test results, discussions and documentation. Research subjects consisted of Class V students totaling 20 students. The average percentage of completeness of learning outcomes in research conducted in the first cycle of meeting 1 was 60%, in cycle I meeting 2 was 70%, the average learning outcomes in cycle II meeting 1 was 80%, in cycle II meeting 2 was 90%. The conclusion obtained from this study is the CTL approach can improve learning outcomes Using Fractions in Problem Solving, namely about multiplication and division of fractions.</p>

Students’ misconceptions on the algebraic prerequisites concept: operation of integer numbers and fractions

Numbers operation is one of the algebraic prerequisites concepts that students must understand before understanding the algebraic material. Understanding the wrong prerequisite concept can lead to misconceptions. This research aimed to describe students’ misconceptions on the algebraic prerequisites concept, causative factors, and alternative solutions. This research was qualitative descriptive research using diagnostic test methods and interview. Three students who did the most and varied misconceptions in completing the diagnostic test were chosen to be the subject of this research. The results showed the subject misconceptions experienced on the algebraic prerequisites concept, namely the operation of integers and fractions. The misconceptions experienced by the subject occurred in the integer addition, integer subtraction, integer division, multiplication with zero numbers, fractions addition, and fractions division. The factors that cause misconception are preconception, associative thinking, incomplete or incorrect reasoning, wrong intuition, student ability. Alternative solutions to overcome the misconceptions are re-explain and cognitive conflict. The teacher must know the misconceptions, causative factors and alternative solutions to overcome students’ misconceptions on the algebraic prerequisites concept so that students will not experience misconceptions when understanding the algebraic material in the next stages.