Teaching Of Arithmetic Research Articles

Hardware description of a simplified 4-bit softcore processor with BCD capabilities

The objective of the work reported in this paper is to improve a 4-bit softcore processor previously designed in Verilog language, keeping its compact size. This processor was thought to be used as academic and didactic tool for teaching as computers architecture subject as digital circuits subject in the technology faculty of the Universidad Distrital. The new features include arithmetic instruction with input carry, BCD operations enabling, rotating instructions, implementation of input and output register banks, increase of the number of general purpose registers of the data memory, and the reduction of the execution clock cycles per instruction. Additionally, the assembler software was enabled to support macro-instructions to make easy the comprehension of some composed functions. As result, a very compact softcore processor was obtained, by means of a Verilog description done in a single file. This implementation occupies only the 2% of the medium-size FPGA used for the application, reaching a maximum possible working clock frequency of 929 Mhz.

CONCEPTION AND MISCONCEPTION IN TEACHING ARITHMETIC AT PRIMARY LEVEL

CONCEPTION AND MISCONCEPTION IN TEACHING ARITHMETIC AT PRIMARY LEVEL

The Committee of Fifteen and the First Movements about the Teaching of Algebra in the Brazilian Primary School

At the end of the XIX century, movements that propose the reform of the primary school in the United States are started. The aim of this paper is to find out what changes proposed to the American teaching of mathematics are, specifically about the teaching of algebra and the knowledge related to it, while seeking indications of the circulation of those ideas in Brazil. To perform an historiographic research, which aims to the writing of a historic narrative, we use the theoretical contributions of the Cultural History based on Burke and Chartier and the studies about the circulation and appropriation of ideas by Oliveira and Warde. As sources of the research are the reports of those movements, textbooks on algebra and arithmetic teaching, notes from a conference given by Othello S. Reis about the insertion of algebra in the primary school, and other documents. It was found that a Committee of fifteen was created to propose changes in the U.S. primary school because of a previous study, done by the Committee of ten. One of the proposals of both committees can be highlighted: the teaching of algebra topics in the two last years of the primary school. The ideas of the committee about algebra were brought to Brazil, in an explicit way, in one conference presented by Othello S. Reis, and it was revealed that those ideas had already been presented in Antonio Trajano’s textbooks, in editions that preceded the committee’s study.

Počeci razvoja nastavnih sredstava u nastavi računa u mlađim razredima osnovne škole

The need to count multi-digit numbers has encouraged people to design aids that can help them do so, and that make it easier for students to count today. The paper defines the concept of teaching aids, gives an overview of the beginnings of the development of teaching aids for arithmetic in different cultures and presents some old teaching aids used in Serbia in the late nineteenth and early twentieth century. The aim of this paper is to point out the basics of the development of teaching aids (teaching aids) in the teaching of arithmetic in the younger grades of primary school. The purpose of this paper is to acquaint teachers with the beginnings of the development of teaching aids for arithmetic and the possibilities of their application, in order to have a more diverse approach to students during the processing of teaching content about numbers and arithmetic. The review was done by historical and comparative method.

Development of arithmetic fluency: A direct effect of reading fluency?

The present longitudinal study investigated the developmental trajectories of addition, subtraction, and multiplication fluency; their relationships to general cognitive functions; and potential interrelations between reading fluency and growth in arithmetic fluency for different operations. The central prediction was that measures of arithmetic fluency for different operations would be differentially related to reading fluency because of variations in the timing and format of arithmetic instruction. Panel data on children’s arithmetic fluency and reading fluency performance were collected twice per year in third, fourth, and fifth grades (N = 449). For each operation tested (addition, subtraction, and multiplication), a series of bivariate (reading/arithmetic) latent growth and autoregressive latent trajectory models were constructed. After controlling for background cognitive variables, significant short- and long-term relationships to reading fluency were observed only for multiplication fluency. Specifically, reading fluency in early third grade predicted both immediately subsequent multiplication fluency scores and the slope of growth in multiplication fluency across subsequent grade levels. Exploratory analyses of covariate effects showed that whole number line estimation accuracy was related to growth in multiplication and subtraction fluency, while general verbal ability had a unique relationship to subtraction fluency that was not observed for either addition or multiplication. Overall, results indicate that children’s level of reading fluency and differences among arithmetic operations should be considered both when conducting research and when making instructional decisions about how to build students’ arithmetic fluency. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

PEMBELAJARAN MATEMATIKA DENGAN PENDEKATAN REALISTIC MATHEMATICS EDUCATION (RME) BERBASIS SOAL OPEN – ENDED UNTUK MENINGKATKAN KOMUNIKASI MATEMATIKA

This research aims to determine the feasibility and effectiveness of the application of learning using social arithmetic teaching books with Realistic Mathematics Education (RME) approach based on Open-Ended problem. The research design used in this research is Research and Development (R and D) with Plomp model. Subjects in this study were students of Class VIII SMP Islam Terpadu Askhabul Kahfi 2017 / 2018. implementation design using Posttest Only Control-Group Design. The analysis used in the form of analysis of expert validation results and effectiveness test. Post test results on the class performed by the action are compared to the non-action class and to ensure it is done by (1) Complete Test, (2) Different Test, and (3) Simple Linear Regression Test. Based on the results of research and discussion, obtained the conclusion that (1) Arithmetic learning devices with RME approach developed valid is used based on the expert expert judgment. And according to the results of small and large class test, and (2) Arithmetic learning tools with RME approach developed effectively. This is indicated by (a) the average value of evaluation of classroom communication skills using 73, 42 (μ 70) and 76,6% (π 75%) classical completeness; (b) the average rate of classes using the application of mathematics learning tools with RME approach based on open-ended problem (73,42) is greater than the class that does not use the application of mathematics learning tool with RME approach based on open-ended problem (64,57) and (c) from the regression test obtained tcount = 2.012, tcount (2.012) ttable (1.99834).

EDUCATION, UPBRINGING AND CARE ON THE BANDS «HOME NEWSPAPER» (1904‒1906)

KRASIŃSKA Izabela – Dr. habil., Professor, Institute of Journalism and Information, Humanities Department, Jan Kokhanovsky University, ul. Svetokrzyska, 21D, Kielce, 25-406, Poland E-mail address: izabela.krasinska@ujk.edu.pl ORCID: https://orcid.org/0000-0002-5897-9333 To cite this article: Krasinska, I. (2019). Szkolnictwo, wychowanie i opieka na lamach «Gazety Domowej» (1904‒1906) [Education, upbringing and care on the bands «Home Newspaper» (1904–1906)]. Liudynoznavchi studii. Seriia «Pedahohika» – Human Studies. Series of «Pedagogy » , 9/41, 132–148. doi: 10.24919/2413-2039.9/41.175704 [in Polish]. Article history Received: May 28, 2019 Received in revised form: June 25, 2019 Accepted: July 20, 2019 Available online: September 24, 2019 Journal homepage: http://lssp.dspu.edu.ua/ p-ISSN 2313-2094 e-ISSN 2413-2039 © 2019 The Author. Human studies. Series of «Pedagogy» published by Drohobych Ivan Franko State Pedagogical University & Open Journal Systems. This is an open access article under the CC BY-NC-SA 4.0 license ( http://creativecommons.org/licenses/by-nc-sa/4.0/ ). On March 2, 1863, Tsar Alexander II issued an epitome on the enfranchisement peasants whose purpose was, inter alia, to pull the peasants away from the Polish Kingdom from the participation in the January Uprising, which broke out in the lands of the Russian partition in 1863. The collapse of this national-liberation spurt against the tsarist partitioner in Poland caused numerous repressions, persecution and restrictions in the social, economic and cultural life or educational. An example of this was the withdrawal of the Polish language from the general usage among others in the offices and schools and the substitution him in Russian. In the Polish Kingdom, strict concession’s system orders were imposed for publishing the press and filling the editors of the new the uprising periodicals. For example, a so-called position of a responsible editor was created who was responsible for his press crimes title. It was also difficult to launch a new magazine, because it depended on the consent of the Press Committee in St. Petersburg. Earlier, however it was necessary to apply for the support of the Governor-General of Warsaw. The development of the press in the Polish Kingdom was also limited by the introduced on 17 September 1869, preventive censorship, which prevented the free information flow from the publisher to the reader. In such difficult times there has been an appearance on the publishing and publishing house’s market of Warsaw, which was the capital of the Polish Kingdom, the new weekly magazine «Home Newspaper». The periodical was published regularly from January to December 1904, and its editor was known Warsaw’s journalist Feliks Fryze (1843–1907). Although as you could find out from the first issue of the weekly magazine, it had a practical character, it is still the case today that it may be a valuable source for research into education, upbringing and looking after children, young people and adults. On its pages we can information about the creation and functioning of the new school facilities: female schools, household schools, the Artistic School for Women, School of the Fine Arts in Warsaw and even School of the Political Sciences in Lviv. It was written about the organized reading, writing and arithmetic teaching courses for the craftsmen or workers which were held the most often in the evening after their work ended. Some attention of «Home Newspaper» also devoted to the issues of caring and educational. She informed readers about organized for children from the poor Warsaw workers’ families of the summer and medical colonies, where they could rest in the bosom of the nature and strengthen the body. Children were sick for the rickets were sent at the expense of the public charity organizations to the health resort in Ciechocinek. Teachers from the Polish Kingdom owned also the holiday homes in Zakopane, Warsaw and Zielonka; in addition, a health resort in Zakopane was established for them. Among other things, it was written about the activity of the Warsaw Christian Society for the Protection of Women, which act was approved on December 10, 1903. The society provided the necessary assistance to young single travelling women and teenage girls from the provinces who came to Warsaw in looking for a job so that they would have not become victims of the so-called «life traders». It also tried to guarantee them them the accommodation, work and even to teach them a profession. «Home Newspaper» also reported about many other organizations of the care and education, including for the servants or teenage boys from the poor families. Funding. The article has been partially funded as a part of the implementation of the research work from April 4, 2019 to December 31, 2019: Social and cultural press to 1939 , No. 665078. The competition for the mini GRANTS for financing the activities related to maintaining the continuity of the conducted scientific research or artistic activity from the resources of the Jan Kochanowski University in Kielce in 2019.

The Teaching of Arithmetic in the Teacher Training Course and the Constitution of an Expert in the Systematization of this Knowledge in Times of the New School (1950-1970)

This text seeks to highlight the processes of production, systematisation and objectivation of mathematical knowledge practised by the teacher Rizza de Araújo Porto in her trajectory, seeking to identify the constitution of her expertise in teacher training courses in the Normal courses, in Nova Escola times. In order to base the research, evidence was collected on how an expert constitutes itself in the pedagogical field, given its representativeness in its field of activity, showing the transformations of this notion over time. The text is guided by the questions: how was its convocation by the State to solve a practical problem concerning the formation of teachers in times of the New School? What are the supporting contexts that enabled the systematisation of the professional knowledge produced by it? In what way did the objectification of this knowledge occur and how did they become part of the professional training of teachers? The sources examined show the occurrence of processes of constitution of knowledge by teacher Rizza Porto, its systematisation and objectification, and the importance of putting mathematics to teach arithmetic in the route of fundamental knowledge in the course of teacher training, thus evidencing her expertise.

Research and Design of Block Cipher Special Instruction Set

The existing instructions are used to implement the block cipher algorithm with low efficient. So this paper classifies the operations in the cryptographic algorithm, and analyses the characteristics of bit width, combination and parallel mode in the cipher algorithm of different operations. Further develop the parallelism of S-box and shift instructions, improve the hybrid computing ability of arithmetic operation instructions, research and design new types of instructions for data position transformation, such as extract shift, shift insertion, data grouping and data mixing. At the last, this paper implements the cipher algorithm with the new instruction, such as DES, IDEA, BEST and other block cipher algorithms. The number of instructions is 14% ∼ 35% of Haswell processor, and 40% to 68% of the COBRA cipher processor.

Using Arm’s scalable vector extension on stencil codes

Data-level parallelism is frequently ignored or underutilized. Achieved through vector/SIMD capabilities, it can provide substantial performance improvements on top of widely used techniques such as thread-level parallelism. However, manual vectorization is a tedious and costly process that needs to be repeated for each specific instruction set or register size. In addition, automatic compiler vectorization is susceptible to code complexity, and usually limited due to data and control dependencies. To address some of these issues, Arm recently released a new vector ISA, the scalable vector extension (SVE), which is vector-length agnostic (VLA). VLA enables the generation of binary files that run regardless of the physical vector register length. In this paper, we leverage the main characteristics of SVE to implement and optimize stencil computations, ubiquitous in scientific computing. We show that SVE enables easy deployment of textbook optimizations like loop unrolling, loop fusion, load trading or data reuse. Our detailed simulations using vector lengths ranging from 128 to 2048 bits show that these optimizations can lead to performance improvements over straightforward vectorized code of up to 1.57$$\times$$. In addition, we show that certain optimizations can hurt performance due to reduced arithmetic intensity and instruction overheads, and provide insight useful for compiler optimizers.

A complementary survey on the current state of teaching and learning of Whole Number Arithmetic and connections to later mathematical content

Whole Number Arithmetic (WNA) appears as the very first topic in school mathematics and establishes the foundation for later mathematical content. Without solid mastery of WNA, students may experience difficulties in learning fractions, ratio and proportion, and algebra. The challenge of students’ learning and mastery of fractions, decimals, ratio and proportion, and algebra is well documented. Most of this research has focused on either fractions, decimals, ratio and proportion, algebra, or WNA. There is a lack of research that addresses the connection between these relevant topics. Within WNA, most research focuses on counting, computation, or solving word problems. There is a lack of research that investigates connections within WNA. This special issue is intended to bridge this research gap by explicitly highlighting the conceptual knowledge of counting, calculations, and quantity relationships, as well as the structure of word problems within and beyond WNA.

Surveying Middle-Grades Teachers' Reasoning About Fraction Arithmetic in Terms of Measured Quantities

We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. These components—each of which was grounded in past research—were attention to referent units, partitioning and iterating, appropriateness, and reversibility. A second part of the survey asked about teachers' professional preparation and history. We administered the survey to a national sample of in-service middle-grades mathematics teachers in the United States and received responses from 990 of those teachers. We analyzed responses to items in the first part of the survey using the log-linear diagnostic classification model to estimate each teacher's profile of strengths and weaknesses with respect to the four components of reasoning. We report on the diversity of profiles that we found and on relationships between those profiles and various aspects of teachers' professional preparation and history. Our results provide insight into teachers' knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling.

일제강점기 초등수학교육에 관한 연구

This study examined the legal basis of elementary school mathematics education during the 36 - year period of Japanese colonial rule. For this purpose, the education - related laws promulgated in the period of Japanese colonial rule were investigated and the major changes in the contents related to elementary mathematics education were analyzed. Compared to other subjects, elementary mathematics education was developed in a relatively stable and consistent manner. At the same time, there seemed to be a considerable difference between elementary mathematics education in the early and late 36th year of Japanese colonial rule. Arithmetic education has been changed to “Sansu” education, and arithmetic education, which was centered on numbers and calculations, has expanded to include figures, geometry, and algebraic calculations.

算数教育におけるパフォーマンス・アセスメントに 関する基礎的研究 ─ 算数教育におけるパフォーマンスの核心としての数学化に着目して ─

算数教育におけるパフォーマンス・アセスメントに 関する基礎的研究 ─ 算数教育におけるパフォーマンスの核心としての数学化に着目して ─

C. Kamiiの構成論的算数教育論の研究(II) : 筆算形式の授業実践の検討を中心として

C. Kamiiの構成論的算数教育論の研究(II) : 筆算形式の授業実践の検討を中心として

Mediating primary mathematics: measuring the extent of teaching for connections and generality in the context of whole number arithmetic

This paper is centred around a framework for studying teaching—Mediating Primary Mathematics (MPM)—developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the meditational means—both artefact- and human-based—employed by teachers. Detailed analysis of differences observed across these lessons shows that the mathematics taught can go beyond localized procedures and counting-based methods, and engage learners in mathematical activity that involves affordances for making connection and generalizing, particularly with respect to counting with composite units, a key developmental stage in WNA.

Áhrif Royaumont-málþingsins 1959 á íslenskt námsefni í stærðfræði fyrir börn

Málþing var haldið árið 1959 í Royaumont, Frakklandi, um nýja hugsun um skólastærðfræði. Royaumont-málþingið olli nokkrum straumhvörfum í hugsun um skólastærðfræði og rannsóknum á því sviði. Nýjar hugmyndir um skólastærðfræði, sem ræddar voru þar, voru nefndar nýja stærðfræðin, New Math, og tengdust hreyfingu, kenndri við Bourbaki, um endurskoðun á framsetningu stærðfræði með nútímalegum hætti, mathematique moderne. Í kjölfar málþingsins var tekið upp norrænt samstarf um greiningu á stöðu stærðfræðimenntunar á Norðurlöndum, námskrárgerð og samningu kennslubóka í tilraunaskyni. Stofnuð var nefnd, Nordiska kommittén för modernisering av matematikundervisningen, NKMM, sem stóð fyrir vinnu að verkinu á árunum 1960–1967. Megináhersla norrænu nefndarinnar var á námsefni fyrir 7 –12. bekk og ætlunin var að efnið yrði hægt að þýða og staðfæra í hverju landi fyrir sig. Einnig voru ráðnir sérfræðingar um námsefni 1.–6. bekkjar. Danskur höfundur, Agnete Bundgaard, og finnsk samstarfskona hennar, Eeva Kyttä, voru ráðnar til að rita kennslubókaflokk fyrir tvö fyrstu árin frá sjö ára aldri og Agnete Bundgaard ritaði ein kennslubækur fyrir næstu fjögur aldursstig. Flokkurinn var þýddur á íslensku frá og með 1966.Kennslubókaflokkur þessi, sem oft er nefndur Bundgaard-námsefnið, er greindur með tilliti til tillagna, sem settar voru fram á Royaumont-málþinginu um námsefni í stærðfræði fyrir barnaskóla, og borinn saman við eldra og yngra námsefni.Niðurstöður sýna að áhrif tillagna, sem kynntar voru á málþinginu, um að leggja áherslu á formgerð talnakerfisins og setja efnið fram með hjálp mengjafræðilegra hugtaka, voru mikil en dvínuðu smám saman í síðari kennslubókum. Framsetning á tölum og talnakerfi byggðum á frumtölum og deilanleika gekk í endurnýjun lífdaga í íslenskri skólastærðfræði, ásamt nálgun (e. approximation) og mati (e. estimation). Enn fremur komu síðar fram nýir efnisþættir sem ræddir voru í Royaumont, til dæmis tölfræði og líkindareikningur.

Learning and using our base ten place value number system: theoretical perspectives and twenty-first century uses

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship. It suggests that, rather than being content with accurate calculation for numbers with few digits, arithmetic instruction should develop understanding of the overall structure of the base ten place value system (including decimal fractions), and develop comfort with large (and small) numbers that are known only approximately. This would include emphasizing the role of the constituent parts (here called place value parts) into which place value notation decomposes any decimal number. Beyond this, understanding large numbers, and how numbers function in the real world, entails approximation. The notion of relative error (and its variant, percent error) is presented as a useful way to think about error. Relative error behaves in manageable ways under addition and multiplication, and any real number can be well approximated (i.e., with small relative error) by a base ten number with a small number of (non-zero) place value parts. Examples are given of using approximate computation with large numbers to clarify interesting questions.

Mathematicians and teachers sharing perspectives on teaching whole number arithmetic: boundary-crossing in professional development

Teachers and mathematicians hold different perspectives on the teaching and learning of whole number arithmetic. Though these perspectives may be complementary, sharing them across communities is challenging. An unusual professional development course for primary school teachers, initiated and taught by research mathematicians, provided a setting for productive sharing of both mathematical and pedagogical perspectives. Drawing on the theory of commognition, I analyze two lesson segments, one, designed by one of the mathematician-instructors, included a discussion of an alternate method for performing vertical subtraction; the other, initiated by a 3rd grade teacher, is a discussion of an authentic classroom activity. Through these analyses, and drawing on the notion of boundary as sociocultural differences between communities, I reveal some mechanisms of the perspective-sharing that took place, and discuss what and how the parties learned from and with each other. I also highlight the role of a participant-observer researcher as a broker in this process, supporting events of boundary-crossing in which the parties came to explicate, and sometimes change, their own perspectives on teaching and learning mathematics with respect to the perspectives of others. I propose this PD setting as a model for sharing perspectives across these communities.

Cultural transposition: Italian didactic experiences inspired by Chinese and Russian perspectives on whole number arithmetic

The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of different cultural contexts. We discuss the background theoretical issues of this approach and also give an analysis of two examples of cultural transposition experiences carried out in Italy. In particular, by means of qualitative analysis of some excerpts, discussions, and interviews, we show that the contact with different perspectives coming from China and Russia fostered educational practices and reflections on whole number arithmetic education.