Teaching Of Arithmetic Research Articles

CUDASW++4.0: ultra-fast GPU-based Smith–Waterman protein sequence database search

BackgroundThe maximal sensitivity for local pairwise alignment makes the Smith-Waterman algorithm a popular choice for protein sequence database search. However, its quadratic time complexity makes it compute-intensive. Unfortunately, current state-of-the-art software tools are not able to leverage the massively parallel processing capabilities of modern GPUs with close-to-peak performance. This motivates the need for more efficient implementations.ResultsCUDASW++4.0 is a fast software tool for scanning protein sequence databases with the Smith-Waterman algorithm on CUDA-enabled GPUs. Our approach achieves high efficiency for dynamic programming-based alignment computation by minimizing memory accesses and instructions. We provide both efficient matrix tiling, and sequence database partitioning schemes, and exploit next generation floating point arithmetic and novel DPX instructions. This leads to close-to-peak performance on modern GPU generations (Ampere, Ada, Hopper) with throughput rates of up to 1.94 TCUPS, 5.01 TCUPS, 5.71 TCUPS on an A100, L40S, and H100, respectively. Evaluation on the Swiss-Prot, UniRef50, and TrEMBL databases shows that CUDASW++4.0 gains over an order-of-magnitude performance improvements over previous GPU-based approaches (CUDASW++3.0, ADEPT, SW#DB). In addition, our algorithm demonstrates significant speedups over top-performing CPU-based tools (BLASTP, SWIPE, SWIMM2.0), can exploit multi-GPU nodes with linear scaling, and features an impressive energy efficiency of up to 15.7 GCUPS/Watt.ConclusionCUDASW++4.0 changes the standing of GPUs in protein sequence database search with Smith-Waterman alignment by providing close-to-peak performance on modern GPUs. It is freely available at https://github.com/asbschmidt/CUDASW4.

Literary and Arithmetic Schools of Uktus Factory (1735–1742): A Historical Analysis

This article examines the activities of the schools established at the Uktus Factory, initiated by the proactive policies of V.N. Tatischev during his tenure as the head of the factories (1734–1739), aimed at engaging children from all factory residents in formal education. The study establishes enrollment figures for the schools over three-year intervals, details collective recruitment efforts, and presents the total number of students taught literacy and basic mathematics, alongside an analysis of the social and age demographics of the pupils. It demonstrates that during the establishment of a network of factory schools in 1735–1736, the movement of skilled workers to other factories due to production needs rarely interrupted children’s education, often resulting in a turnover of students at Uktus. The article characterizes the teacher, exiled Nikita Afanasyev, highlighting his proactive approach to enhancing the organization of literacy instruction. It identifies key dates regarding the commencement of arithmetic education at the Uktus Literary School in Yekaterinburg, the founding of the arithmetic school at the Uktus Factory, and the appointment of top students from the Yekaterinburg school to teach Uktus children under the supervision of teachers Fyodor Sannikov and Afanasy Kichigin. The reasons for the closure of the schools at the Uktus Factory in autumn 1742 and the sharp decline in student enrollment from 1743 onwards are also analyzed.

Affective and cognitive factors associated with Chinese and Italian children’s arithmetic performance

BackgroundThis study aimed to investigate the cognitive and affective factors associated with cross-cultural differences in arithmetic tasks.MethodsA total of 404 third- and fourth- graders were recruited from China and Italy to complete exact arithmetic, arithmetic estimation and cognitive tasks (i.e., short-term memory, executive functions, and fluid reasoning). Their mathematical anxiety was also measured.ResultsThe results showed that Chinese children performed better than Italian children in both arithmetic tasks and in shifting task. Italian children performed better in visuospatial updating task and reported higher levels of mathematical anxiety than their Chinese peers. Multi-group path analyses showed that the patterns of relations among cognitive factors (i.e., short-term memory, inhibition and shifting), mathematical anxiety, and arithmetic performance were similar across groups. The only exception was that visuospatial updating uniquely predicted arithmetic estimation for Chinese but not for Italian children.ConclusionsChinese children outperformed their Italian peers in the exact arithmetic task, likely due to the greater emphasis on arithmetic fluency in Chinese mathematics education, both in schools and at home. They also had a slight advantage than Italian peers in the arithmetic estimation task. The unique link between updating and arithmetic estimation found in Chinese children but not Italian children suggests that, although arithmetic estimation is not emphasized in the curricula of either country, instruction and practice in exact arithmetic may enhance Chinese children’s efficiency in solving arithmetic estimation problems.

THE IMPORTANCE OF MATHEMATICS LEARNING IN DEVELOPING EARLY CHILDHOOD NUMERACY SKILLS

This study describes the importance of mathematics learning in developing early childhood numeracy skills. This research uses a qualitative descriptive method, with the subject being a 3-year-old child. Data collection was done through direct observation and interviews. The results show that children have difficulty understanding the concept of numbers. Still, using appropriate methods such as counting games with candy, number recognition through pictures, and using clay to form numbers can improve children's counting skills. Effective and fun maths learning can provide a strong foundation for children's future thinking and problem-solving skills. Therefore, educators and parents must provide exciting and effective arithmetic education to build a strong foundation for children's cognitive abilities.

PENGARUH PENERAPAN MODUL AJAR ARITMATIKA SOSIAL PADA KEMAMPUAN PEMECAHAN MASALAH DAN PEMAHAMAN LITERASI FINANSIAL

The tendency in math learning in classrooms is for teachers to explain the material according to what is in the available textbooks without making efforts to develop learning in accordance with the contextual realities of students' daily lives. As a result, students face difficulties in solving mathematical problems when encountering issues different from the example problems provided by the instructor. This research aims to implement a problem-based social arithmetic teaching module based on the contextual approach of Papua. The subsequent application's results will be observed to determine if it has an impact on students' problem-solving abilities and financial literacy comprehension in elementary schools. The research stages include preparation, implementation, and evaluation. Data collection for this research is done through observation, interviews, and tests of students' problem-solving abilities and financial literacy comprehension. The research findings indicate that there is a partial difference in problem-solving abilities and financial literacy comprehension between students taught with the arithmetic teaching module and those taught with the conventional teaching module used in schools. It can be concluded that there is a partial influence on students' problem-solving abilities and financial literacy comprehension taught using the arithmetic teaching module and those taught using the conventional teaching module used in schools.

The effect of a Schema-based method on correcting persistent errors in mental arithmetic: an experimental study.

Arithmetic calculation is a fundamental skill for mathematical learning and daily life. However, elementary school students often make errors in practice. Grounded in the schema theory and the memory retrieval theory of mental arithmetic, this study employs a controlled experiment to investigate the effect of a schema-based method in correcting persistent errors in mental arithmetic, specifically in the context of simple addition operations. The experimental group utilizes a schema-based method to help participants rectify incorrect answers in memory retrieval, while the control group did not receive this treatment. The results showed that significant differences emerged between the experimental and control groups in both the post-test performance and the reduction of persistent error count, indicating that the experimental group had rectified incorrect answers in memory; and persistent errors in simple addition were indeed caused by interference from incorrect answers during memory retrieval; and the schema-based method proves to be effective. The findings of this study contribute to enhancing practical mental arithmetic instruction, assisting students in correcting relevant errors, and improving their mental arithmetic abilities. Not only does it offer directive guidance for teaching practices, but it also provides an enlightening reference for promoting innovative teaching methods.

Improving mental arithmetic ability of primary school students with schema teaching method: An experimental study.

Skillful utilization of mental arithmetic can significantly improve students' mathematical computation ability. However, it was observed that primary school students often resort to reiterating the process of written arithmetic in their minds during mental arithmetic, which is not conducive to their numerical ability improvement. This paper devises a set of graphic teaching aids for primary school students' mental arithmetic improvement based on mental arithmetic strategies, schema theory, and working memory. To validate the effectiveness of schema teaching in enhancing mental arithmetic ability among primary school students, a controlled experiment was conducted with two groups of third-grade students randomly selected from a primary school in Jingshan City. The results, obtained through descriptive statistical analysis and the multitrait-multimethod approach (MTMM), indicated that the experimental group (n = 52) demonstrated significant improvements in speed, accuracy, and stability in mental addition and subtraction after a 14-day instruction period in schema teaching. This study offers a potent mental arithmetic teaching strategy for elementary mathematics education, which can lead to a comprehensive enhancement of students' mental calculation abilities. It also holds promise for inspiring innovative teaching methodologies in primary and secondary mathematics education in the future.

Improving Multicore Architectures by Selective Value Prediction of High-Latency Arithmetic Instructions

Improving Multicore Architectures by Selective Value Prediction of High-Latency Arithmetic Instructions

Explaining procedures and interleaving practice in fraction arithmetic

BackgroundExplicit instruction is a pedagogical approach in which students are taught step-by-step procedures for solving problems and practice using the procedures. Despite considerable evidence supporting the use of this general approach, relatively little is known about how varying specific design features impact its effectiveness. AimsThis preregistered study investigated the impact of two design features, explaining rationales for procedures and practicing in interleaved sequence, on the efficacy of explicit instruction in fraction arithmetic. SampleParticipants were 156 sixth to ninth grade children. MethodsChildren received a brief intervention involving explicit instruction in fraction arithmetic procedures. They were randomly assigned to receive or not receive explanations of rationales for the procedures, and to practice different procedures in either interleaved or blocked sequence. ResultsRelative to pretest, accuracy improved on immediate and delayed posttests (Cohen's d = 0.88 and 0.55 respectively). The magnitude of this improvement was not affected by either experimentally-manipulated factor or by both of them together. ConclusionsThe results support the use of explicit instruction in fraction arithmetic, but provide no evidence that explaining rationales for procedures, or interleaving practice thereof, increases the effects of such instruction on procedural knowledge.

The impact of teaching with schemas on structural word challenges

Instruction is adapted for students having a specific learning disability (SLD) that focuses on the fundamental structure of maths recommending problems as an evidence-based practice. Additionally, evidence-based schema-based education is viewed as a practical strategy for students with an SLD. This study expanded upon earlier efforts by (a) utilizing the implementer and a teacher, (b) assessing a flexible intervention's efficiency, and (c) assessing the performance of students on integrated and generalized schema structure issues. There were 12 impaired fourth and fifth graders receiving extra maths teaching in a resource room. The intervention package included arithmetic education based on schema and a problem-solving mnemonic. A multiple-probe approach involving different participant a functional connection was done using groups. Students performed better when given straightforward, generic, and integrated schema structures. The aggregate normalized mean difference between cases (BC-SMD) for this study was 3.05 (CI95 [2.54, 3.60]), while aggregate “Tau-U effect size (ES) was 95% (CI90 [83%, 100%]”).

Design of a High Performance Vector Processor Based on RISIC-V Architecture

This paper proposes a high performance Vector processor based on the high performance Embedded Core which is named TS800. The TS800 is a 4-core processor based on RISC-V architecture, implements IMAFDV instruction set, supports L2 Cache, branch prediction, sequential pipeline, and dual-issue structure. The traditional CPU mainly supports Scalar calculations, or only supports Vector calculations. For applications such as image and signal processing, there are a large number of data parallel computing operations. To solve the problem of low performance of parallel data calculations in industrial power applications, it is proposed to add VPU hardware implementation in the TS800. The TS800 can support FFT algorithm, adaptive controllers Reinforcement learning and learning-based underlying algorithm requirements. In this paper, the module and data flow between each processing unit and the control circuit, that is, the hardware realization of VPU module are proposed. Large-area units such as float arithmetic, multiplication and division are multiplexed with the Scalar operator in the CPU, while the control circuit is placed in the VPU-ALU, and the area is small. Units such as arithmetic and logic operation instructions, shift operation instructions, comparison operation instructions, and permutation instruction are implemented through the VPU-ALU, which makes the overall design area smaller and the performance better. At the same time, through the fir, fft, conv, matrix, Signal Converge and variance test, it is proved that while executing the same program, the running time of the cpu only with Scalar is 1.44 to 9.55 times that of the CPU with Vector module, which can support the underlying algorithm of the adaptive controller.

HEaaN.MLIR: An Optimizing Compiler for Fast Ring-Based Homomorphic Encryption

Homomorphic encryption (HE) is an encryption scheme that provides arithmetic operations on the encrypted data without doing decryption. For Ring-based HE, an encryption scheme that uses arithmetic operations on a polynomial ring as building blocks, performance improvement of unit HE operations has been achieved by two kinds of efforts. The first one is through accelerating the building blocks, polynomial operations. However, it does not facilitate optimizations across polynomial operations such as fusing two polynomial operations. The second one is implementing highly optimized HE operations in an amalgamated manner. The written codes have superior performance, but they are hard to maintain. To resolve these challenges, we propose HEaaN.MLIR, a compiler that performs optimizations across polynomial operations. Also, we propose Poly and ModArith, compiler intermediate representations (IRs) for integer polynomial arithmetic and modulus arithmetic on integer arrays. HEaaN.MLIR has compiler optimizations that are motivated by manual optimizations that HE developers do. These include optimizing modular arithmetic operations, fusing loops, and vectorizing integer arithmetic instructions. HEaaN.MLIR can parse a program consisting of the Poly and ModArith instructions and generate a high-performance, multithreaded machine code for a CPU. Our experiment shows that the compiled operations outperform heavily optimized open-source and commercial HE libraries by up to 3.06x in a single thread and 4.55x in multiple threads.

Back to basics: A role of reading, writing, and arithmetic teaching

This study has assessed the role of reading, writing, and arithmetic teaching among adult learners in Saudi Arabia. A quantitative approach was used by recruiting 186 students divided into three groups, namely, the write to learn (WTL) group, traditional teaching group, and individual technology use (ITU) group. Statistical Package for Social Sciences (SPSS) was used for the analysis of the arithmetic and literacy test scores of the students. The findings showed that the performance of the WTL group was most effective among the three groups. The results showed that the learning capacity of adults could be improved by refining their writing and reading skills. The formative feedback, collaborative environment, and engagement helped improve the learning scores. It shows that the use of information and communication technology (ICT) should be accurately implemented along with the formation of a collaborative environment.

Addressing to Challenges about Technique, Strategy and Equity in Arithmetic Learning

Evaluation in academic organizations can be tailored to learners, preservice professionals, or educators, as individuals or as representations of a class, and for a variety of objectives. One of the primary goals of evaluation in math learning is to produce facts that may be utilized to form a decision on or enhance arithmetic education. This generates problems about which components of arithmetic proficiency must be tested, as much as when and why. Issues linked to the evaluation method and the establishment of examinations that can properly measure arithmetic ability in all of its intricacy, challenges associated to academic strategy and planning dependent on evaluation information, in addition the inverse linkage with evaluation and planning, and concerns linked to equity, like gender problems or the performance disparity of majority and minority students are all covered in this review article. The report demonstrates an understanding of the relationship among evaluation, educating, and understanding. There are significant connections among the three main categories, which have an influence on evaluation validity and necessitate the continuing evolution of evaluation procedures in quantitative education.

Contemporary Reinterpretation of the Abacus as an Arithmetic Teaching Aid

The research goal of this study is to explore the direction of the abacus by reinterpreting the role and utility of the abacus in a modern way to highlight what advantages it can be and to apply it to future learners and educational fields. Abacus education using an abacus needs to be approached from the perspectives of ‘Practical Education Theory’ and ‘Experience-oriented Education Theory’, which have a theoretical basis for experiential learning. With the development of math and arithmetic skills through the abacus learning using the teaching aid, future learners can raise their mathematical competence by positively forming a mathematical attitude such as awareness, interest, and self-concept of the subject. In order for this, the recognition of the abacus teaching aid needs to be diversified. This study suggested that the usefulness of the abacus, as a concrete manipulative, can be the tool to raise students' ‘affective competency’ for the development of mathematical skills such as attitude and interest, not just a numerical and arithmetic teaching aid. The harmonious development of both cognitive and affective achievement is important to enable students to engage in learning while maintaining interest in mathematics subjects. For this purpose, it is important for students to gain confidence in math classes, and abacus learning can be actively used in the educational field in terms of improving confidence in math classes.

Perbandingan Metode Pembelajaran NHT dan STAD pada Kemampuan Pemecahan Masalah Matematika

Mathematical problem fixing capability is one of the factors in attaining the desires of arithmetic education. Problem solving is the management of a problem using a method as a result of which it succeeds in finding the desired goal. Innovative learning is expected to increase mathematical problem-solving skills and be able to form students excited in learning. In the learning process using nht learning examples and STAD learners are actively involved. This study aims to find out the differences in students' mathematical problem-solving skills through nht and STAD type cooperative learning models. This research is experimental. The samples on this experimental were students of SMP Darussalam which consisted of 2 classes with 35 students in each class. The results of the study discovered that there are differences in students' mathematical problem-solving skills through nht and STAD type cooperative learning models. Both examples are effectively used in the learning of linear equations.

The Impact of the Implementation of Monitoring and Evaluation Reforms on the Performance of Public Elementary School Literacy and Arithmetic Education Programs in Nairobi County, Kenya

The Impact of the Implementation of Monitoring and Evaluation Reforms on the Performance of Public Elementary School Literacy and Arithmetic Education Programs in Nairobi County, Kenya

The Application of Fuzzy Delphi Method (FDM) in the Development of Fun-Driven Mobile Learning (FDML) Model for Teaching of Arithmetic in Saudi Schools

One of the methods used in Design and Development Research (DDR) is the Fuzzy Delphi Method (FDM). It is a systematic method for the development and validation of the model. This article aims to use this method to validate a Fun-Driven Mobile Learning (FDML) Model for Teaching Arithmetic. In phase 1 of design and development research, based on the opinion of teachers as subject matter experts, the need to develop the FDML model was justified. In phase 2, the model developed, comprised of thirty-two teaching activities grouped into four clusters. This article presents results on suitability and overall usefulness of the model components derived from the collective opinion of the 15 experts involved in Phase 3 of the study. The data analysis was conducted through the fuzzy Delphi method using a 7-point Likert scale. The outcome indicates a consensus of 93.4 percent of experts at a threshold value of ≤0.02. The suggested components of the FDML model include an integral planning reference for the application of the model and provided alternative validation procedures for model developers in mathematics education and educational technology.

Number Manipulation Strategy: A Model of Experiential Instruction and Interest in Arithmetic Learning of Pupils of Lower Basic Level in Enugu State, Nigeria

The study investigated the efficacy of the number manipulation strategy (NUMAS) as a model of experiential instruction and interest in arithmetic learning for pupils of lower basic levels. The population of the study consisted of 1205 lower basic III level pupils of the 2018/2019 session in Igbo-Etiti Local Government Area (L.G.A.) of Enugu State. A sample of 121 primary five pupils from 4 schools out of 53 primary schools in the study area was randomly sampled. The 121 pupils were composed of 42 males and 79 females used for the study. The study was guided by four research questions and four hypotheses. The hypotheses were tested at a p<.05 level of significance. The instruments used for the study were Arithmetic Test (ART) and Mathematics Interest Inventory Questionnaire (MIIQ) developed by the researcher. The ART and MIIQ instruments were faces validated by experts and their reliability indexes were 0.85 and 0.79 respectively, established using Cronbach alpha and split-half methods respectively. The data obtained with the instruments were analyzed using mean, standard deviations (SD), t-test and analysis of covariance (ANCOVA) statistics. Mean and SD was used in answering the research questions, while t-test and ANCOVA statistics were used in testing the hypotheses at P<.05 level of significance. The findings of the study showed that NUMAS is effective in teaching arithmetic, especially in enhancing the addition and subtraction skills acquisition of the pupils. Gender was found not to be a significant factor of variance in arithmetic achievement when the teaching of arithmetic is NUMAS based. The use of NUMAS was recommended to teachers, lower basic mathematics textbook authors and stakeholders in education, to ensure that NUMAS is adopted and adapted for use in Mathematics classroom instruction and learning.

Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching-to-a-target.

Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching-to-a-target.