How does Rasch modeling reveal difficulty and suitability level the fraction test question?

This article explains how to analyze test items in arithmetic operation with fractions to obtain the items' level of difficulty and fitness. Data were collected by using multiple-choice questions given to 50 fourth-grade students of an elementary school in Tasikmalaya city. The answers were then analyzed using the Rasch model and Winsteps 3.75 application, a combination of standard deviation (SD) and logit mean values (Mean). The score data of each person and question were used to estimate the pure score in the logit scale, indicating the level of difficulty of the test items. The categories were difficult (logit value +1 SD); very difficult (0.0 logit +1 SD); easy (0.0 logit -1 SD); very easy (logit value –SD). Three criteria were used to determine the level of difficulty and fitness of the questions: the Outfit Z-Standard/ZSTD value; Outfit Mean Square/MNSQ; and Point Measure Correlation. It resulted in a collection of test items suitable for use with several levels of difficulties, namely, difficult, very difficult, easy, and very easy, from the previous items, which had difficult, medium, and easy categories. Rasch model can help categorize questions and students' ability levels.

Multifeature Contrast Enhancement Algorithm for Digital Media Images Based on the Diffusion Equation

This paper studies the processing of digital media images using a diffusion equation to increase the contrast of the image by stretching or extending the distribution of luminance data of the image to obtain clearer information of digital media images. In this paper, the image enhancement algorithm of nonlinear diffusion filtering is used to add a velocity term to the diffusion function using a coupled denoising model, which makes the diffusion of the original model smooth, and the interferogram is solved numerically with the help of numerical simulation to verify the denoising processing effect before and after the model correction. To meet the real-time applications in the field of video surveillance, this paper focuses on the optimization of the algorithm program, including software pipeline optimization, operation unit balancing, single instruction multiple data optimization, arithmetic operation optimization, and onchip storage optimization. These optimizations enable the nonlinear diffusion filter-based image enhancement algorithm to achieve high processing efficiency on the C674xDSP, with a processing speed of 25 posts per second for 640 × 480 size video images. Finally, the significance means a value of super pixel blocks is calculated in superpixel units, and the image is segmented into objects and backgrounds by combining with the Otsu threshold segmentation algorithm to mention the image. In this paper, the proposed algorithm experiments with several sets of Kor Kor resolution remote sensing images, respectively, and the Markov random field model and fully convolutional network (FCN) algorithm are used as the comparison algorithm. By comparing the experimental results qualitatively and quantitatively, it is shown that the algorithm in this paper has an obvious practical effect on contrast enhancement of digital media images and has certain practicality and superiority.

Travelling Salesman Problem Generalized Interval Arithmetic

The travelling salesman problem is one of the famous combinatorial optimization problem and has been intensively studied in the last decades. We present a new extension of the basics problem, where travel times are specified as a range of possible values. Keywords: Fuzzy sets, Arithmetic operation on interval, least common method, travelling salesman problem.

ANALISIS KESULITAN BELAJAR SISWA BERKEMAMPUAN MATEMATIKA RENDAH BERDASARKAN GENDER

This study aims to fully describe the learning difficulties of students with low mathematical abilities in solving arithmatic division operations based on gender. This research is a descriptive qualtative research with research subjects consisting of 1 female student and 1 male student with low math ability in class IV-A SDN Bugih 1 Pamekasan with the test instrument for the comlpetion of the division count operations aninterviews. The results showed that on thr indicators of difficulty in understanding the concept, the results of the study learning difficulities in female subject (S1) and male subject (S2) in solving the division arithmetic operation, namely the two subjects did not know the concept of division as repeated subtraction. On the indicator of difficulty in applying the principle, the two subjects were unable to do the tiered division correctly because the wo principle of division to the long division. Whereas in the indicator of difficulty in solving verbal problems, the two subjects were unable to write down what wa known and what was asked of the story problem correclty.

ANALYZING CONTENT KNOWLEDGE OF PROSPECTIVE ELEMENTARY SCHOOL TEACHERS ON THE MATERIAL OF FRACTIONAL ARITHMETIC OPERATIONS

Teacher quality is one of the most influential factors in student learning. In-depth material knowledge (content) is very important for prospective teachers who will one day become teachers. Thus, analyzing and describing the Content Knowledge (CK) of prospective teachers needs to be done. The purpose of this study is to describe the CK of prospective elementary school teachers (SD/MI) on the material of fractional arithmetic operations. The subjects of this study were three students from Ar-Raniry State Islamic University of Banda Aceh. This research includes qualitative descriptive research, so that the data were analyzed using qualitative data analysis, namely data reduction, data presentation, and drawing conclusions. Data collection in this study was carried out through tests and combined with interviews so that the instruments used were test questions and interview guidelines. The study results indicate that the content knowledge of the three elementary teacher candidates was still weak, there were teacher candidates who did not understand the arithmetic operation hierarchy and still made carelessness in the concept of fractional arithmetic operations.

The Beauty of Mathematics: Learning Mathematics by Questioning

Mathematics problems may seem to have no real use in life, but this could be further from the truth. The use of mathematics is everywhere in our daily lives and, without discovering it; we apply mathematics ideas, as well as the skills we learn from executing mathematical challenges every day. Unfortunately, mathematics feedback at national examinations is deficient. A mean of between 23 to 29 percent for 5 years in a row from 2014 to 2018 is a clear indication that the training of students today for tomorrow’s workplace with concept development in context, problem solving through interactive experiences and understanding through application is missed. Over this period, the evaluation of the outcome has also shown a standard deviation almost equal to the mean or even greater than the mean for instance 2016 for paper 2 (refer to Kenya National Examinations Council Report) is a clear sign that there is a big disparity from the mean and a likelihood of a number of students scoring zeros or below 10 percent. This dismal performance in national examinations particularly in mathematics demonstrates that contextual curricula and instructions that encourage numerous structures of learning like relating, transferring, applying, experiencing and collaborating are not achieved. Therefore, this article looks into different contexts in which students learn and how they broaden their abilities to make connections, enjoy discovery, and apply the knowledge learnt. These are abilities they will need throughout their daily lives and careers. Being able to do arithmetic is of little ultimate use to an individual unless he or she can apply it. Each arithmetic operation is explored in detail for its applications in the real world problems. Real life challenges motivate ideas and provide additional settings for practice.

The Role of Phonological and Visual Working Memory in Carry Operations or Intermediate Solutions in Complex Mental Arithmetic

<p>The present research comprises four experiments designed to explore the role of visual and phonological working memory resources in carry operations or intermediate solutions in complex mental addition and multiplication. A special consideration was given to the effect of arithmetic operation on the relative involvement of visual and phonological resources in complex addition and multiplication. A pilot study was conducted prior to the experiments, aiming to examine the suitability of visual and phonological stimuli for change detection and working memory capacity estimation. Two staff of Victoria University of Wellington with normal or corrected vision attended the pilot study as participants. Pilot Experiments 1 to 4 tested the suitability for probing visual working memory (VWM) capacity of two types of visual stimulus with different feature dimensions: bars of different orientations and Gabor patches with different orientations and spatial frequencies. A single-probe change-detection experimental paradigm was used, with participants making decisions about whether or not probe items were the same as memory items presented previously. Both presentation durations and set sizes were manipulated. Stable estimates of visual working memory capacities were found when Gabor patches with varied spatial frequencies were used, suggesting its utility as a probe for estimating visual working memory capacity. Pilot Experiment 5 was designed to examine the suitability of pronounceable consonant-vowel-consonant non-words as a probe of phonological working memory (PWM). Valid estimates of PWM capacity were found for both participants, suggesting the suitability of phonological non-words as phonological stimuli of assessing PWM capacities and interfering with information phonologically-represented and maintained in working memory. Experiments 1 to 4 investigated the relative involvement of visual and phonological working memory resources in carry operations or intermediate solutions in mental addition and multiplication. Fifty-six undergraduate students of Victoria University of Wellington participated all experiments, and 48 of them provided valid data for final analysis. A dual-task interference paradigm was used in all experiments, with arithmetic tasks and visual/phonological change-detection tasks either performed alone, or simultaneously. For arithmetic tasks, double-digit addition problems and multiplication problems comprising one single-digit and one double-digit were presented horizontally and continuously, and participants reported the final solutions verbally. For visual change-detection tasks, study items were visually presented to participants for 1,000ms before they disappeared. After a 4000ms retention interval, a probe item was presented and participants judged whether the probe item was the same as one of the memory items. For phonological change-detection tasks, phonological nonwords were verbally presented to participants sequentially. After a 4000ms retention interval, a probe nonword was presented to participants, and they indicated whether or not the probe was the same as one of the study non-words. Both numbers of carry operations involved in the arithmetic problems (zero, one, and two) and levels of visual/phonological loads (low, medium, and high) were manipulated in all experiments. For all experiments, the effect of the number of carry operations on calculation performance was observed: arithmetic problems involving more carry operations were solved less rapidly and accurately. This effect was enlarged by concurrent visual and phonological loads, evidenced by significant interactions between task conditions and number of carry operations observed in the accuracy analyses of the arithmetic tasks in all experiments except Experiment 2, in which multiplication problems were solved under visual loads. These findings suggest that both visual and phonological resources are required for the temporary storage of intermediate solutions or carry information in mental addition, while for mental multiplication, only evidence for a role of phonological representations in carry operations was found. For all experiments, the greater performance impairment of carry problems than no-carry problems associated with the presence of working memory loads was not further increased by increasing load level: There were no significant three-way interactions between task conditions, number of carry operations and load levels in accuracy analyses of arithmetic tasks. One possible explanation for this absence of significant three-way interactions might be attributable to some participants switching between phonological and visual working memory for the temporary storage of carrier information or intermediate solutions as a result of decreasing amount of available phonological or visual working memory resources. In conclusion, the findings of the present research provide support for a role of both visual and phonological working memory resources in carry operations in mental addition, and a role of phonological working memory resources in carry operation in mental multiplication. Thus, it can be concluded that solving mental arithmetic problems involving carry-operations requires working memory resources. However, these results contradict the prediction of the Triple Code Model, which assumes addition mainly relies on visual processing, and multiplication mainly relies on verbal processing, while complex mental arithmetic is solved with the aid of visual processing regardless of the arithmetic operation. Thus, these results challenge the operation-specific involvement of working memory resources in complex mental arithmetic. However, it should be noted that the same arithmetic problems were solved three times by the same participants, which might have encouraged more activation in phonological processing than visual processing due to the practice effect.</p>

The Role of Phonological and Visual Working Memory in Carry Operations or Intermediate Solutions in Complex Mental Arithmetic

<p>The present research comprises four experiments designed to explore the role of visual and phonological working memory resources in carry operations or intermediate solutions in complex mental addition and multiplication. A special consideration was given to the effect of arithmetic operation on the relative involvement of visual and phonological resources in complex addition and multiplication. A pilot study was conducted prior to the experiments, aiming to examine the suitability of visual and phonological stimuli for change detection and working memory capacity estimation. Two staff of Victoria University of Wellington with normal or corrected vision attended the pilot study as participants. Pilot Experiments 1 to 4 tested the suitability for probing visual working memory (VWM) capacity of two types of visual stimulus with different feature dimensions: bars of different orientations and Gabor patches with different orientations and spatial frequencies. A single-probe change-detection experimental paradigm was used, with participants making decisions about whether or not probe items were the same as memory items presented previously. Both presentation durations and set sizes were manipulated. Stable estimates of visual working memory capacities were found when Gabor patches with varied spatial frequencies were used, suggesting its utility as a probe for estimating visual working memory capacity. Pilot Experiment 5 was designed to examine the suitability of pronounceable consonant-vowel-consonant non-words as a probe of phonological working memory (PWM). Valid estimates of PWM capacity were found for both participants, suggesting the suitability of phonological non-words as phonological stimuli of assessing PWM capacities and interfering with information phonologically-represented and maintained in working memory. Experiments 1 to 4 investigated the relative involvement of visual and phonological working memory resources in carry operations or intermediate solutions in mental addition and multiplication. Fifty-six undergraduate students of Victoria University of Wellington participated all experiments, and 48 of them provided valid data for final analysis. A dual-task interference paradigm was used in all experiments, with arithmetic tasks and visual/phonological change-detection tasks either performed alone, or simultaneously. For arithmetic tasks, double-digit addition problems and multiplication problems comprising one single-digit and one double-digit were presented horizontally and continuously, and participants reported the final solutions verbally. For visual change-detection tasks, study items were visually presented to participants for 1,000ms before they disappeared. After a 4000ms retention interval, a probe item was presented and participants judged whether the probe item was the same as one of the memory items. For phonological change-detection tasks, phonological nonwords were verbally presented to participants sequentially. After a 4000ms retention interval, a probe nonword was presented to participants, and they indicated whether or not the probe was the same as one of the study non-words. Both numbers of carry operations involved in the arithmetic problems (zero, one, and two) and levels of visual/phonological loads (low, medium, and high) were manipulated in all experiments. For all experiments, the effect of the number of carry operations on calculation performance was observed: arithmetic problems involving more carry operations were solved less rapidly and accurately. This effect was enlarged by concurrent visual and phonological loads, evidenced by significant interactions between task conditions and number of carry operations observed in the accuracy analyses of the arithmetic tasks in all experiments except Experiment 2, in which multiplication problems were solved under visual loads. These findings suggest that both visual and phonological resources are required for the temporary storage of intermediate solutions or carry information in mental addition, while for mental multiplication, only evidence for a role of phonological representations in carry operations was found. For all experiments, the greater performance impairment of carry problems than no-carry problems associated with the presence of working memory loads was not further increased by increasing load level: There were no significant three-way interactions between task conditions, number of carry operations and load levels in accuracy analyses of arithmetic tasks. One possible explanation for this absence of significant three-way interactions might be attributable to some participants switching between phonological and visual working memory for the temporary storage of carrier information or intermediate solutions as a result of decreasing amount of available phonological or visual working memory resources. In conclusion, the findings of the present research provide support for a role of both visual and phonological working memory resources in carry operations in mental addition, and a role of phonological working memory resources in carry operation in mental multiplication. Thus, it can be concluded that solving mental arithmetic problems involving carry-operations requires working memory resources. However, these results contradict the prediction of the Triple Code Model, which assumes addition mainly relies on visual processing, and multiplication mainly relies on verbal processing, while complex mental arithmetic is solved with the aid of visual processing regardless of the arithmetic operation. Thus, these results challenge the operation-specific involvement of working memory resources in complex mental arithmetic. However, it should be noted that the same arithmetic problems were solved three times by the same participants, which might have encouraged more activation in phonological processing than visual processing due to the practice effect.</p>

Implementation three-step algorithm based on signed digit number system by using neural network

The need for a simple and effective system that works with high efficiency features such as high processing speed, the ability to solve problems by learning method and accomplish the largest amount of data processing accurately and in little time produces that system, which attracted the efforts of the researcher to employ neural networks in computing away from the complexities that burden traditional computers. We presented a model for the design of the arithmetic circuit for the process of addition the sign digit numbers in a new way to deal with the arithmetic operations, which employment of the use of neural networks, this model includes a theoretical and practical simulation of them. The model relied on the implementation of the addition process based on a three-step algorithm adopted by the signed systems. Which is characterized by the possibility of execution in a parallel way, and therefore it provides the advantage of completion of arithmetic operation regardless of the length of their operands, or in other words, whatever the number of bits in the operands. The simulation of the model is done by entering operands for 6 addition operations (each one has operands are 15-bit length) to be executed simultaneously.

Design and Performance Analysis of Low Power High Speed Adder and Multiplier Using MTCMOS in 90nm, 70nm, 25nm and 18nm Regime

Nowadays, VLSI technology mainly focused on High-Speed Propagation and Low Power Consumption. Addition is an important arithmetic operation which plays a major role in digital application. Adder is act as an important role in the applications of signal processing, in memory access address generation and Arithmetic Logic Unit. When the number of transistors increases in system designs, makes to increase power and complexity of the circuit. One of the dominant factors is power reduction in low power VLSI technology and to overcome the power dissipation in the existing adder circuit, MTCMOS technique is used in the proposed adder. The design is simulated in 90nm, 70nm, 25nm and 18nm technology and then comparison is made between existing and proposed system in the context of energy, area and delay. In this comparison, the efficiency metrics power and delay are found to be reduced 20% from the existing adder and the proposed adder is used for the design of low power multiplier.