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1
Greenwood, Jonathan Jay. "On The Nature of Teaching and Assessing “Mathematical Power” and “Mathematical Thinking”." Arithmetic Teacher 41, no. 3 (1993): 144–52. http://dx.doi.org/10.5951/at.41.3.0144.
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What exactly is “mathematical power” to omeone who has always identified mathematics as being the mastery of facts, such as the multiplication table, and procedures, such as the long division algorithm? What does it mean to “think mathematically” to a teacher who always struggled wit11 story problems as a student? To those teachers who fit these descriptions, and a sizable number do. assessing students mathematical power and mathematical thinking is even more bewildering.
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Setiadi, Nanang. "The Use of Realistic Mathematics Education (RME) to Help Indonesian 5th-Grade Students to Learn Multiplication and Division." Southeast Asian Mathematics Education Journal 10, no. 1 (2020): 41–53. http://dx.doi.org/10.46517/seamej.v10i1.98.
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Abstract This paper discusses the use of Realistic Mathematics Education (RME) as an alternative approach to enhance Indonesian 5th-grade students’ ability in multiplication and division. It presents the analysis of Indonesian 5th-grade students’ difficulties in applying stacking method for multiplication and division. Furthermore, it describes a mathematics teaching learning practice to stimulate students constructing their strategies, mathematical models and number sense in solving mathematical problems that involve multiplication and division. The teaching learning practice aims to apply RME for helping students develop their multiplication and division ability.Findings shows that stacking methods for multiplication and division are difficult for the students. The main students’ problem in multiplication and division stacking methods is in reapplying the steps of the methods. The steps taken to improve the learning process by implementing RME are: (1) analyze in detail the difficulties of students in multiplication and division stacking methods, (2) provide contexts of mathematical problems that can stimulate students to think mathematically, (3) hold a class mathematics congress, and (4) conduct a test to measure students’ achievement. Based on the students’ achievement, there has been several improvements. After RME, there were more students whose grades passed the Minimum Mastery Criteria. Moreover, there was a student who got 100. Then, the average test was higher. Meanwhile, there were only 3 children whose grades were 0. Thus, the application of RME has helped the 5th-grade students to improve their ability in multiplication and division.
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Moyer, Patricia Seray. "Links to Literature: A Remainder of One: Exploring Partitive Division." Teaching Children Mathematics 6, no. 8 (2000): 517–21. http://dx.doi.org/10.5951/tcm.6.8.0517.
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Children's literature can be a springboard for conversations about mathematical concepts. Austin (1998) suggests that good children's literature with a mathematical theme provides a context for both exploring and extending mathematics problems embedded in stories. In the context of discussing a story, children connect their everyday experiences with mathematics and have opportunities to make conjectures about quantities, equalities, or other mathematical ideas; negotiate their understanding of mathematical concepts; and verbalize their thinking. Children's books that prompt mathematical conversations also lead to rich, dynamic communication in the mathematics classroom and develop the use of mathematical symbols in the context of communicating. The National Council of Teachers of Mathematics (1989) emphasizes the importance of communication in helping children both construct mathematical knowledge and link their informal notions with the abstract symbols used to express mathematical ideas.
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Sidney, Pooja Gupta, and Martha Wagner Alibali. "Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division." Journal of Numerical Cognition 3, no. 1 (2017): 31–57. http://dx.doi.org/10.5964/jnc.v3i1.71.
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When children learn about fractions, their prior knowledge of whole numbers often interferes, resulting in a whole number bias. However, many fraction concepts are generalizations of analogous whole number concepts; for example, fraction division and whole number division share a similar conceptual structure. Drawing on past studies of analogical transfer, we hypothesize that children’s whole number division knowledge will support their understanding of fraction division when their relevant prior knowledge is activated immediately before engaging with fraction division. Children in 5th and 6th grade modeled fraction division with physical objects after modeling a series of addition, subtraction, multiplication, and division problems with whole number operands and fraction operands. In one condition, problems were blocked by operation, such that children modeled fraction problems immediately after analogous whole number problems (e.g., fraction division problems followed whole number division problems). In another condition, problems were blocked by number type, such that children modeled all four arithmetic operations with whole numbers in the first block, and then operations with fractions in the second block. Children who solved whole number division problems immediately before fraction division problems were significantly better at modeling the conceptual structure of fraction division than those who solved all of the fraction problems together. Thus, implicit analogies across shared concepts can affect children’s mathematical thinking. Moreover, specific analogies between whole number and fraction concepts can yield a positive, rather than a negative, whole number bias.
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Крюков, V. Kryukov, Зольников, Konstantin Zolnikov, Евдокимова, and S. Evdokimova. "Problems of modeling the basic elements CMOS LSI dual-purpose CAD." Modeling of systems and processes 6, no. 4 (2014): 41–44. http://dx.doi.org/10.12737/4045.
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The paper considers problems of modeling the basic elements of micro-schemes, creation of mathematical, informational and software taking into account the division of responsibilities between enterprises and modeling capabilities of ionizate-organizational and structural effects.
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Simon, Martin A. "Prospective Elementary Teachers' Knowledge of Division." Journal for Research in Mathematics Education 24, no. 3 (1993): 233–53. http://dx.doi.org/10.5951/jresematheduc.24.3.0233.
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Prospective teachers' knowledge of division was investigated through an open-response written instrument and through individual interviews. Problems were designed to focus on two aspects of understanding division: connectedness within and between procedural and conceptual knowledge and knowledge of units. Results indicated that the prospective teachers' conceptual knowledge was weak in a number of areas including the conceptual underpinnings of familiar algorithms, the relationship between partitive and quotitive division, the relationship between symbolic division and real-world problems, and identification of the units of quantities encountered in division computations. The research also characterized aspects of individual conceptual differences. The research results suggest conceptual areas of emphasis for the mathematical preparation of elementary teachers.
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Flores, Alfinio, Erin E. Turner, and Renee C. Bachman. "Research, Reflection, and Practice: Posing Problems to Develop Conceptual Understanding: Two Teachers Make Sense of Division of Fractions." Teaching Children Mathematics 12, no. 3 (2005): 117–21. http://dx.doi.org/10.5951/tcm.12.3.0117.
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Several scholars (e.g., Brown and Walter 1990; English 1997; Silver 1994) have highlighted the benefits of students posing mathematical problems (for example, students become better problem solvers). Posing mathematical problems can also help teachers develop their own mathematical knowledge and understanding. Teachers who learned mathematics mostly as “rules without reasons” now must learn how to teach for conceptual understanding. This article describes how two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students. Each teacher taught a combined fourth-fifth grade in an urban school. The problems that the teachers posed and solved were collected during an initial session and from the draft of an article they wrote. Additional insights and information were obtained from interviews.
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Manger, Terje, and Ole-Johan Eikeland. "Gender Differences in Mathematical Sub-Skills." Research in Education 59, no. 1 (1998): 59–68. http://dx.doi.org/10.1177/003452379805900107.
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Gender differences in mathematical sub-skills Significant gender differences favouring boys were found among Norwegian sixth-grade students in total mathematical test score and in the sub-scores of numeracy, measurement, fractions, geometry and word problems. No significant differences were found in addition and subtraction or in multiplication and division. Items requiring an understanding of decimal numbers discriminated in favour of the boys. The study revealed the dominance of boys in the upper ranges of ability in mathematics, showing that small average gender differences can hide large differences in a highly able group of students.
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Fuson, Karen C. "Toward Computational Fluency in Multidigit Multiplication and Division." Teaching Children Mathematics 9, no. 6 (2003): 300–305. http://dx.doi.org/10.5951/tcm.9.6.0300.
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Traditionally in the United States and Canada, students have first learned how to compute with whole numbers and then have applied that kind of computation. This approach presents several problems. First, less-advanced students sometimes never reach the application phase, so their learning is greatly limited. Second, word problems usually appear at the end of each section or chapter on computation, so sensible students do not read the problems carefully: They simply perform the operation that they have just practiced on the numbers in the problem. This practice, plus the emphasis on teaching students to focus on key words in problems rather than to build a complete mental model of the problem situation, leads to poor problem solving because students never learn to read and model the problems themselves. Third, seeing problem situations only after learning the mathematical operations keeps students from linking those operations with aspects of the problem situations. This isolation limits the meaningfulness of the operations and the ability of children to use the operations in a variety of situations.
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Oshanova, N. T. "MATHEMATICAL FOUNDATIONS OF MUSIC BY AL-FARABI." BULLETIN Series of Physics & Mathematical Sciences 71, no. 3 (2020): 24–30. http://dx.doi.org/10.51889/2020-3.1728-7901.03.
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This article discusses the mathematical foundations of al - Farabi music, and suggests the main actions of arithmetic operations with Farabi relations to obtain musical intervals. Farabi drew attention to some problems for the study of musical art. This article provides an extensive understanding of how the three main problems are needed to get the ratio. Musical intervals have different values. You can divide them, multiply them, and listen to them. In music theory, you need to be familiar with the mathematical foundations for working with ratios, as well as arithmetic operations like multiplication, division, and addition. Farabi not only gives a scientific idea of the ratio of sounds, but also reveals the mathematical foundations of the emergence of harmony and musical melodies.
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Peck, Sallie, and Japheth Wood. "Elastic, Cottage Cheese, and Gasoline: Visualizing Division of Fractions." Mathematics Teaching in the Middle School 14, no. 4 (2008): 208–12. http://dx.doi.org/10.5951/mtms.14.4.0208.
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Representation is one of the five Process Standards from Principles and Standards for School Mathematics. This Standard proposes that prekindergarten through grade 12 instructional programs should enable students to “select, apply, and translate among mathematical representations to solve problems” (NCTM 2000, p. 67). To implement a program that meets this Standard, teachers themselves must have attained this level of proficiency.
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Filippenko, Igor. "NON-TRADITIONAL CALCULATIONS OF ELEMENTARY MATHEMATICAL OPERATIONS: PART 1. MULTIPLICATION AND DIVISION." EUREKA: Physics and Engineering 4 (July 31, 2018): 49–58. http://dx.doi.org/10.21303/2461-4262.2018.00686.
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Different computational systems are a set of functional units and processors that can work together and exchange data with each other if required. In most cases, data transmission is organized in such a way that enables for the possibility of connecting each node of the system to the other node of the system. Thus, a computer system consists of components for performing arithmetic operations, and an integrated data communication system, which allows for information interaction between the nodes, and combines them into a single unit. When designing a given type of computer systems, problems might occur if: – computing nodes of the system cannot simultaneously start and finish data processing over a certain time interval; – procedures for processing data in the nodes of the system do not start and do not end at a certain time; – the number of computational nodes of the inputs and outputs of the system is different. This article proposes an unconventional approach to constructing a mathematical model of adaptive-quantum computation of arithmetic operations of multiplication and division using the principle of predetermined random self-organization proposed by Ashby in 1966, as well as the method of the dynamics of averages and of the adaptive system of integration of the system of logical-differential equations for the dynamics of number-average states of particles S1, S2 of sets. This would make it easier to solve some of the problems listed above.
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Salim, Salim. "Media Medan Perkalian dan Pembagian Bilangan Bulat." Idealmathedu: Indonesian Digital Journal of Mathematics and Education 7, no. 2 (2020): 107–15. http://dx.doi.org/10.53717/idealmathedu.v7i2.213.
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Mathematics is considered as a difficult subject for some students, leading to a decrease in students’ interest and motivation in understanding mathematical concept. In the process of classroom teaching and learning, mathematics that seems complicated and makes a bad impression for some students is an obstacle for them in solving daily mathematical problems. To deal with this obstacle, a media innovation in mathematics teaching and learning is deemed necessary as a bridge for students to understand the abstract concepts of mathematical objects through the manipulation of real objects. This paper aims to present how to create and use the media of Medan Perkalian dan Pembagian Bilangan Bulat for elementary school students. This media are quite appropriate as a learning medium used to help students understand the concept of multiplication and division, especially for grade II of elementary school students. Using this medium, students are not only capable to deal with multiplication and the division of integers but also easily understand the concept of multiplication and integers division.
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Lakso, Alan N. "INTERPRETING FRUIT GROWTH: PROBLEMS AND POSSIBLE SOLUTIONS." HortScience 25, no. 9 (1990): 1180b—1180. http://dx.doi.org/10.21273/hortsci.25.9.1180b.
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Fruits of different species grow in different patterns (such as the “double sigmoid” of stone fruits and grapes or the apparent single sigmoid of apples), and each has periods of cell division followed by periods of only cell expansion. It should not be expected that one mathematical growth description would hold for all species, or even at all times of the season for one species. Perhaps hybrid growth models need to be developed, although specific questions asked about fruit growth may be satisfactorily answered with models of only parts of the fruit growth period of interest.
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Caliandro, Christine Koller. "Research, Reflection, Practice: Children's Inventions for Multidigit Multiplication and Division." Teaching Children Mathematics 6, no. 6 (2000): 420–26. http://dx.doi.org/10.5951/tcm.6.6.0420.
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Children can invent their own methods for solving multidigit multiplication and division problems without learning the conventional algorithms that we normally teach them. Strong arguments can be made for the importance of encouraging children to invent their own arithmetic. Steffe (1994) says, “Children, when faced with their first arithmetical problems, use their current mathematical schemes to attempt to solve them” (p. 3) and “ ‘knowledge’ that involves carrying out actions or operations cannot be instilled ready-made into students or children but must, quite literally, be actively built up by them” (p. 4). These exciting thoughts make a great deal of sense to me, and they correspond to the way that I like to teach.
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Mulligan, Joanne T., and Michael C. Mitchelmore. "Young Children's Intuitive Models of Multiplication and Division." Journal for Research in Mathematics Education 28, no. 3 (1997): 309–30. http://dx.doi.org/10.5951/jresematheduc.28.3.0309.
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In this study, an intuitive model was defined as an internal mental structure corresponding to a class of calculation strategies. A sample of female students was observed 4 times during Grades 2 and 3 as they solved the same set of 24 word problems. From the correct responses, 12 distinct calculation strategies were identified and grouped into categories from which the children's intuitive models of multiplication and division were inferred. It was found that the students used 3 main intuitive models: direct counting, repeated addition, and multiplicative operation. A fourth model, repeated subtraction, only occurred in division problems. All the intuitive models were used with all semantic structures, their frequency varying as a complex interaction of age, size of numbers, language, and semantic structure. The results are interpreted as showing that children acquire an expanding repertoire of intuitive models and that the model they employ to solve any particular problem reflects the mathematical structure they impose on it.
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Ortiz-Laso, Zaira, and José-Manuel Diego-Mantecón. "Strategies of Pre-Service Early Childhood Teachers for Solving Multi-Digit Division Problems." Sustainability 12, no. 23 (2020): 10217. http://dx.doi.org/10.3390/su122310217.
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Unlike previous research, this study analyzes the strategies of pre-service early childhood teachers when solving multi-digit division problems and the errors they make. The sample included 104 subjects from a university in Spain. The data analysis was framed under a mixed-method approach, integrating both quantitative and qualitative analyses. The results revealed that the traditional division algorithm was widely used in problems involving integers, but not so frequently applied to problems with decimal numbers. Often, number-based and algebraic strategies were employed as an alternative to the traditional algorithm, as the pre-service teachers did not remember how to compute it. In general, number-based strategies reached more correct solutions than the traditional algorithm, while the algebraic strategies did not usually reach any solution. Incorrect identifications of the mathematical model were normally related to an exchange of the dividend and divisor roles. Most pre-service teachers not only failed to compute the division, but also to interpret the obtained solution in the problem context. The study concludes that, during their schooling, students accessing the Degree in Early Childhood education have not acquired the necessary knowledge and skills to solve multi-digit division problems, and thus the entrance requirements at the university must be rethought.
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Carpenter, Thomas P., Ellen Ansell, Megan L. Franke, Elizabeth Fennema, and Linda Weisbeck. "Models of Problem Solving: A Study of Kindergarten Children's Problem-Solving Processes." Journal for Research in Mathematics Education 24, no. 5 (1993): 428–41. http://dx.doi.org/10.5951/jresematheduc.24.5.0428.
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Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5 children were not able to answer any problems correctly. The results suggest that children can solve a wide range of problems, including problems involving multiplication and division situations, much earlier than generally has been presumed. With only a few exceptions, children's strategies could be characterized as representing or modeling the action or relationships described in the problems. The conception of problem solving as modeling could provide a unifying framework for thinking about problem solving in the primary grades. Modeling offers a parsimonious and coherent way of thinking about children's mathematical problem solving that is relatively straightforward and is accessible to teachers and students alike.
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Silver, Edward A., Lora J. Shapiro, and Adam Deutsch. "Sense Making and the Solution of Division Problems Involving Remainders: An Examination of Middle School Students' Solution Processes and Their Interpretations of Solutions." Journal for Research in Mathematics Education 24, no. 2 (1993): 117–35. http://dx.doi.org/10.5951/jresematheduc.24.2.0117.
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In this study, about 200 middle school students solved an augmented-quotient division-with-remainders problem, and their solution processes and interpretations were examined. Based on earlier research, semantic-processing models were proposed to explain students' success or failure in solving division-with-remainder story problems on the basis of the presence or absence of an adequate interpretation provided by the solver after obtaining a numerical solution. In this study, students' solutions and their attempts and failures to “make sense” of their answers were analyzed for evidence that supported or refuted the hypothesized semantic-processing models. The results confirmed that the models provide a solid explanation of students' failure to solve division-with-remainder problems in school settings. More generally, the results indicated that student performance was adversely affected by their dissociation of sense making from the solution of school mathematics problems and their difficulty in providing written accounts of their mathematical thinking and reasoning.
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Skvortsova, Svitlana, Oksana Оnoprienko, and Ruslana Romanyshyn. "Mathematical Word Problems That Contain a Constant in the Course of Mathematics of Primary School in Ukraine." Journal of Vasyl Stefanyk Precarpathian National University 8, no. 1 (2021): 46–64. http://dx.doi.org/10.15330/jpnu.8.1.46-64.
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The article is devoted to the research of the place of the mathematical word problems in the course of mathematics of primary school in Ukraine. The researchers define the results in the study of solving math problems, find out the essence of the process of solving math problems, form primary school students’ ability to solve math problems that contain a constant. Among the mentioned are to find the fourth proportional, do the proportional division and find the unknown number by two differences. The paper deals with the organization of educational research of students in order to identify common and distinctive features of the mathematical structures of these types of math problems and their influence on the method of solution. Based on the methodological system of teaching primary school learners to solve math problems by S. Skvortsova, taking into account the essence of the concept of “ability to solve math problems” and the methodical system of forming the ability to solve certain types of math problems, it has been proposed a system of drilling activities for the generalization of mathematical structures and methods of solving math problems that contain a constant value.
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Goetz, Albert. "Cost Allocation: An Application of Fair Division." Mathematics Teacher 93, no. 7 (2000): 600–603. http://dx.doi.org/10.5951/mt.93.7.0600.
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Although the subject of cost allocation has been extensively discussed in the literature of political economics, it has been generally neglected in mathematical literature. However, cost allocation affords a practical extension of fair-division techniques–one that is readily accessible to secondary school students and that gives them a simple yet powerful application of mathematics to real-world problem solving. A study of the concepts and the mathematics involved in cost allocation is most appropriate in a discrete mathematics course or a modeling course, but a case can be made for including this topic in other courses, as well. This article presents a typical cost-allocation problem with possible solutions and includes suggestions for presenting similar problems in the classroom. The basics of the problem follow closely from Young (1994).
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Fauzan, Ahmad, Yerizon Yerizon, Fridgo Tasman, and Rendy Novri Yolanda. "Pengembangan Local Instructional Theory Pada Topik Pembagian dengan Pendekatan Matematika Realistik." JURNAL EKSAKTA PENDIDIKAN (JEP) 4, no. 1 (2020): 01. http://dx.doi.org/10.24036/jep/vol4-iss1/417.
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This research aimed to develop local instruction theory that is valid, practical, and effective to help elementary school students developing their mathematical problem-solving skills. Therefore a sequential activityis design on dailybasis to encourage students to develop their ability to solve mathematical problems, especially on the topic division. To achieve the goal, realistic mathematics approach was implemented to grade three elementary students in the learning process. The designed activities were validated by experts on the aspects of mathematical contents, language, didactical process based on realistic mathematical approach. Data were analyzed with descriptive statistics and parametric statistics. The validation results show that the local instruction theory was valid, and the implementation shows that the local instruction theory is practical and effective in improving students' mathematical problem-solving skills.
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Parajuli, Krishna Kanta. "Basic Operations on Vedic Mathematics: A Study on Special Parts." Nepal Journal of Mathematical Sciences 1 (October 31, 2020): 71–76. http://dx.doi.org/10.3126/njmathsci.v1i0.34175.
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Vedic Mathematics was rediscovered and reconstructed by Sri Bharati Krishna Tirthaji from ancient Sanskrit texts Veda early last century between 1911 – 1918 is popularly known today is Vedic Mathematics. It is an extremely refined, independent and efficient mathematical system based on his 16 formulae and some sub-formulae with simple rules and principles.
 The main purpose of this paper is to communicate a new approach to Mathematics, offering simple, direct, one-line, mental solutions to mathematical problems. In the way of basic mathematical operations like addition, subtraction, multiplication and division can be done in simple ways, and results are obtained quickly and can be checked in a minute by using the Vedic techniques. In this system, for any problem, there is always one general technique and also some special pattern problems. This paper especially concentrates only on the specific pattern of elementary operation of Vedic Mathematics.
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Parajuli, Krishna Kanta. "Basic Operations on Vedic Mathematics: A Study on Special Parts." Nepal Journal of Mathematical Sciences 1 (October 31, 2020): 71–76. http://dx.doi.org/10.3126/njmathsci.v1i0.34175.
Full textAbstract:
Vedic Mathematics was rediscovered and reconstructed by Sri Bharati Krishna Tirthaji from ancient Sanskrit texts Veda early last century between 1911 – 1918 is popularly known today is Vedic Mathematics. It is an extremely refined, independent and efficient mathematical system based on his 16 formulae and some sub-formulae with simple rules and principles.
 The main purpose of this paper is to communicate a new approach to Mathematics, offering simple, direct, one-line, mental solutions to mathematical problems. In the way of basic mathematical operations like addition, subtraction, multiplication and division can be done in simple ways, and results are obtained quickly and can be checked in a minute by using the Vedic techniques. In this system, for any problem, there is always one general technique and also some special pattern problems. This paper especially concentrates only on the specific pattern of elementary operation of Vedic Mathematics.
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Pasalbessy, Chyntia, Wilmintjie Mataheru, and Carolina Selfisina Ayal. "PENERAPAN MODEL PEMBELAJARAN KOOPERATIF TIPE STUDENT TEAMS ACHIEVEMENT DIVISION (STAD) UNTUK MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH DAN PENALARAN MATEMATIS." Jurnal Magister Pendidikan Matematika (JUMADIKA) 2, no. 1 (2020): 16–20. http://dx.doi.org/10.30598/jumadikavol2iss1year2020page16-20.
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The mathematical problem solving ability is important for students to solve problems in mathematics learning. The purpose of this study was analyzed the difference in improvement of mathematical problem solving ability between students who use STAD type of cooperative learning model and direct teaching. This type research is experimental research with a quantitative appoarch. The subjects in this study were eighth-grade students of the SMP Kalam Kudus Ambon in the first semester of the 2019/2020 academic calendar, which consisted of two classes. Methods of data collection through an Initial Ability Mathematics test and a mathematical problem solving ability test. The result showed that there was a difference increase in ability of problem solving between students who obtain learning by using the STAD type cooperative learning models and direct teaching
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Matějík, M. "Calculus of variations and its application to division of forest land." Journal of Forest Science 50, No. 9 (2012): 439–46. http://dx.doi.org/10.17221/4639-jfs.
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The paper deals with an application of the least squares method (LSM) for the purposes of division and evaluation of land. This method can be used in all cases with redundant number of measurements, in this case of segments of plots. From the mathematical aspect, the minimisation condition of the LSM is a standardised condition &sum; pvv = min., minimising the Euclidean norm ||v||<sub>E</sub> of an n-dimensional vector of residues of plot segments at simultaneous satisfaction of the given conditions. The traditional procedure of calculus of variations with the use of Lagrangian function is shown. If some additional conditions are included in the calculation, on the basis of the criteria presented in this article it is possible to evaluate the degree of deformation of the selected solution in relation to the measured quantities. The application of the method of adjustment of condition measurements may help solve the problems of parcel division on the basis of intersection of the parcel layers according to the real-estate cadastre and according to previous land records, valuation, typological, price and other map sources.
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Tarnowski, Wojciech. "Partition of the Optimality Problems in Mechatronics." Solid State Phenomena 199 (March 2013): 641–47. http://dx.doi.org/10.4028/www.scientific.net/ssp.199.641.
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In the paper two examples of division of the mathematical model for optimization are presented: a drive composed of an electric motor and mechanical transmissions, and an electromagnetic multi-coil linear drive. The first example shows that each step of the mechanical transmission may be optimized separately, if an overall power efficiency and a mass are taken as the optimality criteria for the whole drive, provided the adequate coordination variables are adopted, and these are ratios of the gears. In the other example it is demonstrated that the whole problem may be divided into three sub-problems, accordingly to the computing environment: ordinary differential equations are applied to model a mechanical part, and partial differential equations are modelling an electromagnetic field and a voltage distribution, with the moving core. The transient position of the core is the coordination variable. Finally, methodological suggestions on the systematic way of decomposing a design problem into sub-problems are proposed.
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Zheltkova, Valeriya V., Dmitry A. Zheltkov, Zvi Grossman, Gennady A. Bocharov, and Eugene E. Tyrtyshnikov. "Tensor based approach to the numerical treatment of the parameter estimation problems in mathematical immunology." Journal of Inverse and Ill-posed Problems 26, no. 1 (2018): 51–66. http://dx.doi.org/10.1515/jiip-2016-0083.
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AbstractThe development of efficient computational tools for data assimilation and analysis using multi-parameter models is one of the major issues in systems immunology. The mathematical description of the immune processes across different scales calls for the development of multiscale models characterized by a high dimensionality of the state space and a large number of parameters. In this study we consider a standard parameter estimation problem for two models, formulated as ODEs systems: the model of HIV infection and BrdU-labeled cell division model. The data fitting is formulated as global optimization of variants of least squares objective function. A new computational method based on Tensor Train (TT) decomposition is applied to solve the formulated problem. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. The method demonstrated a better performance in comparison with some other broadly used global optimization techniques.
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Jitendra, Asha, Caroline M. DiPipi, and Ed Grasso. "The Role of a Graphic Representational Technique on the Mathematical Problem Solving Performance of Fourth Graders: An Exploratory Study." Australasian Journal of Special Education 25, no. 1-2 (2001): 17–33. http://dx.doi.org/10.1017/s1030011200024830.
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The purpose of this within‐subject comparisons exploratory study was to examine the influence of a graphic representational strategy on the problem solving performance of fourth graders, including special education students with learning problems. We employed a preliminary design experiment, prior to conducting a formal experimental or quasi‐experimental study, to gain insights into factors that may inhibit or enhance implementation of the intervention, especially in the context of real world of classroom (Gersten, Baker, & Lloyd, 2000). Students received teacher‐led strategy instruction in problem solving using a whole group (8 to 9 students) format followed by guided practice in applying the strategy during cooperative groups. Results indicate that students’ word problem solving performance increased from the pretest to posttest on multiplication and division problems. In addition, some students were able to generalise the skill to untaught problems. Implications of the representational strategy for solving word problems by elementary students and special education students with learning problems are discussed.
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Julie, Hongki. "The elementary school teachers’ ability in adding and subtracting fraction, and interpreting and computing multiplication and division fraction." International Journal of Science and Applied Science: Conference Series 1, no. 1 (2017): 55. http://dx.doi.org/10.20961/ijsascs.v1i1.5114.
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<p class="Abstract">The purpose of this study was to describe the elementary school teachers’ mathematical skills on the numbers, especially fractions after they have participated in a workshop. The teachers’ abilities which would be described by the researcher in this study were the ability to interpret, to order, to add and subtract, to interpret the meaning of the multiplication and division, to multiply and divide, and to make problems about fractions. In this paper, the author just only would describe the teachers’ mathematical skills in adding and subtracting two fractions, interpreting the multiplication and division of two fractions, multiplying and dividing two fractions. This capability was described base on the results of a test given to teachers after they have attended the workshop. Research subjects in this study were 17 Kanisius Demangan elementary school teachers at Yogyakarta. Of the 17 teachers, 16 teachers could add and subtract two fractions. Six teachers of 17 teachers could interpret what was the meaning of multiplication of two fractions. One teacher could interpret what was the meaning of division of two fractions. All of the teachers could divide two fractions. Sixteen teachers of 17 teachers could multiply two fractions.</p>
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Starkl, Reinhard. "The Solution of Embedding Problems in the Framework of GAPs with Applications on Nonlinear PDEs." Advances in Mathematical Physics 2009 (2009): 1–46. http://dx.doi.org/10.1155/2009/120213.
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The paper presents a special class of embedding problems whoes solutions are important for the explicit solution of nonlinear partial differential equations. It is shown that these embedding problems are solvable and explicit solutions are given. Not only are the solutions new but also the mathematical framework of their construction which is defined by a nonstandard function theory built over nonstandard algebraical structures, denoted as “GAPs”. These GAPs must not be neither associative nor division algebras, but the corresponding function theories built over them preserve the most important symmetries from the classical complex function theory in a generalized form: a generalization of the Cauchy-Riemannian differential equations exists as well as a generalization of the classical Cauchy Integral Theorem.
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Sanz, Maria T., Emilia López-Iñesta, Daniel Garcia-Costa, and Francisco Grimaldo. "Measuring Arithmetic Word Problem Complexity through Reading Comprehension and Learning Analytics." Mathematics 8, no. 9 (2020): 1556. http://dx.doi.org/10.3390/math8091556.
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Numerous studies have addressed the relationship between performance in mathematics problem-solving and reading comprehension in students of all educational levels. This work presents a new proposal to measure the complexity of arithmetic word problems through the student reading comprehension of the problem statement and the use of learning analytics. The procedure to quantify this reading comprehension comprises two phases: (a) the division of the statement into propositions and (b) the computation of the time dedicated to read each proposition through a technological environment that records the interactions of the students while solving the problem. We validated our approach by selecting a collection of problems containing mathematical concepts related to fractions and their different meanings, such as fractional numbers over a natural number, basic mathematical operations with a natural whole or fractional whole and the fraction as an operator. The main results indicate that a student’s reading time is an excellent proxy to determine the complexity of both propositions and the complete statement. Finally, we used this time to build a logistic regression model that predicts the success of students in solving arithmetic word problems.
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Sidik, Geri Syahril, and Agus Ahmad Wakih. "KESULITAN BELAJAR MATEMATIK SISWA SEKOLAH DASAR PADA OPERASI HITUNG BILANGAN BULAT." NATURALISTIC : Jurnal Kajian Penelitian Pendidikan dan Pembelajaran 4, no. 1 (2020): 461–70. http://dx.doi.org/10.35568/naturalistic.v4i1.633.
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One of the goals of teaching mathematics in elementary schools is students are able to understand mathematical concepts, explain the interrelationships of the concepts and apply algorithmic concepts in a flexible, accurate, efficient and precisely in solving their daily problems. The elementary schools nowadays show that there are still found many students who have difficulty in solving problems related to the subject matter, especially on arithmetic operations of integers. This research is a qualitative descriptive study. Students in first grade are given a worksheet to solve individually by writing out the work steps clearly. Six students were chosen as research subjects to be analyzed. The sixth research subject consists of 2 subjects who have high mathematical abilities, 2 medium, and 2 low mathematical abilities. The difficulty of the subject was observed by examining the worksheet's answer and giving clinical interviews related to the results of his work. Based on the results of data analysis, the difficulty of learning mathematics of elementary school students in integer operations is: 1) students have difficulty understanding the purpose of the question so that it incorrectly translated into mathematical sentences; 2) students have difficulty operating numbers that contain negative signs; 3) 95% of students have difficulty understanding the meaning of equal sign (=); 4) students have difficulty carrying out the division operations.
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Adiba, Asfa Riha Farah. "REALISTIC MATHEMATIC EDUCATION (RME) DALAM MENINGKATKAN HASIL BELAJAR SISWA MI DI MALANG." Elementeris : Jurnal Ilmiah Pendidikan Dasar Islam 2, no. 2 (2020): 47. http://dx.doi.org/10.33474/elementeris.v2i2.8694.
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This study is to find out the learning problems in MI Cemorokandang kedungkandang malang, namely about the problem of low student learning outcomes and students' knowledge of mathematics subjects in class III on multiplication and division material. This study uses a realistic mathematic education learning model. Studying mathematics is including increasing students' knowledge in thinking logically, rationally, critically, carefully, effectively, and efficiently. Therefore, as a teacher must be able to apply effective and efficient learning so students can understand to work on and solve mathematical learning problems. However, the teacher cannot apply it because the teacher does not understand the problems that arise from the model, the media or the characteristics of their students. In this case the researcher will discuss realistic mathematics learning in class III at MI Cemorokandang Kedungkandang Malang, the problems experienced by teachers in mathematics learning are low levels and the problems faced by students in learning mathematics at MI Cemorokandang Kedungkandang Malang
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Kolesnikova, Yu V. "Comparative Analysis of the Effectivenessof the Using of Direct and Generalized Conditional Reinforcement in the Development of a Skill of Solving of Simple Arithmetic Problems in a Child with ASD." Autism and Developmental Disorders 71, no. 2 (2021): 52–58. http://dx.doi.org/10.17759/autdd.2021710206.
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Within the framework of the applied behavior analysis, a comparison of the effectiveness of the direct and the generalized reinforcement was made during the teaching the skill of distinguishing arithmetic operations in mathematical problems. The study was conducted in two phases over two weeks with a 9-year-old girl with autism spectrum disorder (ASD). The first phase included training of multiplication and addition tasks, using tangible reinforcement, compared to the training of the arithmetic performance in division and subtraction tasks, using generalized reinforcement. The second phase included the training of discrimination between different arithmetic operations, but tangible and generalized reinforcements were used in variable mode. The results showed no differences in the effectiveness of both generalized and tangible reinforcements in the teaching process. The participant successfully learned to discriminate between different arithmetic operations as addition, multiplication, subtraction and division in single-component tasks.
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Fuentes, Sarah Quebec. "Party Time." Teaching Children Mathematics 23, no. 8 (2017): 462–65. http://dx.doi.org/10.5951/teacchilmath.23.8.0462.
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In this month's Problem Solvers Solutions, second and fifth graders solve a problem that provides a real-world context relevant to students' lives, while addressing mathematical concepts including addition, division, negative numbers, and the mean. The experiences of the diverse grade range of students demonstrate that the task has multiple entry points and can be implemented in a variety of ways. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. Find detailed submission guidelines for all departments at http://www.nctm.org/WriteForTCM.
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Agushaka, Jeffrey O., and Absalom E. Ezugwu. "Advanced arithmetic optimization algorithm for solving mechanical engineering design problems." PLOS ONE 16, no. 8 (2021): e0255703. http://dx.doi.org/10.1371/journal.pone.0255703.
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The distributive power of the arithmetic operators: multiplication, division, addition, and subtraction, gives the arithmetic optimization algorithm (AOA) its unique ability to find the global optimum for optimization problems used to test its performance. Several other mathematical operators exist with the same or better distributive properties, which can be exploited to enhance the performance of the newly proposed AOA. In this paper, we propose an improved version of the AOA called nAOA algorithm, which uses the high-density values that the natural logarithm and exponential operators can generate, to enhance the exploratory ability of the AOA. The addition and subtraction operators carry out the exploitation. The candidate solutions are initialized using the beta distribution, and the random variables and adaptations used in the algorithm have beta distribution. We test the performance of the proposed nAOA with 30 benchmark functions (20 classical and 10 composite test functions) and three engineering design benchmarks. The performance of nAOA is compared with the original AOA and nine other state-of-the-art algorithms. The nAOA shows efficient performance for the benchmark functions and was second only to GWO for the welded beam design (WBD), compression spring design (CSD), and pressure vessel design (PVD).
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Nuraida, Elis Muslimah, and Ratu Ilma Indra Putri. "THE CONTEXT OF ARCHIPELAGO TRADITIONAL CAKE TO EXPLORE STUDENTS’ UNDERSTANDING IN INTEGERS DIVISION CLASS VII." Jurnal Pendidikan Matematika 14, no. 1 (2019): 91–100. http://dx.doi.org/10.22342/jpm.14.1.7400.91-100.
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This study aims to explore the students’ mathematical understanding in integer division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study was conducted on VII grade students of Palembang 1 Junior High School. The learning path (Hypothetical Learning Trajectory) in design research plays an important role as a research design and instrument. The Hypothetical Learning Trajectory (HLT) was developed together with a series of activities using the context of archipelago traditional cakes such as: omelette roll, bakpia, milk pie, etc. The medium used in this study was the Students’ Activity Sheet. The results of this study indicate that exploration using the context of traditional archipelago cakes can help students understanding in multiplication and division of integers. The conclusion of this study is the use of archipelago traditional cakes as starting point in mathematics learning in integer division operation material helps the students to explore their understanding in solving mathematics problems.
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Jatisunda, Mohamad Gilar, and Dede Salim Nahdi. "Kemampuan Pemecahan Masalah Matematis melalui Pembelajaran Berbasis Masalah dengan Scaffolding." Jurnal Elemen 6, no. 2 (2020): 228–43. http://dx.doi.org/10.29408/jel.v6i2.2042.
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One of the main goals of school mathematics is the achievement of mathematical problem-solving abilities through problem-based learning. It is expected that these abilities can be achieved well by students. However, the complexity of the problem and minimum confidence become a problem when students experience complex situations created in the problem-based learning process. Scaffolding becomes essential because of the differences in each student's knowledge stored in long term memory. The purpose of the study was to analyze differences in mathematical problem-solving abilities with two different learning and based on initial mathematical abilities. Learning in the experimental class is problem-based learning with scaffolding, and then control class learning is problem-based without scaffolding. The research method used was a quasi-experimental design with a matching-only pretest-posttest control group design. Sample selection using purposive sampling to get samples with the same characteristics, the total number of samples is 60 students with each division 30. The initial mathematics ability has the same role in the mathematical problem-solving ability in the experimental and control classes. That is when students are in the high category then the ability of severe mathematical problem-solving. However, when the two classes are compared, the results are significantly different. Scaffolding becomes a factor that distinguishes the ability to solve mathematical problems.
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Zavedeev, A. I. "Increasing of Reliability of Spacecraft Control System on Base of Robust Diagnostic Models and Division Principle in Parity Space." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 4 (2020): 249–56. http://dx.doi.org/10.17587/mau.21.249-256.
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Different directions of creation high reliability integrate spacecraft control system are discussed on base of robust diagnostic models and division principle in parity space. Problems of synthesis spacecraft control system algorithms are examined with incomplete apriory and distorted current information, action of uncontrolled and random factors, information losses and equipment failures. The structure of onboard attitude control system is synthesized and control algorithms are chosen, which guarantee robust stability and failure stability in presence indignant factors and obstacles. An instrumental structure and operational modes of spacecraft attitude control system are described. Methods of dynamic research, computer technology and modeling particularities are indicated. Diagnostic and reconfiguration algorithms for onboard complex of connection, navigation, geodesy satellites and earth inspectoral satellite in prolonged space flight utilization are proposed. Testing procedure is contains two stage: discovering and eliminating faults. Given mathematical system model is researched by means of difference signals, which forms with arise at fault emergence. The failure character is established by deciding rules on base difference signals and measures to it eliminating are took. Questions of onboard spacecraft control system failure stable improving are discussed on base principle reconfiguration with apply to adaptive logic in testing and diagnostic algorithms. The mathematical system model is researching with implementation of analytic reserving. Difference signals are formed, which arise at fault appearance. The adaptive approach to development testing and diagnostic systems provide for realization of flexible logic of control system function to take into account factual onboard equipment state. Special attention is devote to problem influence liquid fuel reactive engine agility on spacecraft control attitude system dynamic characteristics and precision. The effectiveness of prepositional approaches and algorithms is confirmed by mathematical modeling results for several actual technical systems. Recommendations to their practical applications are given.
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Антонова, И., and I. Antonova. "REGIONS WITH HIGH CONCENTRATION OF SINGLE-INDUSTRY TOWNS: PROBLEMS OF DATA QUALITY IMPROVEMENT." Bulletin of Kemerovo State University. Series: Political, Sociological and Economic sciences 2018, no. 3 (2018): 62–68. http://dx.doi.org/10.21603/2500-3372-2018-3-62-68.
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With all the diversity of studies of single-industry towns’ development problems, little attention has been given to the quality of statistical data: neither the selective character of official statistics nor the difference between a single-industry town and a municipality are taken into account. The latter makes it impossible to use mathematical methods to simulate the spatial development of towns. The purpose of the current research is to identify the problems of assessment for regions with high concentration of monotowns and to introduce some ways of improving the quality of data by using the case of the Kemerovo region. Research methods include collection and grouping of data on the single-industry towns of the Kemerovo region taking into account the administrative-territorial division of the region, the construction of the logarithmic model of distribution of cities and towns according to the «rank-size» rule and evaluation compliance of the received distribution with the Zipf rule. As a result of research, the author proposes directions of improvement of data on towns and obtained results. In particular, the study specifies the conformity of Kuzbass towns to the Zipf law. The results can be applied in the field of forecasting and management of single-industry towns’ development at the regional level.
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SKALA, VACLAV. "INTERSECTION COMPUTATION IN PROJECTIVE SPACE USING HOMOGENEOUS COORDINATES." International Journal of Image and Graphics 08, no. 04 (2008): 615–28. http://dx.doi.org/10.1142/s021946780800326x.
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There are many algorithms based on computation of intersection of lines, planes etc. Those algorithms are based on representation in the Euclidean space. Sometimes, very complex mathematical notations are used to express simple mathematical solutions. This paper presents solutions of some selected problems that can be easily solved by the projective space representation. Sometimes, if the principle of duality is used, quite surprising solutions can be found and new useful theorems can be generated as well. It will be shown that it is not necessary to solve linear system of equations to find the intersection of two lines in the case of E2 or the intersection of three planes in the case of E3. Plücker coordinates and principle of duality are used to derive an equation of a parametric line in E3 as an intersection of two planes. This new formulation avoids division operations and increases the robustness of computation. The presented approach for intersection computation is well suited especially for applications where robustness is required, e.g. large GIS/CAD/CAM systems etc.
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Harada, Takabayashi, Kobayashi, Sakakibara, and Kohno. "Theoretical Analysis of Interference Cancellation System Utilizing an Orthogonal Matched Filter and Adaptive Array Antenna for MANET." Journal of Sensor and Actuator Networks 8, no. 3 (2019): 48. http://dx.doi.org/10.3390/jsan8030048.
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This study provides a mathematical model and theoretical analysis of an interference cancellation system combining an orthogonal matched filter (OMF) and adaptive array antenna that is called the extended OMF (EOMF). In recent years, an increase in the number of applications of mobile ad hoc networks (MANETs) is expected. To realize a highly reliable MANET, it is essential to introduce a method for cancelling the interference from other nodes. This research focuses on a scheme based on Code Division Multiple Access (CDMA) that enables simultaneous multiple access and low latency communication. However, there are problems with deteriorating performance due to the near–far problem and the increase in the amount of interference as the number of users increases. Additionally, another problem is that the spreading sequence of each user is unknown in a MANET. The OMF is expected to be a solution to these problems. The OMF performs interference cancellation by generating and subtracting a replica of the interference signal that is contained in the received signal. However, the OMF may generate an incorrect replica in the near–far problem. The EOMF compensates for the OMF’s weakness by combining the OMF with an adaptive array antenna. In this research, optimal parameters are derived from mathematical modelling and theoretical analysis of the EOMF. Specifically, the optimal weight vector and the minimum mean squared error that allow the adaptive algorithm to converge are derived and obtained from the numerical results.
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Wang, Xin, and Bo Luo. "Application of Service Modular Design Based on a Fuzzy Design Structure Matrix: A Case Study from the Mining Industry." Mathematical Problems in Engineering 2021 (June 15, 2021): 1–19. http://dx.doi.org/10.1155/2021/5067092.
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The development of customized service is an important way to transform and upgrade China’s mining industry. However, in practice, there remain problems, such as the slow market response speed of service providers and the contradiction between the large-scale development of service providers and the personalized service needs of service demanders. This paper uses the theory and method of service modular design to solve these problems and explores the process-based service modular design method. Service modular design depends largely on the determination of the relationship between service activities and the reasonable division of modules. However, previous research has rarely made use of modular design methods and modeling tools in the mining service context. At the same time, evaluations of the relationship between service activities relying on knowledge and those relying on experience have been inconclusive. Therefore, this paper proposes a service modularization design method based on the fuzzy relation analysis of a design structure matrix (DSM) that solves the optimal module partition scheme. Triangular fuzzy number and fuzzy evidence theory are used to evaluate and fuse the multidimensional and heterogeneous relationship between service activities, and the quantitative processing of the comprehensive relationship between service activities is carried out. On this basis, the service module structure is divided, followed by the construction of the mathematical programming model with the maximum sum of the average cohesion degree in the module and the average coupling degree between modules as the driving goal. The genetic algorithm is used to solve the problem, and the optimal module division result is obtained. Finally, taking the service modular design of SHD coal production enterprises in China as an example, the feasibility of the proposed method is verified.
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Novakovsky, L., I. Novakovska, O. Bredikhin, M. Stetsiuk, and L. Skrypnyk. "Risks and problems of forming united territorial communities in Ukraine." Agricultural Science and Practice 6, no. 2 (2019): 66–75. http://dx.doi.org/10.15407/agrisp6.02.066.
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Aim. To determine the specifi cities of uniting territorial communities at the national and regional levels during the process of power decentralization, to generalize the experience of its legal and organizational provisions, the practice of reforming local self-government in the EU member states, to estimate the risks of decentralization in Ukraine in general and in rural area in particular, and to establish the directions of its development at the fi - nal stage. Methods. Monographic, mathematical-statistical, cartographic, abstract-logical, comparative, analytical analysis. Results. The work conducted during the fi rst stage of decentralization reform (2014–2018), was esti- mated by the Council of Europe as the most successful reform in progress in Ukraine. As of January 01, 2015, 85.2 % of territorial communities were located in rural areas, where agriculture is the prevailing kind of the popula- tion’s activity. Thus, power decentralization and reforming local self-governance refers to rural population, fi rst and foremost. However, the study has confi rmed that the implementation of reforming remedies has been restrained, as the main provisions of decentralization have not been enshrined in the Constitution, there are no defi nite plans on developing united communities, it is impossible to overcome the removal of local councils from managing land resources beyond the boundaries of settlements, the reform is being blocked by regional and district state authori- ties. Conclusions. Current system of rural population settlements, characterized by a considerable number of small villages, the specifi city of territorial organization of power (40 % of local councils have less than 1,000 residents) and village and town budgets, subsidized for almost 50 %, are prerequisites of uniting communities as the only way of forming sustainable local self-governance. The centralization of authorities by the executive branch regarding governance over territories, low spreading of local self-governance and absence of land resources in communal ownership, fi nancial limitedness of councils prove that without principal changes in the current position, most ter- ritorial communities will still remain unsustainable in legal, organizational and fi nancial aspects. The experience of implementing decentralization tasks in regions demonstrates that the level of organizational and explanatory work and control over reforming should be enhanced considerably. The issues of regulating the division of mountainous territories and setting higher bonuses and benefi ts, improving budget limits of the communities via taxation system, enhancing the role of cities of regional signifi cance as centers of united territorial communities should be settled at the legislative level. At this stage, the risks of implementing decentralization in Ukraine are as follows: the impos- sibility of completing the plan of implementing the remedies of its second stage without amending the Constitution, unclear mechanisms of implementing the remedies of reforming local self-governance, because regional councils are too politicized, while state regional administrations perform functions, non-relevant for them, and resist; the absence of promising plans of social and economic development of territorial communities restrains the process of substantiating their capability and the terms of implementing decentralization; ignoring the requirements related to needless district councils in cases called «one district – one community»; absence of actions in terms of determining the boundaries of communities or changing the boundaries of districts; absence of work in refl ecting the process of land division by ownership forms in the State Cadaster; untimely solving the problems of human resources for executive bodies of territorial communities and delegating relevant authorities to them.
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Kusumadewi, Rida Fironika, Imam Kusmaryono, Ibnu Jamalul Lail, and Bagus Ardi Saputro. "Analisis Struktur Kognitif Siswa Kelas IV Sekolah Dasar dalam Menyelesaikan Masalah Pembagian Bilangan Bulat." Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang 3, no. 2 (2019): 251. http://dx.doi.org/10.31331/medivesveteran.v3i2.875.
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Pembelajaran yang lebih ditekankan pada prosedur dan hasil dalam penyelesaian masalah tidak akan mengaktifkan strukur kognitif (berpikir) siswa dan tidak meningkatkan kemampuan berpikir matematis. Siswa hanya akan meniru prosedur yang dilakukan guru. Penelitian ini merupakan studi kasus pembelajaran matematika di kelas IV sekolah dasar pada materi pembagian bilangan bulat. Tujuan penelitian adalah mendeskripsikan struktur kognitif siswa dalam menyelesaikan masalah. Penelitian menggunakan metode kombinasi (kualitatif-kuantitatif) dengan desain concurrent embedded. Teknik pengumpulan data dilakukan secara trianggulasi yaitu observasi partisipan, wawancara yang mendalam, serta studi dokumentasi. Hasil penelitian menunjukkan bahwa struktur kognitif Siswa A memiliki struktur kognitif komparatif dan siswa B memiliki struktur kognitif penalaran logis. Siswa menggunakan struktur kognitif untuk memproses informasi dan menciptakan makna dengan cara (1) membuat koneksi, (2) menemukan pola, (3) mengidentifikasi aturan, dan (4) mengabstraksikan prinsip-prinsip.
 Kata kunci: struktur kognitif, berpikir matematis, bilangan bulat.
 
 ABSTRACT
 
 Learning that is more emphasized on procedures and results in solving problems will not activate the cognitive structure (thinking) of students and does not improve the ability to mathematical thinking. Students will only imitate the procedures performed by the teacher. This research is a case study of mathematics learning in the fourth grade of elementary school in integer division material. The research objective is to describe the cognitive structure of students in solving problems. The study uses a combination method (qualitative - quantitative) with concurrent embedded design. The data collection technique is done in triangulation, namely participant observation, in-depth interviews, and documentation studies. The results showed that the cognitive structure of class IV students reached the level of comparative cognitive structure (group A) and cognitive structure of logical reasoning (group B). Students use cognitive structures to process information and create meaning by (1) making connections, (2) finding patterns, (3) identifying rules, and (4) abstracting principles
 Keywords: cognitive structure, mathematical thinking, integers.
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Dereli, Serkan, and Mahmut Uç. "Exponential Computing Digital Circuit Design Developed for FPGA-based Embedded Systems." Academic Perspective Procedia 3, no. 1 (2020): 291–300. http://dx.doi.org/10.33793/acperpro.03.01.59.
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Digital systems consist of thousands of digital circuit blocks operating in the background, working in their simplest form such as addition, subtraction, multiplication, division. In exponential expressions like square roots and cube roots, just like these circuits, it is found in many digital systems and performs tasks. Although these processes seem to be used only in circuits carrying out mathematical operations, they actually take an active role in solving many engineering problems. In this study, a digital circuit design that computes both the integer and a floating point exponent of a 32-bit floating-point number has been realized. This digital circuit, which is coded with VHDL language, can be used from beginner to advanced level in FPGA based systems. This digital circuit, which is coded with VHDL language, can be used from beginner to advanced level in FPGA based systems. In addition, three floating IP cores - logarithm, multiplication and exponent - were used in this digital circuit, and results were obtained with a total of five finite state machines in sixty-six clock pulse time.
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Putri, Desinta Ayudia Wanda, Intan Hartiningrum, and Reny Sari Dewi. "Estimasi Biaya Pengembangan Aplikasi Pemantauan Tagihan Menggunakan Metode Function Points." JURIKOM (Jurnal Riset Komputer) 7, no. 1 (2020): 78. http://dx.doi.org/10.30865/jurikom.v7i1.1970.
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An Enterprise Resource Planning (ERP) software estimation project is carried out so that the allocation of funds owned does not result in underestimation or over-estimation. Under-estimation occurs because of the lack of allocation of resources so that it can potentially lead to project failure while Over-estimation occurs because of the allocation of excessive resources. Cost estimation analysis will be based on the calculation of Function Points. The study explains the division of work scope of the Bill Monitoring software (MONITA) at the company PT XYZ. The research stage starts with the study of literature, analysis of the stages of the Fuction Points method containing questionnaires, interviews with stakeholders, data analysis, calculations, and conversion of cost estimation efforts. In mathematical calculations on the Bill Monitoring software (MONITA) produces an estimated effort of 1,792.66 people / hour and a total cost of 90,457,909. Comparative analysis between the Function Point method in Bill Monitoring (MONITA) software can be taken into consideration by PT XYZ in solving problems for developing software
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Ventegodt, Søren, Tyge Dahl Hermansen, Trine Flensborg-Madsen, Maj Lyck Nielsen, and Joav Merrick. "Human Development VIII: A Theory of Deep Quantum Chemistry and Cell Consciousness: Quantum Chemistry Controls Genes and Biochemistry to Give Cells and Higher Organisms Consciousness and Complex Behavior." Scientific World JOURNAL 6 (2006): 1441–53. http://dx.doi.org/10.1100/tsw.2006.257.
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Deep quantum chemistry is a theory of deeply structured quantum fields carrying the biological information of the cell, making it able to remember, intend, represent the inner and outer world for comparison, understand what it “sees”, and make choices on its structure, form, behavior and division. We suggest that deep quantum chemistry gives the cell consciousness and all the qualities and abilities related to consciousness. We use geometric symbolism, which is a pre-mathematical and philosophical approach to problems that cannot yet be handled mathematically. Using Occams razor we have started with the simplest model that works; we presume this to be a many-dimensional, spiral fractal. We suggest that all the electrons of the large biological molecules orbitals make one huge “cell-orbital”, which is structured according to the spiral fractal nature of quantum fields. Consciousness of single cells, multi cellular structures as e.g. organs, multi-cellular organisms and multi-individual colonies (like ants) and human societies can thus be explained by deep quantum chemistry. When biochemical activity is strictly controlled by the quantum-mechanical super-orbital of the cell, this orbital can deliver energetic quanta as biological information, distributed through many fractal levels of the cell to guide form and behavior of an individual single or a multi-cellular organism. The top level of information is the consciousness of the cell or organism, which controls all the biochemical processes. By this speculative work inspired by Penrose and Hameroff we hope to inspire other researchers to formulate more strict and mathematically correct hypothesis on the complex and coherence nature of matter, life and consciousness.
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ARANA, ANDREW, and PAOLO MANCOSU. "ON THE RELATIONSHIP BETWEEN PLANE AND SOLID GEOMETRY." Review of Symbolic Logic 5, no. 2 (2012): 294–353. http://dx.doi.org/10.1017/s1755020312000020.
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Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.In this paper our major concern is with methodological issues of purity and thus we treat the connection to other areas of the planimetry/stereometry relation only to the extent necessary to articulate the problem area we are after.Our strategy will be as follows. In the first part of the paper we will give a rough sketch of some key episodes in mathematical practice that relate to the interaction between plane and solid geometry. The sketch is given in broad strokes and only with the intent of acquainting the reader with some of the mathematical context against which the problem emerges. In the second part, we will look at a debate (on “fusionism”) in which for the first time methodological and foundational issues related to aspects of the mathematical practice covered in the first part of the paper came to the fore. We conclude this part of the paper by remarking that only through a foundational and philosophical effort could the issues raised by the debate on “fusionism” be made precise. The third part of the paper focuses on a specific case study which has been the subject of such an effort, namely the foundational analysis of the plane version of Desargues’ theorem on homological triangles and its implications for the relationship between plane and solid geometry. Finally, building on the foundational case study analyzed in the third section, we begin in the fourth section the analytic work necessary for exploring various important claims about “purity,” “content,” and other relevant notions.