Multiplication Of Whole Numbers Research Articles

EMPOWERMENT OF STUDENTS WITH DISABILITIES AND FAMILIES IN UNDERSTANDING THE LEARNING PROCESS AT SDN 03 KEDOYA UTARA

The purpose of this service activity is to empower inclusive schools by utilizing mobile-based interactive learning media to understand the concept of integer multiplication at SDN Kedoya Utara 03. State Elementary School (SDN) Kedoya Utara 03 is one of the inclusive schools in West Jakarta City with 12 students with disabilities (learning difficulties, slow learning, and low mentally disabled). However, only 2 students with learning disabilities (learning difficulties, slow learners) participated in this activity according to their parents' permission. The mobile-based interactive learning media that we teach is the Math Games application: Math for Kids, for planting the concept of multiplication with animations made with programming languages. The implementation methods used in this activity are (1) preparation (Introduction, Education), (2) Implementation (Learning, Workshop, Assistance), and (3) Evaluation (Understanding, Recognition). Based on the results of this activity, there is an increase in understanding of the concept of number multiplication in students with disabilities and workshop activities for children and teachers run well, which is evidenced by enthusiastic teachers practicing the Math Games application: Math for Kids. This activity can be used as a reference material for learning other materials, especially multiplication of whole numbers in other schools.

The Flow Matrix Offers a Straightforward Alternative to the Problematic Markov Matrix

The Flow matrix is a novel method to describe and extrapolate transitions among categories. The Flow matrix extrapolates a constant transition size per unit of time on a time continuum with a maximum of one incident per observation during the extrapolation. The Flow matrix extrapolates linearly until the persistence of a category shrinks to zero. The Flow matrix has concepts and mathematics that are more straightforward than the Markov matrix. However, many scientists apply the Markov matrix by default because popular software packages offer no alternative to the Markov matrix, despite the conceptual and mathematical challenges that the Markov matrix poses. The Markov matrix extrapolates a constant transition proportion per time interval during whole-number multiples of the duration of the calibration time interval. The Markov extrapolation allows at most one incident per observation during each time interval but allows repeated incidents per observation through sequential time intervals. Many Markov extrapolations approach a steady state asymptotically through time as each category size approaches a constant. We use case studies concerning land change to illustrate the characteristics of the Flow and Markov matrices. The Flow and Markov extrapolations both deviate from the reference data during a validation time interval, implying there is no reason to prefer one matrix to the other in terms of correspondence with the processes that we analyzed. The two matrices differ substantially in terms of their underlying concepts and mathematical behaviors. Scientists should consider the ease of use and interpretation for each matrix when extrapolating transitions among categories.

Upaya Peningkatan Kemampuan Perkalian dengan Menggunakan Media Batang Napier di SDN 34/I Muara Bulian

One of the subjects that most students experience problems and find it difficult to understand the concepts is mathematics. The task of a teacher is not only to transfer knowledge or convey learning knowledge to students in the classroom. The majority of students explained that subjects related to calculations were subjects that were difficult to understand. The purpose of this research was to assist teachers in improving students' abilities by using stem napier media. The Napier rod is a tool that can help find the product of a number. Napier rods can be used by students to assist in calculating multiplication and division operations. This calculation tool is designed to simplify heavy multiplication tasks. This multiplication bar or napier bar prop is used to calculate multiplication of whole numbers.

The Hidden Role of Contract Terms: The Case of Credit Card Minimum Payments in Mexico

This paper argues that thresholds in financial contracts act as implicit nudges in consumers’ decisions. Exploiting a regulatory change to credit card minimum payments in Mexico, we find that a 1-percentage point change in minimum payments leads to a 0.87-percentage point change in actual payments, both expressed as a percentage of total balances. We decompose the effect of minimum payments into a constraining effect and a reference effect. The former captures the effect of minimum payments as a binding constraint and accounts for 59% of its total effect. The latter captures any remaining impact of changes in minimum payments beyond their constraining effect and represents 41% of the total. In turn, 67% of the reference effect is explained by the multiple heuristic: the tendency of consumers to pay whole-number multiples of the minimum payment. This paper was accepted by Kay Giesecke, finance.

UPAYA MENINGKATKAN PEMAHAMAN SISWA TENTANG KONSEP PERKALIAN BILANGAN CACAH DENGAN MENGGUNAKAN PENDEKATAN REALISTIK DI KELAS II SEKOLAH DASAR

This research is motivated by the low understanding of students in learning mathematics about the concept of multiplication. This makes students' understanding of multiplication of whole numbers still low. Based on these problems, efforts are made to improve understanding of the concept of multiplication of whole numbers by using a realistic approach. This study begins with giving pretest to students, aiming to get an idea of understanding the concept of multiplication of whole numbers. This research method uses Classroom Action Research which consists of four stages, namely; planning, implementation, observation, and reflection. This research was carried out in two cycles, where from each 
 cycle there was a significant increase so that a realistic approach could be applied to the material of multiplication of whole numbers..

(두 자리 수)×(두 자리 수)의 계산 원리에 대한 초등학교 3학년 학생들의 이해 분석: 직사각형 배열 모델을 중심으로

Along with the significance of distributive property playing a fundamental role in providing explanations for multi-digit multiplication of whole numbers, the array model has been widely used to teach distributive property effectively. Given this, the purpose of this study was to investigate how third graders could understand multiplication in (two digits) × (two digits) and how their understanding could be expanded and applied to algebraic ideas after being taught reconstructed units of multiplication using the array model. The results of this study showed that most students represented the principle of computation between two-digit number and two-digit number using the array model as well as reasoned which picture represented the product of two numbers. Also, the participating students successfully applied the principle to the computation between three-digit number and two-digit number, and some students represented the product of two numbers by using variables (e.g., □, △). This paper concludes with some implications on how to teach multiplication of whole numbers in elementary mathematics.

Strategies Used by Grade 6 Learners in the Multiplication of Whole Numbers in Five Selected Primary Schools in the Kavango East and West Regions

This research paper reports strategies used by Grade 6 learners in multiplying whole numbers in five selected primary schools in Kavango East and West regions. A total of 200 learners’ mathematics exercise books were analysed in order to identify the commonly used strategies by learners in multiplying whole numbers. A total of ten teachers teaching grade 6 mathematics were also requested to complete a questionnaire which required them to indicate the strategies that they employed in class when teaching multiplication of whole numbers. The teachers indicated that they used a variety of strategies including repeated addition, complete-number (Including doubling), partitioning and compensation to teach multiplication of whole numbers. The results also disclosed that the majority of the learners’ mathematics exercise books reflected the use of the traditional method of repeated addition contrary to the teachers’ claims. It was also found that a few of the learners used other strategies such as long method, short method and learner “invented” strategies. Additionally, the mathematics curriculum for upper primary learners (Grade 4-7 mathematics syllabus) requires learners to use paper and pencil algorithms to carry out multiplication of whole numbers without calculators (Ministry of Education, Arts & Culture [MoEAC], 2015, p. 2). However, at Grade 6, learners were expected to use paper and pencil algorithms to multiply numbers within the range 0-100000. Analysis of the learners’ exercise books indicated that the majority were not able to multiply a two digit by a single digit, a two digit by a two digit and a three digit by a two digit number.

Using Coordinated Measurement With Future Teachers to Connect Multiplication, Division, and Proportional Relationships

We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as an equation, to support future teachers' understanding of these topics. We also used 2 types of length-based math drawings–double number lines and strip diagrams–as media with which to represent relationships among quantities and solve problems. To illustrate the promise of this approach, we share data in which future secondary mathematics teachers generated and explained without direct instruction sound methods for dividing by fractions and solving proportional relationships. The results are noteworthy, because these and other topics related to multiplication pose perennial challenges for many teachers.

Teaching whole-number multiplication to promote children\u2019s proportional reasoning: a practice-based perspective from Japan

Whole-number arithmetic is a core content area of primary mathematics, which lays the foundation for children’s later conceptual development. This paper focuses on teaching whole-number multiplication (WNM) to build a stepping stone for children’s proportional reasoning. Our intention in writing this paper is to obtain a practice-based perspective on the teaching of WNM, given the growing attention being given to significant connections between children’s understanding of multiplication and their proportional reasoning. To this end, we review studies on teaching WNM that were conducted in Japan. Our review highlights several aspects of teaching WNM that are integral to building an initial understanding of proportional relationships. Linear representations such as tape diagrams and number lines are also found to help make explicit the important properties of proportional relationships that can be used progressively across grade levels.

J0520301 固有直交分解を用いた遠心ブロワ内部流動解析結果の分析手法に関する研究

Needs for low noise turbo machineries have been increased. To extract the pressure fluctuation dominant to the noise, proper orthogonal decomposition (POD) was applied to unsteady computational fluid dynamics (CFD) results of a centrifugal blower in a vacuum cleaner. We extracted a time series of static pressure distribution in the diffuser, applied the POD to these data and compared the results of a measurement. The result was that the first six POD modes made a 99.4% contribution in terms of the L_2 norm. In the scope of this research, the first six modes were revealed to surrogate the pressure fluctuation sufficiently. Also, the data storage was reduced to less than 2.0% of one of the original unsteady results. Next, frequency spectra were obtained by applying discrete Fourier transform (DFT) to the expansion coefficients. The spectra of the expansion coefficients had a peak near whole-number multiples of the BPF. The noise, the frequency of which is BPF, causes the majority of the noise that occurs in the diffuser. Therefore, we found using both the POD and DFT that we could both reduce the dramatic data storage and extract the pressure fluctuation dominant to the noise.

Using Constructed Knowledge to Multiply Fractions

Observe fourth graders' thinking in action as they connect the multiplication of whole numbers to arrays.

Models for products

This paper explores how models can support productive thinking. For us a model is a thing, a tool to help make sense of something. We restrict attention to specific models for whole-number multiplication, hence the wording of the title. They support evolving thinking in large measure through the ways their users redesign them. They assume new forms, come to be seen and understood in different ways. We show how work that learners do with models can help them to transform, not simply their understanding of key concepts, but also how they come to view themselves as thinkers and learners, as collaborators in a social process that their work and thinking help to constitute. We draw on recent research on core knowledge, especially by Carey, Spelke, and Tomasello, to clarify how models, as we view them here, can underpin specific actions that support emerging understanding.

Multiplication and the Reference Sum Method

Difficulty in doing multiplication problems is common among pupils in primary schools. The main source of the problem is the difficulty to recall all the basic facts of multiplication. A method called the “Reference Sum Method” provides an alternative method to the conventional method of doing multiplication of whole numbers. This paper analyses the effectiveness of the use of the “Reference Sum Method” in helping pupils with difficulties in recalling all the basic multiplication facts, to improve their performance in doing multiplication problems. The study involved ten Year 4 Malaysian Primary school pupils in an urban primary school. The multiplication problems in the research were multiplication of two digit numbers by two digit numbers.

Mathematics Skills of 17-Year-Olds in the United States: 1978 to 2004

Overall scale scores from the National Assessment of Educational Progress (NAEP) indicate that there was only minimal improvement in the mathematics performance of high school students between 1978 and 2004. Using recently released data from the Long-Term Trend (LTT) NAEP, this study describes the content covered on the LTT NAEP and the performance of 17-year-old students on that content. In addition, it demonstrates that although overall gains in performance were small, there were areas within mathematics in which performance improved substantially and others in which students in 2004 did not do as well as their counterparts of the 1970s and 1980s. Specifically, performance on 3 items involving multiplication of whole numbers by fractions deteriorated but performance improved on most tasks involving percents and geometry. Performance was stable on most items assessing algebraic reasoning and logical reasoning and was stable or improved modestly on items assessing estimation, interpretation of tables and graphs, and understanding of integers.

Lattice Multiplication in a Preservice Classroom

Maurer defines an algorithm as being “a precise, systematic method for solving a class of problems” (1998, p. 21). This article discusses lattice multiplication, which is an algorithm for multiplication, and my preservice students' conceptual understanding of it. The conceptualization of the algorithm from the multiplication of whole numbers to the multiplication of polynomials is also explored.

Teacher to Teacher: Indian Lightning Multiplication

In addition to teaching content area information, we as teachers also want to help our students develop a conceptual framework for mathematics. Without this conceptual framework, students often have trouble internalizing new information and mastering topics. For example, a student who does not really understand whole-number multiplication will more than likely have difficulty multiplying binomials. For this reason, in an introductory algebra course, a teacher needs a way to reinforce multiplication skills in an age-appropriate way while laying the groundwork for algebra topics involving multiplication.

"You Have to Count the Squares": Applying Knowledge in Pieces to Learning Rectangular Area

This article extends and strengthens the knowledge in pieces perspective (diSessa, 1988, 1993) by applying core components to analyze how 5th-grade students with computational knowledge of whole-number multiplication and connections between multiplication and discrete arrays constructed understandings of area and ways of using representations to solve area problems. The results complement past research by demonstrating that important components of the knowledge in pieces perspective are not tied to physics, more advanced mathematics, or the learning of older students. Furthermore, the study elaborates the perspective in a particular context by proposing knowledge for selecting attributes, using representations, and evaluating representations as analytic categories useful for highlighting some coordination and refinement processes that can arise when students learn to use external representations to solve problems. The results suggest, among other things, that explicitly identifying similarities and differences between students' past experiences using representations to solve problems and demands of new tasks can be central to successful instructional design.

William Prout: early 19th century physician-chemist.

In the early 19th century, the discoveries of new substances in the healthy and diseased body spawned a search for chemical explanations for physiologic phenomena to guide medical diagnosis and control therapy. William Prout's work on the nature and treatment of diseases of the urinary organs established his reputation as one of Britain's most distinguished physiological chemists. Prout was very skeptical of chemical remedies because of possible side effects, but he suggested iodine treatment for goiter. He emphasized that a satisfactory diet should include carbohydrates, fats, protein, and water. In 1824, he showed that the acid of the gastric juice was hydrochloric acid. Prout applied chemical methods and reasoning to physiology and was criticized for his view that the body's vital functions could be explained by chemistry. His remedy for lack of progress in animal chemistry was for physiologists to become chemists. Prout stimulated much discussion on atomic theory by his hypothesis that the atomic weights of all chemical elements are whole-number multiples of the atomic weight of hydrogen and that the chemical elements were condensed from hydrogen atoms.

Decadal to millennial cyclicity in varves and turbidites from the Arabian Sea: hypothesis of tidal origin

We have analyzed a Late Holocene record, almost 5000 years long, consisting of varved sediments deposited in the oxygen-minimum zone (OMZ) off Pakistan. We searched for cyclicity in the series of varve thickness (“varve” cycles), of unusually large excursions in varve thickness (“agitation” cycles), and of abundance of turbidites (“turbidite” cycles). We found the following high-frequency cycles (periods between 10 and 100 years) in one or several of the three types of series as follows: near 12.4, 14–15, 16.8, 18.6 (strong, agitation), 25–26 (strong, turbidite), 29–31 (strong, agitation), 39 (varve), 44 (strong, turbidite), 51–54 (strong, agitation), 56 (strong, varve), 64 (strong, turbidite), 69, 77 (strong, turbidite), 82 (very strong, agitation), and 95 years (strong, varve). Low-frequency cycles center around 99–115, 125 (very strong, varve), 164, 177, 202, 242–255 (strong, agitation and turbidite), 280 (strong, varve; doubled, turbidite), 340–370 and 460–490 years. Some cycles of varve thickness match the cyclicity of turbidite frequency (12.3, 14–15, 25–26, 245–255 years) but similarities between spectra are not striking. Taken as a whole, however, the sequence of cycles detected (by autocorrelation and standard Fourier analysis) seems to contain a large proportion of multiples of the basic tidal cycles 4.425 (lunar perigee cycle) and 9.3 years (lunar half-nodal cycle). This impression is supported by testing the three binned spectra for whole-number multiples and fractions as well as whole-number beat structure. We therefore propose that a large proportion of the cyclicity detected can be ascribed to tidal action. Our record also contains evidence for the presence of the 1470-year cycle previously reported from the glacial-age Greenland ice record. The main harmonics of this Greenland cycle can be tied to the pattern of periods seen in the varved sediments. We hypothesize that tidal action produces the cycle, and that the reason for its great length is the requirement that maximum tidal activity has to fall into a narrow seasonal window to be geologically effective.

Bridging the Gap: Using Interactive Computer Tools to Build Fraction Schemes

Teaching fractions has been a complex and largely unsuccessful aspect of mathematics instruction in the elementary grades for many years. Students' understanding of fraction concepts is a big stumbling block in their mathematical development. Some researchers have pointed to children's whole-number knowledge as interfering with, or creating a barrier to, their understanding of fractions (Behr et al. 1984; Streefland 1993; Lamon 1999). This article illustrates an approach to constructing fraction concepts that builds on children's whole-number knowledge using specially designed computer tools. This approach can help children make connections between whole-number multiplication and their notion of a fraction as a part of a whole, thus bridging the gap between whole-number and fraction knowledge.