Division Of Fractions Research Articles

Exploration Into The Ability of Fifth-Grade Students To Solve Decimal Problems Using Proportional Reasoning

Proportional Reasoning is a complex mathematical way of thinking about interconnected ideas such as multiplication and division of whole numbers, fractions, ratios, powers, measurements, and percent. This research aims to identify students' thinking processes in solving decimal problems that require proportional reasoning. This research was conducted on 5th grade elementary school students in Klaten, Central Java, Indonesia, using test instruments, interviews and documentation studies. The test given consists of five types of questions, namely tests on questions that require students to use additive, multiplicative thinking skills, use reasonable or appropriate ratios, build unit structures (groupings), and understand invariants. The research results found that the proportional reasoning indicator that was more dominantly used by students was the ability to think multiplicatively, while the sub-indicators were writing and completing calculations but the final results were not correct. Apart from that, other findings explain that the low ability is due to the prerequisite material not being mastered, students not understanding the questions, and students not understanding the concept of the topic. Thus, these results confirm that proportional reasoning abilities in grade 5 elementary school are still quite low.

Design and Implementation of Digital Integrated Circuit Based Frequency Dividers

This research aims to research the basic fractional frequency division. This article first introduces the theory of the dualmode prescaler method, and then use this method to calculate the number of integer frequency divisions and show that how to achieve the target fractional division ratio. after that, Verilog code is used to implement fractional frequency division, and using simulation to show the operation of the divider. The simulation shows that the designed fractional frequency divider can be implemented by evenly inserting different values of integer frequency dividers. However, the experiment in this article may has time error in the output signal, because the accurate 50% duty cycle cannot be achieved. In addition, the frequency division period is not completely uniform. Finally, the challenges and limitations of fractional frequency division technology in theory and practice will be summarized.

의미론적 정합성 관점에서 분수의 연산 단원 분석: 의미 관계와 수량 유형을 중심으로

Mathematical concepts are derived from real-world situations, and their construction and application can be facilitated when real-world meanings and mathematical meanings are aligned. According to educational psychology research, the depth of interpretation and use of operations depend on whether the semantic relations between the objects presented in the problem situation and the potential mathematical relations are consistent. This study analyzed the semantic relations between objects in problem situations and the semantic alignment between the quantity types of objects and visual models in the fraction operation units of elementary school mathematics textbooks. The analysis revealed that, in problem situations, symmetric relationships were predominantly presented in fraction addition, subset-set relationships in fraction subtraction, and asymmetric relationships in fraction multiplication and division. Regarding quantity types, continuous quantities were presented more often than discrete ones, and in most cases, the quantity type of the object matched that of the visual model, though a few did not. Based on these findings, implications were drawn for selecting problem situations and instructional models that align with mathematical meanings and support student understanding from the perspective of mathematics learning psychology.

A Mixed Approach for Clock Synchronization in Distributed Data Acquisition Systems.

Proper timing synchronization is important when data from sensors are acquired by different devices. This paper proposes a simple but effective solution for System on Chip (SoC) architectures that integrates a general-purpose Field Programmable Gate Array (FPGA) with a CPU. The proposed approach relies on a network synchronization protocol implemented in software, such as Network Time Protocol (NTP) or Precision Time Protocol (PTP), and uses the FPGA to generate a clock reference that is maintained in step with the synchronized system clock. The clock generated by the FPGA is obtained from the FPGA oscillator via appropriate fractional clock division. Clock drift is avoided via a software program that periodically compares the FPGA and the system counters, respectively, and adjusts the fractional clock divider in order to slightly adjust the FPGA clock frequency using a Proportional Integral controller. A specific implementation is presented on the RedPitaya platform, generating a 1 MHz clock in step with the NTP synchronized system clock. The presented system has been used in a distributed data acquisition system for fast transient recording in the neutral beam test facility for the ITER nuclear fusion experiment.

ПЕРСПЕКТИВЫ ВВЕДЕНИЯ В КУЛЬТУРУ БРУСНИКИ ОБЫКНОВЕННОЙ (V. VITIS-IDAEA L.) В УСЛОВИЯХ МАГАДАНСКОЙ ОБЛАСТИ

Vaccinium vitis-idaea L. - common lingonberry occupies a special place in nature due to the value of its food and medicinal and prophylactic properties. Work on domestication of lingonberry is very limited. In Russia, extensive research on lingonberry selection was carried out at the Kostroma Forest Experimental Station. The result of this work was 4 varieties of lingonberry. In the Magadan Region, the work on domestication of lingonberry is of a pioneering nature. The object of the study were samples of common lingonberry plants (Vaccinium vitis-idaea L.). The collection of material for the research was carried out in 2023 in the Priokhotsk zone of the Magadan region, in the Olsky district, during the phase of active fruiting of plants - in September. For the study, 17 samples of partial plants of common lingonberry were selected. Evaluation of the productivity components of the studied samples revealed a high degree of variability in the components of the yield. The strongest variability was observed in the number of shoots (CV = 43.5%). The average degree of variability was noted for the length of shoots (CV = 16.34%) and their foliage (CV = 15.22%), the indicators varied, respectively, within 6 - 10 cm and 9 - 19 leaves. According to the fractional division, 47% of the fruits of the selected samples correspond to the medium fraction, the rest - to the small one. The average fruit weight in the samples was highly variable (CV = 46.14%). The average fruit diameter, depending on the sample, could be either 5.6 mm or 11.2 mm (CV=18.97%). As a result of studying and analyzing the samples of common lingonberry, 7 specimens were identified that were of interest for further work. Based on the results of office observations, it was established that the lingonberry samples selected and placed in laboratory conditions showed low resistance to stressful situations and weak viability in unnatural conditions.

The Role of Units Coordination in Preservice Elementary Teachers' Mathematical Knowledge for Teaching

ABSTRACT This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number addition and subtraction and for mathematical knowledge for teaching fraction multiplication and division. An analysis of PSTs’ written responses to two different types of tasks (referent unit and appropriateness of proportional reasoning) revealed that some aspects of mathematical knowledge for teaching rational number and the multiplicative conceptual field are associated with units coordination (referent unit tasks), whereas others are not (appropriateness tasks). A logistic regression of PSTs’ conceptions of multidigit number on their scores on these tasks provided empirical evidence that the most sophisticated conceptions of multidigit number (corresponding with having interiorized three levels of units) were associated with referent unit tasks but not associated with appropriateness of proportional reasoning tasks. Together, these findings support the claim that units coordination has promise for explaining the relationship between teachers’ mathematical knowledge for teaching multidigit addition and subtraction and fraction multiplication and division. Implications for teacher education are discussed.

Conceptual and Procedural Understanding in the Division of Algebraic Fractions

This study investigated the correlation between conceptual and procedural understanding of the division of algebraic fractions among junior high school students at a government-run university. It utilized descriptive and correlational research designs involving 109 enrolled Grade 8 students as study respondents. A validated algebra test questionnaire was the instrument used for the division of algebraic fractions. The Pearson product-moment correlation or Pearson r was used to assess the correlation between data variables. The findings revealed that the students poorly exhibited conceptual and procedural understanding in the division of algebraic fractions. There was a strong, highly positive, significant correlation between the students’ conceptual and procedural understanding in the division of algebraic fractions, which indicated that students' conceptual understanding goes hand in hand with their procedural understanding. Therefore, the higher the level of student conceptual understanding, the higher the level of procedural understanding and vice-versa.

Exploring the Link between Diabetes and Acquired Bisalbuminemia: Case Reports and Literature Review

Bisalbuminemia, characterised by the division of the albumin fraction on serum protein electrophoresis without an increase in concentration, is a rare protein anomaly that can present as either congenital or acquired. While congenital bisalbuminemia has a genetic basis, acquired bisalbuminemia is often associated with various underlying conditions, including excessive use of beta- lactam antibiotics, pancreatic fistula, and certain monoclonal immunoglobulins. Recent interest has emerged regarding the potential relationship between bisalbuminemia and diabetes mellitus. This study aims to explore the role of diabetes in acquired bisalbuminemia through the presentation of two cases and a review of relevant literature. Case 1 describes a 68-year-old female with recurrent pneumorespiratory infections, leading to the discovery of bisalbuminemia and subsequent diagnosis of diabetes mellitus. Case 2 involves a 71-year-old patient presenting with worsening lower back pain and bisalbuminemia, ultimately leading to a diagnosis of diabetes mellitus. Discussion highlights the significance of diabetes as a potential contributing factor to acquired bisalbuminemia, as suggested by previous case reports and prospective studies. While further research with larger cohorts is needed to confirm these findings, the inclusion of diabetes biological workup in bisalbuminemia cases may aid in early detection and management. In conclusion, this study underscores the potential association between uncontrolled diabetes and acquired bisalbuminemia, suggesting the importance of assessing for diabetes in such cases to improve diagnostic approaches for this rare condition.

Conceptualizations and representations of fraction division in online open access GeoGebra resources

Dividing fractions is often difficult for students to understand. Many GeoGebra applets have been developed to support students’ understanding of fraction division, but it is less clear how fraction division is conceptualized and represented in these tool-based resources. This study aimed to examine the quality of the GeoGebra applets for fraction division by attending to the conceptualizations, representations, and cognitive actions prevalent in these digital resources. The results reveal that a majority of the existing applets conceptualize fraction division as measurement while other conceptualizations of fraction division are underrepresented. Among the various representations used, the length model in the form of fraction bar and area model are the predominant choices, with the number line representation being notably less prominent. The results from this study also show that although most applets attempt to visualize the process of fraction division, there are limited opportunities in most applets for users to enact mental actions associated with fraction division, such as partitioning, unitizing, iterating, and disembedding. These results not only increase our understanding of the affordances and limitations of existing applets for fraction division so that we can become more intentional in our choice of them but also inform the design of new applets that support students’ development of a rich and robust understanding of fraction division.

Cross-notation knowledge of rational numbers predicts fraction arithmetic.

Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. To examine the extent to which children's earlier knowledge of cross-notation magnitude predicted subsequent performance in fraction addition and subtraction as well as fraction multiplication and division longitudinally. Three hundred and fifty-four Chinese children (Mage = 112.1 months). During the first wave of assessment, a range of cognitive abilities of children were measured, including within-notation fraction and decimal magnitude comparisons, whole-number arithmetic fluency, non-verbal intelligence, attentive behaviours, counting recall, word-level reading, and phonological awareness. Twelve months later, the same children were assessed again with two tasks of fraction arithmetic: fraction addition and subtraction as well as fraction multiplication and division. Multiple linear regressions showed that within-notation fraction and decimal magnitude knowledge predicted fraction addition and subtraction longitudinally, after the effects of working memory, nonverbal intelligence, language skills, attentive behaviour, and whole-number arithmetic were controlled. Cross-notation magnitude knowledge made independent contributions to fraction addition and subtraction longitudinally beyond the influence of within-notation fraction and decimal magnitude knowledge and other covariates. However, within-notation fraction and decimal magnitude knowledge were not associated with fraction multiplication and division, whereas cross-notation magnitude knowledge remained a unique predictor. These findings suggest that it may be useful to incorporate cross-notation knowledge in the assessments of children's mathematics abilities and teaching.

Penerapan Model Problem Based Learning Untuk Meningkatkan Hasil Belajar Matematika Tentang Perkalian dan Pembagian Pecahan

Student learning outcomes in learning fractions in elementary school are still low, to overcome this problem an effective model is needed. This research aims to describe the improvement in learning outcomes for multiplication and division of fractions using the PBL model in class V of SD Negeri 057761 Kwala Gebang. The research was carried out in two cycles, namely cycle I and cycle II. Each cycle consists of four stages, namely planning, implementation, observation and reflection. The subjects of this research were 7 class V students at SD Negeri 057761 Kwala Gebang. Research results: RPP observations in cycle I averaged 83.33%, increasing to 97.22% in cycle II. In the observation results from the teacher aspect of cycle I, the average was 73.21%, increasing to 96.42% in cycle II. In the observation results from the student aspect of cycle I, the average was 64.28%, increasing to 92.85% in cycle II. Meanwhile, the learning outcomes of students in cycle I obtained 54.54% completeness, increasing to 95.45% completeness in cycle II. It can be concluded that the PBL model can improve student learning outcomes in learning multiplication and division of fractions in class V of SD Negeri 057761 Kwala Gebang.

Three Perspectives for Solving Fraction Division Application Problems after “Removing the Equation”

Three Perspectives for Solving Fraction Division Application Problems after “Removing the Equation”

Beyond computation: Assessing in-service mathematics teachers’ conceptual understanding of fraction division through problem posing

Problem posing has long been recognized as a critically important teaching method and goal in the area of mathematics education. However, few studies have used problem posing to assess in-service teachers’ mathematical understanding. The present study investigated in-service teachers’ mathematical understanding of fraction division, which is often considered challenging content in elementary school, from three angles: computation, drawing, and problem posing. Two studies involving 66 and 193 primary and middle school teachers were conducted to reveal the in-service teachers’ mathematical understanding and whether drawing and problem posing affected each other. Although the in-service teachers rarely had the opportunity to pose mathematical problems in their daily teaching, they were able to pose mathematical problems in this study. In addition, problem-posing tasks were more useful in diagnosing the in-service teachers’ conceptual understanding than were computation or drawing. Thus, problem posing seems to have contributed to their conceptual understanding of fraction division on the drawing task.

초등학교 수학 교과의 원격수업에서 나타나는 교사의 수학적 주목하기

This study aims to explore the impact of the characteristics of remote learning on the overall mathematics classroom. Adapting Lobato et al.'s (2013) notion of “noticing as a phenomenon distributed across individual cognition, social interactions, material resources, and normed practices (p. 809),” the present study reports on similarities and differences in mathematical noticing of two elementary teachers who conducted remote learning on fractions division and how what each teacher noticed was shaped by other elements of their classroom. Although the two teachers taught the same lesson with similar tasks, there were distinct differences between the two teachers' classrooms. Similar to previous studies reporting on students' mathematical noticing, the differences in teachers' centers of focus emerged as a result of focusing interactions, features of mathematical tasks, and the nature of mathematical activities during remote learning. We concluded the study by suggesting the importance of focusing on teachers’ mathematical noticing, implications for future research, and effective professional development design for remote learning.

Fraction Division Representation-Experience in a Teacher Education Course Focused on the Reference Unit

This study focuses on the knowledge revealed and developed by Elementary Mathematics teachers, in a teacher education course related to the representation of fraction division and the flexibility of the reference unit. The teachers solved a task aimed at mobilizing (and accessing) their knowledge related to their approaches to the sense of division, representation, and reference unit regarding fraction division. The results suggest that teachers face challenges when representing and justifying fraction divisions using pictorial models, especially when the divisor is a non-unit fraction. This is based in a gap regarding the flexibility of the reference unit to which the numbers refer in their representations, as well as a challenge concerning the sense of fraction division and the different forms of representation. With this research we intend to contribute to reducing the scarcity of empirical studies in the area and the importance of this specialized teachers’ knowledge to deal with this topic.

Automatic Detection of Fiber Optic Gyroscope Intrinsic Frequency Based on Optimal Projection Approximation

To address the complexity and low detection accuracy issues in the intrinsic frequency detection process of fiber optic gyroscopes, a highly precise automatic measurement method based on optimal projection approximation is proposed. Building upon the digital closed-loop fiber optic gyroscope hardware circuit, this method generates a frequency-adjustable square wave with a 25% duty cycle through field-programmable gate array (FPGA) fractional division. Subsequently, it calculates the difference between the high and low levels of the sign bits of the modulated optical intensity signal sampled by the analog-to-digital converter (ADC). This yields an error signal related to the modulation frequency and intrinsic frequency. The modulation frequency is then approximated using the nearest projection of this error signal, thereby achieving automatic detection of the fiber optic gyroscope’s intrinsic frequency. The experimental results indicate that this method, requiring no external auxiliary equipment, enables rapid and highly accurate measurement of the intrinsic frequency of the fiber optic gyroscope. The measurement of intrinsic frequency takes approximately 300 milliseconds, achieving a measurement accuracy of up to 0.001 Hz.

Physical Layer Authenticated Image Encryption for IoT Network Based on Biometric Chaotic Signature for MPFrFT OFDM System.

In this paper, a new physical layer authenticated encryption (PLAE) scheme based on the multi-parameter fractional Fourier transform-Orthogonal frequency division multiplexing (MP-FrFT-OFDM) is suggested for secure image transmission over the IoT network. In addition, a new robust multi-cascaded chaotic modular fractional sine map (MCC-MF sine map) is designed and analyzed. Also, a new dynamic chaotic biometric signature (DCBS) generator based on combining the biometric signature and the proposed MCC-MF sine map random chaotic sequence output is also designed. The final output of the proposed DCBS generator is used as a dynamic secret key for the MPFrFT OFDM system in which the encryption process is applied in the frequency domain. The proposed DCBS secret key generator generates a very large key space of 22200. The proposed DCBS secret keys generator can achieve the confidentiality and authentication properties. Statistical analysis, differential analysis and a key sensitivity test are performed to estimate the security strengths of the proposed DCBS-MP-FrFT-OFDM cryptosystem over the IoT network. The experimental results show that the proposed DCBS-MP-FrFT-OFDM cryptosystem is robust against common signal processing attacks and provides a high security level for image encryption application.

Modified network kinetic model for coal pyrolysis with high-value products and low carbon emissions

Pyrolysis is a clean and efficient technology for the conversion of low-rank coal. Its key product is tar with high value. The complex composition of tar limits its further effective utilization. Although most kinetic models can provide the final distribution of three-phase products in coal pyrolysis, an effective prediction method for the specific composition of tar and gas has not yet been developed. Most numerical models serve to improve the total yield of volatile matter and cannot provide theoretical guidance for the improvement of tar quality or the reduction of carbon emission. Based on the basic assumptions of the CPD (Chemical Percolation Devolatilization) model for product molecules structure and generation mechanism, this paper proposed a more sophisticated method for dividing tar composition, which can achieve the division of light, medium, and heavy fractions of tar components according to boiling point. Light gas composition could be obtained with the combination of FG(Functional Group) submodel. The influence of pyrolysis final temperature, heating rate, and environmental pressure was explored for the yield and distribution of products of 18 coals. The simulation results showed that the total yield of tar was affected by both coal structure characteristics and operating parameters. Under conditions favorable for evaporation, such as low pressure and high temperature, the total yield of tar was positively correlated with the average aromatic core size in coal. Under other conditions, tar release was limited by its volatility. Coal with larger average aromatic core size corresponded to less tar yield instead. The pressure in the operating parameters had the most significant influence on the total yield of tar. The heavy fractions of tar are more sensitive to changes in operational parameters, making working conditions that increase the total yield of tar reduce tar quality. The overall carbon emission of pyrolysis is <1 kg CO2/kg tar, which is far lower than the 2–4 kg CO2/kg tar and 3–9 kg CO2/kg tar of direct and indirect liquefaction processes. Under the conditions of sufficient insulation time and no consideration of secondary reactions, the carbon emission of pyrolysis only depended on the content of carboxyl groups in the precursor functional groups. Therefore, the carbon emission intensity decreased with the increase of coal rank. For the optimization for total tar yield and tar quality, 1 atm pressure and 723–923 K temperature was optimal for low rank coals, while low temperature and heating rate with 10–20 atm pressure or high temperature and heating rate with 45–50 atm pressure were optimal for medium rank coals. For the optimization of light tar yield and tar quality, 6–9 atm pressure was optimal for low-rank coals, and 1–3 atm pressure was optimal for medium-rank coals.

Adaptive variability in children’s conceptual models of division

This study examined whether different types of commonly used mathematical tasks affect how children think about whole number division problems. Prior research suggested that children tend to rely on the partitive model to understand whole number division, which is likely problematic when students transition to learning about fraction division. We assessed variability in correct whole number division problem-solving strategies among 63 elementary school children (41.5% female, 58.5% male, 0% nonbinary/gender expansive; 69.2% White, 10.7% multiracial, 6.1% Black, 4.6% Latino, 3.3% other/unidentified, 6.1% preferred not to answer). Each participant was asked to demonstrate four whole number division problems in each of three contexts (within participants): objects, story problems, and number lines. Most children displayed understanding of multiple conceptual models of division, but strategies varied by context. Story problems elicited partitive models, number lines elicited quotative models, and objects elicited both. Finally, elementary school children used strategies adaptively. Number line representations may afford conceptual connections between earlier-learned whole number concepts and analogous later-learned fraction concepts, supporting the integration of children’s whole number and fraction knowledge.

Computer-based feedback matters when relevant prior knowledge is not activated

BackgroundHow feedback is given may influence its utility. AimWe examined the effect of activated prior knowledge on learning from feedback by manipulating whether knowledge of a foundational concept was activated before solving fraction division problems. Sample and methodsUndergraduates (N = 171) were randomly assigned in a 3 (feedback timing: delayed, immediate, or no feedback) x 2 (knowledge activation: relevant or not) between-subjects design. ResultsIf irrelevant knowledge was activated, immediate feedback enhanced learning as compared to no feedback during the learning task, whereas if relevant knowledge was activated, then there was no impact of immediate feedback. On the posttest, any feedback (immediate or delayed) resulted in greater performance, but feedback timing did not matter. Thus, activating prior knowledge moderates the effect of feedback on learning. ConclusionWhen researchers or practitioners are investigating or giving feedback, they must also consider individual differences of the learner such as the prior knowledge they bring to the task.