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Relevant bibliographies by topics / Multiplication table

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Academic literature on the topic 'Multiplication table'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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Journal articles on the topic "Multiplication table"

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Abrahamson, Dor, and Christian Cigan. "A Design for Ratio and Proportion Instruction." Mathematics Teaching in the Middle School 8, no. 9 (2003): 493–501. http://dx.doi.org/10.5951/mtms.8.9.0493.

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This article describes a method for teaching ratio and proportion in a fifthgrade classroom. Our unit design creates and follows a learning path that begins with revisiting multiplication as repeated addition. It then explores patterns in the multiplication table and moves to the concept of rate as a single column out of the multiplication table. Next, students discuss ratio as two linked rate columns, or a ratio table, then look at two rows out of a ratio table, or a proportion quartet. As a fifth-grade introduction to ratio and proportion, this unit focuses on integer cases, that is, situations in which the question mark in a:b = c:? is an integer. This emphasis fosters multiplicative reasoning in a developmentally appropriate numerical environment.

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Asghari, Amir H. "Wonders of Multiplication Table." Mathematics Enthusiast 22, no. 3 (2025): 375–96. https://doi.org/10.54870/1551-3440.1675.

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Gierdien, Faaiz. "More than multiplication in a 12 × 12 multiplication table." International Journal of Mathematical Education in Science and Technology 40, no. 5 (2009): 662–69. http://dx.doi.org/10.1080/00207390802641684.

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Kadiev, P. A., and I. P. Kadiev. "Formation of orthogonal latin squares by index structuring of n-set multiplication tables." Herald of Dagestan State Technical University. Technical Sciences 47, no. 3 (2020): 71–81. http://dx.doi.org/10.21822/2073-6185-2020-47-3-71-81.

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Objective. Formation of structurally perfect orthogonal Latin squares by the method of index ordering of the multiplication table elements of n-sets based on the multiplication table. Methods. Orthogonal Latin squares are formed by the method of index structuring of n-set multiplication tables. Results. A method is proposed for constructing structurally perfect orthogonal Latin squares of pairs of indexed finite sets of odd dimension, based on the index ordering of an nxn-array of elements in the multiplication table. A distinctive feature of the proposed method for constructing structurally perfect orthogonal squares from elements of two indexed sets of the same dimension is the use by the authors of the method of permutations of elements of the original nxn-matrix configurations, with the formation of index-ordered or index-structured combinatorial configurations. Conclusion. The use of the method for constructing a family of orthogonal Latin squares for pairs of indexed finite sets of the same odd dimension by the elements forming their multiplication table by the method of index structuring based on the principle of functional dependency of the index values on pairs of set elements and index values on pairs of elements from its environment allows creating a specific class orthogonal configuration, which, in terms of element indices, easily demonstrates their orthogonality.

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Grabauskienė, Vaiva, and Oksana Mockaitytė-Rastenienė. "AN EXPRESSION OF MATHEMATICAL CONNECTIONS IN MULTIPLICATION-RELATED THINKING IN THIRD AND FOURTH GRADES OF PRIMARY SCHOOL." ŠVIETIMAS: POLITIKA, VADYBA, KOKYBĖ / EDUCATION POLICY, MANAGEMENT AND QUALITY 11, no. 1 (2019): 9–29. http://dx.doi.org/10.48127/spvk-epmq/19.11.09.

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Mathematical comprehension is closely related to a cognition of mathematical connections. A multiplication is a mathematical operation characterized by complex mathematical connections. Students are early introduced with the multiplication. Therefore, in primary school, not so developed cognition of mathematical connections may become a reason for difficulties in Maths. A functionality of concept is based on a view to a multiplication. The analysis scientific literature revealed that a thinking of multiplication can be either additive or multiplicative. Additionally, the multiplication learning has a variety of additive and multiplicative explanations. Because they use different specificity of visualization, the models are not equally suitable for teaching children about different properties of multiplication. Based on research, in Math classes, students are only introduced with few of the models, not covering a whole variety of them. In the research, a paper and pencil type of survey consisted of 157 participants from 3rd and 4th Grades, eight different classes from four different schools. The students had to fill the table explaining multiplication of 5 x 12 in a form of writing and drawing. The quantitative analysis of results has showed that in Grades 3 to 4, the additive view to multiplication is much more prevalent, in comparison to the multiplicative reasoning. The array model is used often but not in an extensive way. The students do not know other types of multiplicative type models. In conclusion, the results showed that students of Grades 3rd and 4th knew not enough about the mathematical connections. Therefore, teachers should pay more attention to teaching students various ways of visualizing, for children, to obtain a comprehensive understanding of the multiplication process. Acknowledgement. This work was supported by a grant (No. 09.2.1-ESFA-K-728-01-0040) from the ESFA. Keywords: additive reasoning, multiplication learning, multiplicative reasoning, primary mathematics education.

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Tierney, Cornelia C. "Patterns in the Multiplication Table." Arithmetic Teacher 32, no. 7 (1985): 36–40. http://dx.doi.org/10.5951/at.32.7.0036.

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In elementary school, great importance is placed on memorization of number facts. In teaching fifth through eighth graders, 1 have assumed that most of my students had made a concerted effort to memorize facts in earlier grades. I have observed. however, that children who have had a similar amount of practice have a great range of recall. A few students complete tests of 100 multiplication or division facts perfectly in less than three minutes, whereas others are made miserable by the whole process. They skip many problems, look around the room to compare their progress with that of other students, and finally give up with few correct answers. Although those who have memorized the facts do better than others at whole-number arithmetic, they do not always do well in work with fractions.

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Husain, Mariya, and Lubna Ali Mohammed. "Examining the Effectiveness of Using Rhymes on Improving the Learning of Multiplication Times Tables in Year 3 Students in Dubai." International Journal of Emerging Issues in Social Science, Arts, and Humanities 03, no. 01 (2024): 34–45. https://doi.org/10.60072/ijeissah.2024.v3i01.004.

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This study investigates the effectiveness of using rhymes to enhance the learning of multiplication timetables among Year 3students at The Westminster School in Dubai. A total of 66 students were selected and divided into two groups: an experimental group and a control group, each comprising 33 students. Over three weeks, the experimental group learnt the 3, 4, and 8 times tables through specific rhymes—"Row Row Row Your Boat" for the 3 times table, "Twinkle Twinkle Little Star" for the 4 times table, and "This Old Man" for the 8 times table. The control group received traditional instruction without rhymes. The study utilised a pre-test and post-test design to measure the student’s ability to recall multiplication facts before and after the intervention. The outcomes were quantitatively analysed through an independent two-sample T-test and assessed the mean differences in learning outcomes between the control and experimental groups. The results indicated that using rhymes significantly improved the student's understanding and retention of multiplication facts. Students in the experimental group exhibited higher levels of engagement, enthusiasm, and motivation compared to the control group. This increased engagement was reflected in their improved performance on multiplication tests.The findings suggest that incorporating rhymes into mathematics instruction can be a highly effective strategy for teaching multiplication tables, fostering both cognitive and affective gains in students.

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Kan, Fu-Jung, Yan-Haw Chen, Jeng-Jung Wang, and Chong-Dao Lee. "Efficient Scalar Multiplication of ECC Using Lookup Table and Fast Repeating Point Doubling." Mathematics 13, no. 6 (2025): 924. https://doi.org/10.3390/math13060924.

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Reducing the computation time of scalar multiplication for elliptic curve cryptography is a significant challenge. This study proposes an efficient scalar multiplication method for elliptic curves over finite fields GF(2m). The proposed method first converts the scalar into a binary number. Then, using Horner’s rule, the binary number is divided into fixed-length bit-words. Each bit-word undergoes repeating point doubling, which can be precomputed. However, repeating point doubling typically involves numerous inverse operations. To address this, significant effort has been made to develop formulas that minimize the number of inverse operations. With the proposed formula, regardless of how many times the operation is repeated, only a single inverse operation is required. Over GF(2m), the proposed method for scalar multiplication outperforms the sliding window method, which is currently regarded as the fastest available. However, the introduced formulas require more multiplications, squares, and additions. To reduce these operations, we further optimize the square operations; however, this introduces a trade-off between computation time and memory size. These challenges are key areas for future improvement.

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Mehdizadeh, Marzieh. "The multiplication table for smooth integers." Journal of Number Theory 219 (February 2021): 172–97. http://dx.doi.org/10.1016/j.jnt.2020.09.019.

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Krasnobayev, V. A., A. S. Yanko, and D. M. Kovalchuk. "METHODS FOR TABULAR IMPLEMENTATION OF ARITHMETIC OPERATIONS OF THE RESIDUES OF TWO NUMBERS REPRESENTED IN THE SYSTEM OF RESIDUAL CLASSES." Radio Electronics, Computer Science, Control, no. 4 (December 3, 2022): 18. http://dx.doi.org/10.15588/1607-3274-2022-4-2.

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Context. Implementation of modular arithmetic operations of addition, subtraction and multiplication by a tabular method based on the use of the tabular multiplication code. The object of the study is the process of tabular implementation of basic arithmetic operations on the residues of numbers represented in the system of residual classes. Objective. The goal of the work is to develop methods for the tabular implementation of the arithmetic operations of multiplication, addition and subtraction of the residues of two numbers based on the use of the tabular multiplication code. Method. Tabular methods for implementing integer arithmetic modular operations of addition, subtraction and multiplication are proposed for consideration. In order to reduce the amount of equipment for a tabular operating unit of computer systems that implements modular operations of addition, subtraction and multiplication by reducing the coincidence circuits AND in the nodes of the tables for implementing arithmetic operations based on the code of table multiplication, two methods for performing arithmetic modular operations of addition and subtraction have been developed. These methods are based on the code of tabular multiplication, the use of which will reduce the amount of equipment of the tabular operating unit. Thus, despite the difference in the digital structure of the tables of modular operations of addition, subtraction and multiplication based on the use of the tabular multiplication code, two new tabular methods for implementing arithmetic modular operations of addition and subtraction have been created. Based on them, algorithms for tabular execution of modular arithmetic operations of addition and subtraction have been developed. Using these algorithms, it is possible to synthesize a structurally simple, highly reliable and fast table operating unit that operates in a system of residual classes, which is based on three separate permanent storage devices (read-only memory), each of which implements only one fourth of the corresponding complete table of values of the modular operation, what is earlier in the theory tabular arithmetic was supposed to be impossible. Results. The developed methods are justified theoretically and studied when performing arithmetic modular operations of addition, subtraction and multiplication using tabular procedures. Conclusions. The conducted examples of the implementation of integer arithmetic modular operations of addition and subtraction can be considered as presented experiments. The results obtained make it possible to recommend them for use in practice in the design of computer systems operating in a non-positional number system in residual classes. Prospects for further research may be to create a tabular method for implementing integer arithmetic modular division operations based on the use of the tabular multiplication code.

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Dissertations / Theses on the topic "Multiplication table"

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高木, 直史, and Naofumi Takagi. "Powering by a table look-up and a multiplication with operand modification." IEEE, 1998. http://hdl.handle.net/2237/5289.

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Magnusson, Andréa. "Att undervisa om multiplikation i grundskolans tidigare år : Lärares tankar om introduktion, fortlöpande undervisning och tabellträning." Thesis, Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-37586.

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Syftet med denna studie är att belysa hur lärare beskriver sin undervisning av multiplikation i årskurs 1−3 och årskurs 4−6 när det kommer till introduktion, fortlöpande undervisning och tabellträning. Kvalitativa intervjuer med sex lärare har genomförts för att undersöka vilka mål de intervjuade lärarna har med sin multiplikationsundervisning samt hur lärarna beskriver innehållet i sin multiplikationsundervisning. Bakgrunden är att lärares uppfattning om vad multiplikation är samt vad multiplikationsundervisningen ska innehålla påverkar vilka lärandemöjligheter eleverna får. Detta innefattar val av förklaringsmodeller, arbetssätt samt lektionsinnehåll, vilket i högsta grad påverkar elevers förståelseutveckling av multiplikationsbegreppet. Att svenska lärare typiskt sett baserar sin undervisning på läromedel lyfts av forskning som en orsak till att svenska elevers taluppfattning och kunskap om aritmetik är svag. Lärare behöver därför komplettera läromedlens framställning av multiplikation i undervisningen. Studiens resultat visar att lärarnas mål med undervisningen berör områden som enligt läroplan och forskning är viktiga för elevers begreppsförståelse och procedurkunskap, men att viktiga bitar i undervisning verkar saknas. Detta berör undervisning om multiplikativa förklaringsmodeller, räknelagar och begrepp kopplade till multiplikation. Lärarnas undervisning om de grundläggande multiplikationstabellerna, där både strategier för att härleda tabellfakta samt drillövningar av dessa uppges ingå, verkar ligga i fas med vad forskning lyfter fram som viktigt för att uppnå automatisering av tabellerna.<br>The purpose of this study is to illustrate how teachers describe their multiplication teaching in grades 1−3 and 4−6 when it comes to the introduction, continuous teaching and table training. Qualitative interviews with six teachers have been conducted to examine what objectives the interviewed teachers have with their multiplication teaching and how they describe the contents of their multiplication teaching. The reason behind is that teachers’ perception of what multiplication means and their thoughts on what multiplication teaching should cover affects the learning opportunities pupils receive. This includes teachers’ choice of explanatory models, methods and lesson content which highly affects the pupils’ development of understanding regarding the concept of multiplication. The fact that Swedish teachers typically base their teaching on textbooks is indicated by research to be a contributing factor why Swedish pupils’ number sense and understanding of arithmetic is weak. Teachers therefore need to complement the presentations that textbooks contain regarding multiplication in teaching. The result of this study shows that teachers’ teaching objectives affects areas that the curriculum and research highlights as important for pupils’ conceptual understanding and procedural knowledge, but that important pieces seems to be missing in their teaching. These concerns the teaching about the multiplicative models of explanation, mathematical properties and concepts related to multiplication. However, teachers’ teaching about the basic multiplication facts, where both strategies to derive facts and drill exercises of facts is said to be included, seems to correspond largely with what research highlights as important in achieving automaticity in multiplication facts.

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Starepravo, Ana Ruth. "A multiplicação na Escola Fundamental I: análise de uma proposta de ensino." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-13092010-125231/.

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O presente trabalho consiste numa pesquisa qualitativa sobre o ensino e a aprendizagem de matemática, cujo objetivo foi o de propor uma metodologia, fundamentada no construtivismo piagetiano, para ensinar multiplicação nos anos iniciais do Ensino Fundamental. A observação de que o ensino desse conteúdo, em muitas escolas, privilegia a memorização da tabuada e a aplicação de algoritmos, em detrimento da compreensão, mobilizou uma investigação sobre como organizar o ensino dessa noção privilegiando o desenvolvimento da racionalidade e a aquisição de competências que transcendem o âmbito da matemática. Para isso foi realizada uma intervenção de ensino, planejada e desenvolvida pela própria pesquisadora, ao longo de um semestre (21 aulas) em uma turma de terceira série de uma escola da rede municipal de Curitiba. A multiplicação foi explorada em problemas de proporcionalidade simples (situações de correspondência um-para-muitos e de arranjo retangular). A divisão, por ser sua operação inversa, foi explorada em algumas atividades e dados relativos a essa operação foram incorporados ao estudo. As aulas foram gravadas em vídeo e transcritas em diários enriquecidos com observações e comentários da pesquisadora os quais, junto com as produções dos alunos e relatórios feitos pela professora da turma, compuseram nossa base de dados. Na análise buscamos indicativos da ocorrência de uma interação construtiva, caracterizada por progressos nos seguintes âmbitos: relações intelectuais (compreensão das operações aritméticas em questão pelas crianças); relações sociais/morais (conquistas que transcendem o conteúdo matemático); relações didáticas (efeitos sobre o próprio processo interventivo). Os resultados apontam para uma interação de qualidade construtiva uma vez que a intervenção teve efeito de aperfeiçoamento sobre os sujeitos envolvidos. Verificamos a substituição progressiva de estratégias de contagem por estratégias de cálculo, aquisição de competências aritméticas e interações entre as crianças (indícios de uma relação de cooperação). Apontamos ainda para mudanças de atitudes dos alunos no que se refere às seguintes questões: envolvimento nas atividades propostas, relação com a matemática, forma de tratar os problemas apresentados, comunicação e expressão em sala de aula. No âmbito didático destacamos o tratamento dispensado ao erro, usado como estratégia didática, o papel interventivo que a avaliação exerceu no processo de ensino e a importância da escrita para a reflexão do professor sobre a sua própria prática.<br>The present work consists of a qualitative research in education and the mathematics learning that objective was to propose a methodology based on Piaget´s constructivism, to teach multiplication in the early years of Eleentary School. The observation that shows how this content has been treated, in many schools, as a memorization and application matter, rather than a comprehension issue, directed to an investigation how about organize the teaching of this matter prioritizing the development of racionality and the acquisition of competences that go beyond matheatics. For that, a planned learning intervention was developed and made by the researcher herself over a period of one semester (21 classes) in a third grade public school from Curitiba. The multiplication was explored in simple proportionality problems (in one-tomany correspondence and rectangular array problems). The division, as it´s the inverse, was also explored in some activities and the data collected was also included in this study. The classes were recorded in video and a transcript enriched by observations and comments from the the researcher was produced. The transcript, the student´s works and daily reports done by the teacher form our database. In the analysis, we look for indications of a constructive interaction, characterized by progresses in the following areas: intellectual relationships (comprehension of the arithmetical operations used); social/moral relationships (acquisition of non mathematical aptitudes); didactic relationships (effects on the intervention process itself). The results show a constructive quality interaction as the intervention had a development effect on the subjects involved. We verified the progressive substitution of the counting strategies for calculation strategies, the acquisition of arithmetical aptitudes and interaction between the students (signs of a cooperative relationship). Also some attitudes changes were observed in the students regarding the following matters: the engagement in the activities, the relationship with mathematics, the approach on the problems, communication and expressionat the classroom. In the didactic field, we highlight the treatment regarding the errors, used as a didatic strategy, the interfered paper the avaliation exerced to the teaching process and the importance of writing for the teacher´s reflection about its practice.

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Kim, Soulhyang. "Scores : Requiem (2003) : Seven rhythms (2003-04) : Let us memorize the multiplication table! (2004) : Kaleidoscope (2005) : Croquis (2005-06) : Wildflowers (2005-06) : Concerto for piano and orchestra (2005-06)." Thesis, University of Exeter, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432784.

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Lee, Sang Myung (Chris). "Sub-cubic Time Algorithm for the k-disjoint Maximum subarray Problem." Thesis, University of Canterbury. Computer Science and Software Engineering, 2011. http://hdl.handle.net/10092/6494.

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The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. This problem was first introduced by Grenander and brought to computer science by Bentley in 1984. This problem has been branched out into other problems based on their characteristics. k-overlapping maximum subarray problem where the overlapping solutions are allowed, and k-disjoint maximum subarray problem where all the solutions are disjoint from each other are those. For k-overlapping maximum subarray problems, significant improvement have been made since the problem was first introduced. For k-disjoint maximum subarrsy, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(kn^3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. This paper introduces a faster algorithm for the k-disjoint maximum sub-array problem under the conventional RAM model, based on distance matrix multiplication. Also, DMM reuse technique is introduced for the maximum subarray problem based on recursion for space optimization.

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Pasca, Bogdan Mihai. "Calcul flottant haute performance sur circuits reconfigurables." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00654121.

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De plus en plus de constructeurs proposent des accélérateurs de calculs à base de circuits reconfigurables FPGA, cette technologie présentant bien plus de souplesse que le microprocesseur. Valoriser cette flexibilité dans le domaine de l'accélération de calcul flottant en utilisant les langages de description de circuits classiques (VHDL ou Verilog) reste toutefois très difficile, voire impossible parfois. Cette thèse a contribué au développement du logiciel FloPoCo, qui offre aux utilisateurs familiers avec VHDL un cadre C++ de description d'opérateurs arithmétiques génériques adapté au calcul reconfigurable. Ce cadre distingue explicitement la fonctionnalité combinatoire d'un opérateur, et la problématique de son pipeline pour une précision, une fréquence et un FPGA cible donnés. Afin de pouvoir utiliser FloPoCo pour concevoir des opérateurs haute performance en virgule flottante, il a fallu d'abord concevoir des blocs de bases optimisés. Nous avons d'abord développé des additionneurs pipelinés autour des lignes de propagation de retenue rapides, puis, à l'aide de techniques de pavages, nous avons conçu de gros multiplieurs, possiblement tronqués, utilisant des petits multiplieurs. L'évaluation de fonctions élémentaires en flottant implique souvent l'évaluation en virgule fixe d'une fonction. Nous présentons un opérateur générique de FloPoCo qui prend en entrée l'expression de la fonction à évaluer, avec ses précisions d'entrée et de sortie, et construit un évaluateur polynomial optimisé de cette fonction. Ce bloc de base a permis de développer des opérateurs en virgule flottante pour la racine carrée et l'exponentielle qui améliorent considérablement l'état de l'art. Nous avons aussi travaillé sur des techniques de compilation avancée pour adapter l'exécution d'un code C aux pipelines flexibles de nos opérateurs. FloPoCo a pu ainsi être utilisé pour implanter sur FPGA des applications complètes.

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Abdullahi, Beyar, and Karin Nordström. "Automatisering av multiplikationstabellerna : En studie om automatisering av multiplikationstabellerna." Thesis, Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-78361.

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Tidigare forskning har visat att elever har bristande kunskaper i multiplikationstabellerna. Att automatisera tabellerna ger eleverna goda förutsättningar inför övriga matematikområden. Syftet med studien var att skapa kunskap om lärares uppfattning till automatisering av multiplikationstabellerna samt att få kunskap om hur många av lärarnas elever som hade automatiserat tabellerna. Syftet var även att ta reda på vilka metoder lärare använder för att stötta eleverna i detta. Studien genomfördes med enkät som datainsamlingsinstrument och resultatet från enkäten följdes upp med fokusgruppsintervjuer. Resultatet av studien visade att många lärare upplever automatisering av multiplikationstabellerna som viktigt eftersom det underlättar för eleverna inför övriga matematikområden samt att det avlastar elevernas arbetsminne. Metoderna som flest lärare använde i sin undervisning var digitala undervisningsplattformar samt olika arbetsblad som drillträning av tabellerna.<br>Previous research had shown that students lacked knowledge in the multiplication tables. Automating the tables gives students good conditions to succeed in other areas of mathematics. The purpose of this study was to create knowledge about teacher’s perceptions of automating the multiplication tables and to examine how many of the pupils had automated the tables. The purpose was also to identify what methods teachers use to support students in multiplication table automation. The study was conducted with a survey and the results were followed up with focus group interviews. The results showed that many teachers value the automation of the multiplication tables because it prepares the students for other mathematics areas and it relieves the student’s working memory. The methods most teachers used in their teaching were digital teaching platforms and various worksheets such as drill training of the tables.

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Esmenjaud-Genestoux, Florence. "Fonctionnement didactique du milieu culturel et familial dans la régulation des apprentissages scolaires en mathématiques." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2000. http://tel.archives-ouvertes.fr/tel-00697666.

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La thèse s'intéresse à l'accompagnement familial des apprentissages scolaires en mathématiques, mais aussi et surtout à l'organisation non discriminante de ses conditions. La " culture didactique " partagée dans notre société s'adapte de moins en moins aux régulations de la scolarité obligatoire. En effet, en se focalisant sur le repérage des difficultés individuelles et en encourageant les interventions précoces à l'extérieur de l'institution d'enseignement, elle transforme les aléas " ordinaires " de l'apprentissage en dysfonctionnements. Certaines tentatives d'amélioration insistent sur l'information et la communication entre école et parents. Or les discours éloignent souvent de la réalité des actions. Les " exercices à faire à la maison ", en transmettant des comportements, jouent un rôle complémentaire important. Certes, ils font rapidement surgir les divergences, parce qu'ils rendent visibles les contre-performances des élèves, et suggèrent toutes sortes de rectifications. Les devoirs sont par conséquent souvent accusés d'introduire des disparités et de pertuber les relations entre protagonistes. La thèse réexamine ce point de vue, en étudiant d'autres formes d'étude, qui s'ajusteraient mieux aux besoins des institutions didactiques. Pour simplifier la circulation des savoirs mathématiques les plus fréquemment utilisés, la société a mis en place des instruments culturels. Mais certains ont été détournés de leur fonction, ce qui a rompu des équilibres didactiques essentiels. La récitation des tables de multiplication fournit un exemple paradigmatique de la dénégation des transpositions. Les régressions métadidactiques ont en effet lentement modifié une ancienne répartition des tâches entre institutions, jusqu'à dédidactifier tout un pan de l'enseignement du calcul. La thèse éclaire la compréhension de ces phénomènes à l'aide de la Théorie des Situations Didactiques. Elle propose un nouveau concept pour une ingénierie spécifique de l'entraînement et de la familiarisation des élèves avec les connaisances les plus fondamentales : les assortiments didactiques.

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He, Hou-Chun, and 何厚純. "Lookup Table Based Multiplication Technique for GF(2^m)." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/14801395875784364639.

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碩士<br>義守大學<br>資訊工程學系<br>101<br>This thesis presents the look-up table method and Horner rule to speed up finite field multiplication in the standard basis. The polynomial can be simplified by Horner rule, and dividing into many terms. The many terms make a look-up table which is used to calculate the permutations and combinations of the results. The method can reduce the number of shift and bitwise XOR operation. Therefore, the purposes of accelerating multiplication can be applied in a larger finite field operation, such as Elliptic curve cryptography.

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Wu, Tian-Yiou, and 吳天佑. "Fast Scalable Look-up Table Modular Multiplication Used in RSA." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/98277674272064995625.

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碩士<br>逢甲大學<br>產業研發碩士班<br>101<br>With the renovating development of the network technology, the transmission of information has become more convenient and faster; therefore, in the process of network information transmission, information encryption has to be indispensable. Moreover, because of the popularization of the smart phones, how to effectively proceed with information encryption has become a very important issue. RSA is a public key encryption and decryption algorithm which provides rather high security and great popularization, in which the RSA is the modular exponentiation. Because the computing power has become stronger and stronger, the encryption key length has also become longer and longer, which creates a very big problem, that is, the process of encryption has become very difficult and very slow. Therefore, based on the features of the RSA modular exponentiation, this paper presents a set of new hardware architecture to solve the problem of computation time. First, we choose scalable look-up table modular multiplication to serve as kernel unit and improve it. Furthermore, by means of the features of data reuse, we can effectively reduce computation times and further achieve the effect of speeding up the modular exponentiation.

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Books on the topic "Multiplication table"

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Mollet, David. Multiplication tables. Waldorf Education Consultants, 1993.

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subject, Math favorite. Learn Multiplication Table. Independently Published, 2022.

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Montessori, Multiplication. Multiplication Ce1: Multiplication Ce2, Table de Multiplication, Apprendre la Multiplication, Multiplication Jeu. Independently Published, 2020.

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Practise Times Table (Practise Time Tables). Andrew Brodie Publications, 2005.

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Publishing, Baynti. Tables de Multiplication: Apprenez les Tables de Multiplication Mini Poster, Colorful Multiplication Table, Square, Math. Independently Published, 2022.

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Table de multiplication composée. s.n.], 1985.

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Jee, Makhan. Best Multiplication Table: Colorful. Independently Published, 2021.

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Etio, Virginie. Apprendre les Tables de Multiplication: Table de Multiplication - Maths CP CE1 CE2 - Table Multiplication - Calcul Mental - Apprendre les Maths - Maths Primaire - Multiplication Primaire - Tables de Multiplication Primaire - CE2 - Exercices Maths. Independently Published, 2020.

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The Multiplication and Times Table. Arcturus Publishing, 2016.

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design, school. Multiplication Table Learn with Exercise. Independently Published, 2021.

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Book chapters on the topic "Multiplication table"

1

Tyers, Ben. "Multiplication Table." In GameMaker: Studio 100 Programming Challenges. Apress, 2017. http://dx.doi.org/10.1007/978-1-4842-2644-5_100.

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McClain, William Martin. "The multiplication table." In Symmetry Theory in Molecular Physics with Mathematica. Springer New York, 2009. http://dx.doi.org/10.1007/b13137_8.

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Zhao, Xiaoyan, Lianchun Dong, Yue Qiu, and Tiantian Li. "Mathematics Teachers’ Perspectives on Textbooks’ Design in Multiplication Tables." In Recent Advances in Mathematics Textbook Research and Development. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-8426-4_7.

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AbstractThe introduction of the multiplication tables (or nine-times table) is of significance to children’s learning of basic multiplication fact. To fulfil the potential of multiplication tables in mathematics teaching and learning, different mathematics textbooks adopt different designs, presenting distinct features regarding the order of introducing multiplication tables, classroom activities and tasks for building connections, etc. This study collected interview data from 18 primary school teachers with different teaching experience, and aimed to reveal teachers’ viewpoints regarding the differences in textbooks’ design in multiplication tables and how they make impacts on the teaching and learning of multiplication at classroom level.

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Gelfand, Israel M., and Alexander Shen. "The multiplication table and the multiplication algorithm." In Algebra. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_5.

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Olfos, Raimundo, and Masami Isoda. "Teaching the Multiplication Table and Its Properties for Learning How to Learn." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_6.

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AbstractWhy do the Japanese traditionally introduce multiplication up to the multiplication table in the second grade? There are four possible reasons. The first reason is that it is possible to teach. The second reason is that Japanese teachers plan the teaching sequence to teach the multiplication table as an opportunity to teach learning how to learn. The third reason is that memorizing the table itself has been recognized as a cultural practice. The fourth reason is to develop the sense of wonder with appreciation of its reasonableness. The second and the fourth reasons are discussed in Chap. 10.1007/978-3-030-28561-6_1 of this book as “learning how to learn” and “developing students who learn mathematics by and for themselves in relation to mathematical values, attitudes, ways of thinking, and ideas.” This chapter describes these four reasons in this order to illustrate the Japanese meaning of teaching content by explaining how the multiplication table and its properties are taught under the aims of mathematics education. In Chap. 10.1007/978-3-030-28561-6_1, these were described by the three pillars: human character formation for mathematical values and attitudes, mathematical thinking and ideas, and mathematical knowledge and skills.

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Isoda, Masami, Raimundo Olfos, and Takeshi Noine. "The Teaching of Multidigit Multiplication in the Japanese Approach." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_7.

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AbstractMultidigit multiplication in vertical form uses the idea of the distributive law such as 27 × 3 = (20 + 7) × 3 = 20 × 3 + 7 × 3 for using a multiplication table under the base ten place value system. Multiplication in vertical form is not simply repeated addition such as 27 + 27 + 27. In this meaning, through the extension of multiplication from single digit to multidigit by use of vertical form with a multiplication table, students have to integrate their knowledge on the base ten system with the definition of multiplication by measurement (a group of groups; see Chaps. 10.1007/978-3-030-28561-6_3, 10.1007/978-3-030-28561-6_4, 10.1007/978-3-030-28561-6_5, and 10.1007/978-3-030-28561-6_6 of this book) and so on. How does the Japanese approach enable students to develop multiplication in vertical form by and for themselves based on their learned knowledge?This chapter illustrates this process as follows. Firstly, the diversity of multiplication in vertical form is explained in relation to the multiplier and multiplicand, and the Japanese approach in comparison with other countries such as Chile and the Netherlands is clearly illustrated. Secondly, how a Japanese teacher enables students to develop multiplication in vertical form beyond repeated addition is explained with an exemplar of lesson study. Thirdly, the exemplar illustrates a full-speck lesson plan under school-based lesson study which demonstrates how Japanese teachers try to develop students who learn mathematics by and for themselves including learning how to learn (see Chap. 1). Fourthly, it explains the process to extend multiplication in vertical form to multidigit numbers by referring to Gakko Tosho textbooks.

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Sabba, Claudia Georgia, and Ubiratan D’Ambrosio. "An Ethnomathematical Perspective on the Question of the Idea of Multiplication and Learning to Multiply: The Languages and Looks Involved." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_8.

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AbstractThis chapter invites appreciation of the development of an ethnomathematical perspective on the question of the idea of multiplication. The teaching approach described here is grounded on miniprojects that integrate diverse areas of knowledge. It reveals a style of work being performed in the Waldorf Schools of São Paulo, Brazil, where the concept of multiplication is constructed together with the geometry of plane figures through the elaboration of mathematical thinking together with figures mounted on a circular wooden table. The sequence highlights ideas of context connected to the use of cellular phones by the students to introduce the concept of proportionality by taking photos of their bodies and faces, and then using them to study Leonardo da Vinci’s Vitruvian Man.

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Hasan, M. A. "Look-Up Table Based Large Finite Field Multiplication in Memory Constrained Cryptosystems (Extended Abstract)." In Cryptography and Coding. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46665-7_25.

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Kenwrick, Evelyn E. "Multiplication Tables." In Number in the Nursery and Infant School. Routledge, 2022. http://dx.doi.org/10.4324/9781003327950-12.

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Sarkar, Palash, Pradeep Kumar Mishra, and Rana Barua. "New Table Look-Up Methods for Faster Frobenius Map Based Scalar Multiplication Over GF(p n )." In Applied Cryptography and Network Security. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24852-1_35.

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Conference papers on the topic "Multiplication table"

1

Gulyás, Erzsébet. "Connections Between Learning Arithmetic and Object Visual Imagery Ability in Elementary School - Learning the multiplication table." In 1st Budapest International Conference on Education. BME GTK Műszaki Pedagógia Tanszék, 2024. https://doi.org/10.3311/bice2024-001.

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Guo, Han, William Brandon, Radostin Cholakov, Jonathan Ragan-Kelley, Eric P. Xing, and Yoon Kim. "Fast Matrix Multiplications for Lookup Table-Quantized LLMs." In Findings of the Association for Computational Linguistics: EMNLP 2024. Association for Computational Linguistics, 2024. http://dx.doi.org/10.18653/v1/2024.findings-emnlp.724.

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Drožđek, Lara, and Igor Pesek. "PILOT STUDY: AI-BASED WEB APPLICATION FOR MASTERING MULTIPLICATION TABLES." In 19th International Technology, Education and Development Conference. IATED, 2025. https://doi.org/10.21125/inted.2025.1108.

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Karlsson, Natalia, and Wiggo Kilborn. "TEACHING AND LEARNING THE MULTIPLICATION TABLE BY USING MULTIPLICATIVE STRUCTURES: VARIATION AND CRUCIAL PATTERNS." In International Conference on Education and New Developments. inScience Press, 2022. http://dx.doi.org/10.36315/2022v1end010.

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This paper examines and analyzes how students learn multiplication tables, specifically the role of multiplicative structures and how these are used as students learn to master the tables. The analysis is performed in the context of the generalization process related to the teaching activity focusing students’ perception of concepts. The theoretical approach applies Davydov’s concept of theoretical generalization as perception-conception-elementary concept (PCE model) and Vergnaud’s theory of multiplicative structures in three classes: mapping rule (MR), multiplicative comparison (MC), and Cartesian product (CP). For the methodological design, Marton’s variation theory has been chosen. This study includes two teachers and 40 students in two Year 3 classes, followed two years later by one teacher and 25 students in one Year 5 class. The analysis of the outcome is based on documented classroom observations, one-on-one interviews with students and teachers’ reflections on students’ learning outcomes. The conclusion of the study is that the generalization of multiplication is a difficult process for students, especially in the classes MC and PC, and one that sometimes results in challenges to identifying multiplicative situations and relating these to the multiplication tables. This illustrates that teaching activities and teachers’ support are necessary conditions for students’ learning. The study also shows that multiplicative structures can help students to find and systematize crucial patterns in the multiplication table, allowing them to learn the multiplication table in a more efficient and structured manner. During the one-on-one interviews, students actively searched for and found structures and solutions that did not come up during lessons. This shows that multiplicative structures are a suitable didactic tool for identifying patterns in multiplication tables, thereby facilitating learning other than by rote.

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Xie, Fei, Xiaoqian Huang, Shuangyue Liu, Du Tang, Zhengkang Wang, and Yaojun Qiao. "Multiplication-Free Equalization Schemes for 244-Gbps PAM-4 Transmission." In Optical Fiber Communication Conference. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/ofc.2024.w1h.2.

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We propose a multiplication-free equalization scheme using cluster-assisting lookup tables (CLUT). Results demonstrate an 11-order table size reduction compared to traditional LUTs, incurring only a 0.2-dB penalty.

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TANABÉ, Susumu. "Logarithmic vector fields and multiplication table." In Proceedings of the Trieste Singularity Summer School and Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706812_0026.

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Schön, Martin, Martin Ebner, and Georg Kothmeier. "It's just about learning the multiplication table." In the 2nd International Conference. ACM Press, 2012. http://dx.doi.org/10.1145/2330601.2330624.

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Zhao, Yuchen, Lan Gao, Weigong Zhang, Jing Wang, and Dehui Qiu. "Accelerating Look-Up Table based Matrix Multiplication on GPUs." In 2023 IEEE 29th International Conference on Parallel and Distributed Systems (ICPADS). IEEE, 2023. http://dx.doi.org/10.1109/icpads60453.2023.00058.

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Tatuzov, A. L. "Neural network models for teaching multiplication table in primary school." In The 2006 IEEE International Joint Conference on Neural Network Proceedings. IEEE, 2006. http://dx.doi.org/10.1109/ijcnn.2006.247274.

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Habiby, S. F., and S. A. Collins. "Design of an Optical Residue Arithmetic Matrix Vector Multiplier Using Holographic Table Lookup." In Optical Computing. Optica Publishing Group, 1985. http://dx.doi.org/10.1364/optcomp.1985.tud4.

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The design of an optical matrix multiplier is presented. In it elementary residue arithmetic1 addition and multiplication operations are broken into simple parallel mapping units. The input to these units is position-coded and translated via holographically stored tables into useful light valve forms. Addition and multiplication mapping units are then combined into the full matrix-vector multiplier. The matrix elements are provided by a microprocessor-controlled CRT and the vector elements are provided by position coded optical fiber input.

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