Basic Arithmetic Research Articles

Designing arithmetic neural primitive for sub-symbolic aggregation of linguistic assessments

The very first step towards a challenging goal of creation of monolithic generic neuro-symbolic systems is application of sub-symbolic ideas to particular symbolic algorithms like aggregation of fuzzy linguistic assessments during Linguistic Decision Making. A novel theoretical idea is to express this aggregation as structural manipulations and translate them in a neuroalgorithm. Tensor Product Representation (TPR) methodology provides a generic framework of designing neural networks that do not require training and produce an exact result equivalent to the result of symbolic algorithms. This paper demonstrates design of TPR-based arithmetic as a basic building block for expressing linguistic assessments aggregation on a sub-symbolic level and a neural architecture for the basic arithmetic operation.

New Results on Non-Normalized Floating-Point Formats

Compulsory normalization of the represented numbers is a key requirement of the floating-point standard. This requirement contributes to fundamental characteristics of the standard, such as taking the most of the precision available, reproducibility and facilitation of comparison and other operations. However, it also imposes a high restriction in effectiveness of basic arithmetic operation implementation. In many embedded applications may be worth to sacrifice the benefits of normalization for gaining in implementation metrics. This paper analyzes and measures the effect of removing the normalization requirement in terms of precision and implementation savings for embedded applications. We propose several adder and multiplier architectures to deal with non-normalized floating-point numbers, and quantify the accuracy loss and the improvements in hardware implementation. Our experiments show that it is possible to reduce the area and power consumption up to 78 percent in ASIC and 50 percent in FPGA implementations with a reasonable accuracy loss.

Algorithm for obtaining palindromes of the binary number system

The aim of this paper is to describe a new method for searching all binary palindromes that have a given number of the binary digits. The main result is presented in the form of an algorithm. The obtained algorithm is based on the use of the regularity revealed in the course of the study, based on the application of basic arithmetic operations with palindromes that have a various number of the binary digits. The paper also provides examples of using this algorithm to obtain binary palindromes with different number of the binary digits. The algorithm formulated here can be applied to analyse computer data written in the form of a binary code.

Unpacking Mathematics Pedagogical Content Knowledge for Elementary Number Theory: The Case of Arithmetic Word Problems

“Number” is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader’s mathematical misconception, but most of them were unable to precisely indicate the third grader’s error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers’ MPCK in teaching arithmetic word problems.

MXene Ti3C2 memristor for neuromorphic behavior and decimal arithmetic operation applications

MXene Ti 3 C 2 , as the emerging member of two-dimensional (2D) materials family, has been applied to memristor and exhibited fast pulse modulation time and miniaturization size. However, the current abrupt behavior of switching processes hampered its further applications as a neuro-bionic device. Here, we present a facile method to improve the electronic performance of 2D MXene Ti 3 C 2 -based memristor by Ag nanoparticle doping. Compared to the pure Ti 3 C 2 device, the Ag nanoparticle doping method exhibits a bidirectional continuous current transition behavior. Then, the variation trend of excitatory postsynaptic current (EPSC) was analysis in detail, and the transition rule of short-term potentiation (STP) to long-term potentiation (LTP) was systematically summarized. More interestingly, the energy consumption of generate one spike in unit device is as low as 0.35pj. And the memristor has ability to implement decimal arithmetic operations such as addition and multiplication. Exploration of the microstructure and finite element analysis (FEA) shows that the atomic vacancies capture the metal ions to form the filaments. This work provides a facile method to improve the electronic neuromorphic performance of MXene Ti 3 C 2 memristor, which will considerably promote the diversification development of 2D materials in the field of neuro-morphology chips and greatly enhance the practicability of 2D materials. Ag nanoparticles doping method solves the current abrupt behavior of Ti 3 C 2 memristor and then realizes the bidirectional continuous current transition in switching processes. The energy consumption of generate one spike in unit device is as low as 0.35 pj. Moreover, the Al/Ti 3 C 2 :Ag/Pt devices can implement the decimal arithmetic operation. • The Ag nanoparticle doped method in Ti 3 C 2 not only overcomes the challenge of poor electrical performance of the traditional memristor owing to the dissolution of Ag electrode under the electric field, but also realizes the bidirectional continuous current transition in switching processes. • The TEM and FEA indicated that the important “atomic vacancies capture metal ions” behavior in the MXene Ti 3 C 2 functional layer. • The energy consumption of generate one spike in unit device is as low as 0.35 pj. • We systematic demonstrated that the variation trend of excitatory post-synaptic current (EPSC) of Al/Ti 3 C 2 :Ag/Pt device under different pulse conditions. • The Al/Ti 3 C 2 :Ag/Pt device has ability to achieve the basic decimal arithmetic operations such as addition and multiplication, which is the first time to demonstrate this function by 2D material based memristor.

Math study habits on deaf learners

The purpose of this study was to obtain a picture of mathematics learning habits for deaf students. The subjects in this study were 99 deaf students taken purposively in across 4 schools, including, SLB B Karya Murni Ruteng, SMPLBN Semarang, SLB B Don Bosco Wonosobo, and SLB B Denaupakara Wonosobo. The research involved a quantitative and qualitative research design where the quantitative data was taken from a set of questionnaires that included a commitment attitude questionnaire, a disciplinary attitude questionnaire and a commitment attitude questionnaire in learning mathematics; meanwhile, a qualitative data was gained through the observation of learning activities at their schools and at their boarding house. The results of the analysis showed that students’ consistent attitude, disciplined attitude, and attitude of commitment in learning mathematics were in a good category; therefore, we assumed that deaf students maintained good habits in learning mathematics. By having these good study habits, they were expected to acquire basic skills related to basic arithmetic operations that will be applied in life skills such as sewing, making patterns, carpentry, and automotive. Also, good study habits might improve their cognitive skills that impacted their study result and learning achievements that in turn enable them to reach their goals.

INALU: Improved Neural Arithmetic Logic Unit

Neural networks have to capture mathematical relationships in order to learn various tasks. They approximate these relations implicitly and therefore often do not generalize well. The recently proposed Neural Arithmetic Logic Unit (NALU) is a novel neural architecture which is able to explicitly represent the mathematical relationships by the units of the network to learn operations such as summation, subtraction or multiplication. Although NALUs have been shown to perform well on various downstream tasks, an in-depth analysis reveals practical shortcomings by design, such as the inability to multiply or divide negative input values or training stability issues for deeper networks. We address these issues and propose an improved model architecture. We evaluate our model empirically in various settings from learning basic arithmetic operations to more complex functions. Our experiments indicate that our model solves stability issues and outperforms the original NALU model in means of arithmetic precision and convergence.

Bilingualism and numerical cognition

The present study aimed to investigate the relationship between bilingualism and numerical cognition, more specifically, the way English-Portuguese bilinguals solve simple mathematical problems when these are presented in different formats (digits, English, and Portuguese) and whether their language history background has any effect on such behavior. The main results suggest that bilinguals are faster and more accurate in solving mathematical problems presented in digit format and in solving those problems presented in the written format when the language of the stimuli was the one in which they learned basic arithmetic. Also, the participants’ language background experience did not have any significance in their task performance.

Self-identification with a Virtual Experience and Its Moderating Effect on Self-efficacy and Presence

ABSTRACT Effective psychological interventions for anxiety disorders often include exposure to fearful situations. However, individuals with low self-efficacy may find such exposure too overwhelming. We created a vicarious experience in virtual reality, which enables observation of one’s experience from a first person perspective without actual performance and which might increase self-efficacy. With similarities to both traditional vicarious experiences and direct experiences, the level of self-identification with the experience was hypothesized to affect self-efficacy and its relationship with direct experiences. To test this, vicarious experiences with two distinct levels of self-identification were compared in a between-subjects experiment (). After being exposed to a vicarious experience of giving lectures on elementary arithmetic in front of a virtual audience with either a high or low level of self-identification with the public speaker, participants from both conditions actively gave another lecture. The results revealed that self-identification affected people’s self-efficacy after vicarious experience. They further revealed that self-identification is a moderator of (1) the correlation between perceived performance and self-efficacy, (2) the correlation between self-efficacy measured after the vicarious and the follow-up direct experience; and (3) the correlation between the sense of presence reported in the vicarious and in the follow-up direct experience. We anticipate that the first-person-perspective experiences with high-level of self-identification have the potential to be beneficial for training where changing people’s self-efficacy is desirable.

Revisiting Elementary Arithmetic Through the Development of Iterative Sentences: Some Brief Reflections about the Ordering of the Corresponding Teaching Activities

This experience has taken place at the School of Education of the Universidad Complutense de Madrid. The goals of the subjects considered are to show how the computer can help in the teaching-learning process in Primary and/or Secondary Education and to clarify and strengthen the mathematical concepts of our students. Mastering a specific computational language or package is not a goal. We’ll focus here on a very specific problem, discussed and precised together with the second author: implementing arithmetic operators as nontrivial examples of iterative sentences (not exactly using Peano's arithmetic, but a similar constructive approach). We’ll analyse along the article why we believe the best ordering for developing the corresponding algorithm and implementing the code for the operators: power (with positive integer exponent), multiplication (by a positive integer) and addition (of a positive integer), is the reverse ordering in which they are introduced in elementary mathematics or introduced in an axiomatic.

Measurement, modeling and QALYs.

Over the past 30 years, a mainstay of health technology assessment has been the creation of modeled incremental cost-per-quality adjusted life year (QALY) claims. These are intended to inform resource allocation decisions. Unfortunately, the reliance on the construction of QALYs from generic utility scales is misplaced. Those advocating QALY-based lifetime modeled claims fail to appreciate the limitations placed on these constructs by the axioms of fundamental measurement. Utility scales, such as those created by the EQ-5D-3L instrument, are nothing more than multidimensional, ordinal scales. Such scales cannot support basic arithmetic operations. Interval scales can support addition and subtraction; ratio scales the further operations of multiplication and division. Those who advocate the construction of QALYs fail to appreciate that such an operation is only possible if the utility scale is unidimensional and has ratio properties with a true zero. The utility measures available do not meet these requirements. As we cannot produce meaningful utility values, the QALY is an invalid construct. Consequently, cost-per-incremental QALY claims are impossible to sustain and the application of cost-per QALY thresholds meaningless. As utility is a latent, unidimensional variable, the best a measure of utility could achieve would be unidimensionality and interval scaling properties. Where such measures are available, they could support claims for response to therapy. Consequently, there would be no need to continue constructing imaginary lifetime value assessment frameworks. Admitting that the QALY is a fatally flawed construct means rejecting 30 years of cost-per-QALY models.

Integer number sense and notation: A case study of a student with a mathematics learning disability

Although approximately 6% of students have a mathematics learning disability (MLD) also known as dyscalculia, little is known about how MLD impacts students beyond basic arithmetic. In this study we focused on one mathematical topic foundational to algebra – integer operations – and conducted a videotaped design experiment with one student with MLD. Through 14 teaching episodes we explored the ways in which standard mathematical tools (e.g., symbols, representations) were inaccessible and evaluated the design of alternative tools. Our detailed retrospective analysis revealed that the student had an unconventional understanding of integer quantities and symbolic notation, which resulted in issues of accessibility and persistent difficulties. Deliberate attempts to address inaccessibility revealed nuances in the student’s understanding, and suggests that both number sense and notational issues needed to be addressed in tandem. Implications for instruction are discussed.

\u201cGroupitizing\u201d: a strategy for numerosity estimation

Previous work has shown that when arrays of objects are grouped within clusters, participants can enumerate their numerosity more rapidly than when objects are randomly scattered, a phenomenon termed “groupitizing”. Importantly, the magnitude of the grouping advantage correlates with math abilities in children. Here we show that sensory precision of numerosity estimation is also improved when grouping cues are available, by up to 20%. The grouping can be induced by color and/or spatial proximity, and occurs in temporal sequences as well as spatial arrays. The improvement is strongest for participants with the highest thresholds in the random, ungrouped conditions. Taken together with previous research, our data suggest that measurements correlations between numerosity estimation and formal math skills may be driven by grouping strategies, which require a minimal level of basic arithmetic.

The relative effect of pupil absenteeism on literacy and numeracy in the primary school

ABSTRACT A literature search identified only 12 articles which had examined the relative effect of either attendance or absence on primary/elementary school children’s literacy and numeracy. However, with respect to the relative effect of both attendance and absence, no consistent picture emerged from the articles. Furthermore, for each of the articles, the conclusion about the relative effect was based on visual inspection of the relevant statistic. The second problem was overcome in the study presented in this article by using the British Ability Scales Word Reading and Basic Arithmetic scales to assess the literacy and numeracy of eleven-year-old Poor and Better Attenders. Significantly more of the former than the latter were found to have an arithmetic score significantly below their reading score. The article ends with a consideration of the implications of the study for the primary school teacher and of COVID-19 for the study’s findings.

Some diagnostics learning problems on basic arithmetic skills of junior high school students

The main obstacle in mathematics learning at junior high school level is the lack of students’ skills in performing basic operations of integers and fractions. This skill should be impeccable on elementary school level, nonetheless a big number of junior high school students experience impediment to follow the learning activities because they did not have enough pre-requisites on basic arithmetic. The similar circumstances are most probably also taken place at senior high school level. This study investigated students’ skills on basic arithmetic and then presents some analyses of diagnostic learning problems. The crucial findings in this research are various facts that might be ignored by teachers over the years, but they were alleged to be roots of the leading causes of the low student skills and understanding in basic operations of numbers. The diagnostic results will be worthwhile to improve the method and approach of mathematics teaching not only at junior high school but also at elementary school. Accordingly, the article offers several approaches to overcome the problems found in the study.

EFFECTIVENESS STUDIES OF THE LEARNING BASIC MATHEMATICAL OPERATIONS ON USERS USING EDUCATION GAMES WITH ESCALATING DIFFICULTY LEVEL IN SEVERAL TYPES OF GAMES

Mathematic is basic but fundamental knowledge, but in fact many students do not have the motivation to learn it because they think mathematic is boring. Therefore, an innovation is needed to motivate students, one of them is by using an educational game. Racing, shooting and fighting games are the most popular types of games in 2019 according to InvisionCommunity. Shooting game is a genre that used a lot in the educational games for learning math, while racing game and fighting game are not used much for educational games. This research aims to develop and measure the effectiveness of the games from these three genre of games as a means of learning elementary arithmetic at the elementary school level. The effectiveness of an educational game can be observed from the increment in learning outcomes obtained after conducting an experiment. We can know the most effective type of game in this experiment by compare the improvement in learning outcomes after playing all three games. The comparative analysis will be carried out using ANOVA. In this research, we used data from 60 participant with elementary level of education between grade 1 to 3. The results were obtained by calculating the difference in the participants' initial scores obtained from before playing the game and participants’ final scores obtained after playing the educational game. The results show that educational racing games have the highest increase of 6.3% compared to shooter games with 3% increase or fighting games with increase of 4.3%.

Job Satisfaction and Performance of Elementary School Teachers in Southern Papua, Indonesia

The high level of elementary school teacher absenteeism in Papua in general and in Southern Papua in particular has greatly impacted on teachers' performance in educating students. In this point, the elementary school students' inability in mastering basic reading, writing, and arithmetic (3-Rs) should be attributed to the low performance of elementary school teachers of Southern Papua, both inside and outside the classroom. As the researchers have widely identified the job satisfaction as one of the most predicting factors for the job performance, this study seeks to examine the job satisfaction and its eventual effects on job performance of teachers in elementary schools of Southern Papua. A survey approach was used to attain this goal. To collect the data, two types of Indonesian language version of questionnaire were distributed to a total of 1062 informants. In order that all the questionnaire were completely filled up and returned in 100% response rate by the informants, we employed a face-to-face method by asking the consent of each informant to fill-up the questionnaire and returned it directly to our team. Applying the simple linear regression analysis as a tool for analyzing data, the result showed that the coefficient value of R2 is .089 and the ρ value is .000. It inferred that 8.9 % of the job performance of elementary school teachers within the area of Southern Papua, Indonesia, is significantly positively predicted by their personal satisfaction. Though the predicting value of the job satisfaction on the performance of teachers was categorized low (8.9 %), finding of this study may be imperative for the school principals to enhance teachers' job performance in the elementary schools of Southern Papua by promoting their job satisfaction. Finding of this study may supposedly enlarge the existing knowledge on the job satisfaction and performance of teachers by providing an empirical proof from the Southern Papua context.

Multiplication-Related Classes of Complex Numbers

Summary The use of registrations is useful in shortening Mizar proofs [1], [2], both in terms of formalization time and article space. The proposed system of classes for complex numbers aims to facilitate proofs involving basic arithmetical operations and order checking. It seems likely that the use of self-explanatory adjectives could also improve legibility of these proofs, which would be an important achievement [3]. Additionally, some potentially useful definitions, following those defined for real numbers, are introduced.

Os jogos Dominó da Multiplicação e Batalha das Operações como estratégias de fixação das operações básicas de Matemática no 6º ano de uma escola do campo

O artigo tem como objetivo analisar os jogos “Batalha das Operações” e “Dominó da Multiplicação” em uma turma do 6° ano do Ensino Fundamental II de uma escola do campo, localizada no Distrito de Serra Nova, cidade de Rio Pardo de Minas (MG). Buscamos analisar como se dá a utilização dos jogos como forma de ensino e aprendizagem de Matemática envolvendo conceitos e habilidades vinculados às quatro operações básicas, adição, subtração, multiplicação e divisão. Para tanto, foi realizada uma pesquisa de natureza qualitativa, com observações acerca de como os alunos trabalham durante as atividades e suas contribuições para o ensino da Matemática. A utilização dos jogos evidenciou vantagens, tais como raciocínio rápido na resolução de questões envolvendo as quatro operações básicas. Como pontos negativos, destacam-se o barulho com tendência à euforia durante as atividades desta natureza, além do tempo necessário para trabalhar com apenas um jogo.

Clinical Trials to Combat Covid-19 (CTCC): Case Based Approach (CBA) of a NSE Listed Indian Pharmaceutical Company

Purpose Clinical Trials to Combat Covid-19 (CTCC) case study had been developed on a National Stock Exchange (NSE) listed Indian pharmaceutical company. The main intention to develop this case study was to understand how the research and development (RandD) and innovative activities were being performed during crisis period to combat Covid-19. Design / Methodology / Approach The study period to develop this case was May 2020 to June 2020. Published official reports and press releases were considered for the study. Basic arithmetic and statistics had been incorporated for data driven analysis and interpretation. Microsoft Excel (most updated version) had been used for econometrics analysis and visual representation. Content Analysis Technique had been adopted to draw appropriate information, insights, and inferences. Trendline Analysis of the share price had been performed with the help of Y = mx + c regression equation with a univariate variable. Findings Clinical trial endeavor being rendered by the sample company subsequently made enable to obtain approval from the regulatory body (DGCI), which impacted share price increase by 9% and this increment was supported by R Square value 1 (100%) followed by the increment value of 29.64x (where x was independent variable). There was a linear upward trend observed. It had been found that the company became 1st in India to initiate clinical trial to combat Covid-19 on two specific drugs Favipiravir and Umifenovir. The company’s clinical trial study dubbed ‘FAITH trial’ would involve 158 hospitalized patients in India who had moderate symptoms of coronavirus infection. Leadership during the crisis period had also been observed with the dedicated activities of the RandD team of the company. At last, it had been found that the company is extremely optimistic and confident with their dedicated and painstaking efforts to provide the answer of the unknown through their innovative activities and serve the nation as well as the entire world with innovative healthcare solution to combat Covid-19 and finally the company would eagerly wait for those days to come.